Complete Coherent Control of a Strongly Coupled Quantum Dot-Cavity Polariton System
Dory, Constantin; Müller, Kai; Lagoudakis, Konstantinos G; Sarmiento, Tomas; Rundquist, Armand; Zhang, Jingyuan L; Kelaita, Yousif; Vuckovic, Jelena
2015-01-01
Strongly coupled quantum dot-cavity systems provide a non-linear configuration of hybridized light-matter states with promising quantum-optical applications. Here, we investigate the coherent interaction between strong laser pulses and quantum dot-cavity polaritons. Resonant excitation of polaritonic states and their interaction with phonons allow us to observe coherent Rabi oscillations and Ramsey fringes. Furthermore, we demonstrate complete coherent control of a quantum dot-photonic crystal cavity based quantum-bit. By controlling the excitation power and phase in a two-pulse excitation scheme we achieve access to the full Bloch sphere. Quantum-optical simulations are in excellent agreement with our experiments and provide insight into the decoherence mechanisms.
Phonon-mediated population inversion in a semiconductor quantum-dot cavity system
We investigate pump-induced exciton inversion in a quantum-dot cavity system with continuous wave drive. Using a polaron-based master equation, we demonstrate excited-state populations above 0.9 for an InAs quantum dot at a phonon bath temperature of 4 K. In an exciton-driven system, the dominant mechanism is incoherent excitation from the phonon bath. For cavity driving, the mechanism is phonon-mediated switching between ground- and excited-state branches of the ladder of photon states, as quantum trajectory simulations clearly show. The exciton inversion as a function of detuning is found to be qualitatively different for exciton and cavity driving, primarily due to cavity filtering. The master equation approach allows us to include important radiative and non-radiative decay processes on the zero phonon line, provides a clear underlying dynamic in terms of photon and phonon scattering, and admits simple analytical approximations that help to explain the physics. (paper)
Influence of phonon reservoir on photon blockade in a driven quantum dot-cavity system
Gao, Bo; Zhu, Jia-pei; Li, Gao-xiang
2016-03-01
We theoretically investigate the influence of the phonon bath on photon blockade in a simultaneously driven dot-cavity system. An optimal condition for avoiding two-photon excitation of a cavity field is put forward which can be achieved by modulating the phase difference and the strengths of the driving fields. The second-order correlation function and the mean photon number of the cavity field are discussed. In the absence of phonon effect, the strong photon blockade in a moderate quantum dot (QD)-cavity coupling regime occurs, which can be attributed to the destructive quantum interference arisen from different transition paths induced by simultaneously driving the dressed QD-cavity system. The participation of acoustic-phonon reservoir produces new transition channels for the QD-cavity system, which leads to the damage of destructive interference. As a result, the photon blockade effect is hindered when taking the electron-phonon interaction into account. It is also found that the temperature of the phonon reservoir is disadvantageous for the generation of photon blockade.
Nielsen, Per Kær; Nielsen, Torben Roland; Lodahl, Peter; Mørk, Jesper; Jauho, Antti-Pekka
2010-01-01
We investigate the influence of electron-phonon interactions on the dynamical properties of a quantum-dot-cavity QED system. We show that non-Markovian effects in the phonon reservoir lead to strong changes in the dynamics, arising from photon-assisted dephasing processes, not present in Markovian...
Green's functions technique for calculating the emission spectrum in a quantum dot-cavity system
Gomez, Edgar A.; Hernandez-Rivero, J. D.; Vinck-Posada, Herbert
2015-01-01
We introduce the Green's functions technique as an alternative theory to the quantum regression theorem formalism for calculating the two-time correlation functions in open quantum systems. In particular, we investigate the potential of this theoretical approach by its application to compute the emission spectrum of a dissipative system composed by a single quantum dot inside of a semiconductor cavity. We also describe a simple algorithm based on the Green's functions technique for calculatin...
Green's functions technique for calculating the emission spectrum in a quantum dot-cavity system
Gomez, Edgar A; Vinck-Posada, Herbert
2015-01-01
We introduce the Green's functions technique as an alternative theory to the quantum regression theorem formalism for calculating the two-time correlation functions in open quantum systems. In particular, we investigate the potential of this theoretical approach by its application to compute the emission spectrum of a dissipative system composed by a single quantum dot inside of a semiconductor cavity. We also describe a simple algorithm based on the Green's functions technique for calculating the emission spectrum of the quantum dot as well as of the cavity which can easily be implemented in any numerical linear algebra package. We find that the Green's functions technique demonstrates a better accuracy and efficiency in the calculation of the emission spectrum and it allows to overcome the inherent theoretical difficulties associated to the direct application of the quantum regression theorem approach.
Reducing dephasing in coupled quantum dot-cavity systems by engineering the carrier wavefunctions
Nysteen, Anders; Nielsen, Per Kær; Mørk, Jesper
2012-01-01
We demonstrate theoretically how photon-assisted dephasing by the electron-phonon interaction in a coupled cavity-quantum dot system can be significantly reduced for specific QD-cavity detunings. Our starting point is a recently published theory,1 which considers longitudinal acoustic phonons, de...
Sub-Poissonian photon emission in coupled double quantum dots-cavity system
Ye, Han; Peng, Yi-Wei; Yu, Zhong-Yuan; Zhang, Wen; Liu, Yu-Min
2015-11-01
In this work, we theoretically analyze the few-photon emissions generated in a coupled double quantum dots (CDQDs)-single mode microcavity system, under continuous wave and pulse excitation. Compared with the uncoupled case, strong sub-Poissonian character is achieved in a CDQDs-cavity system at a certain laser frequency. Based on the proposed scheme, single photon generation can be obtained separately under QD-cavity resonant condition and off-resonant condition. For different cavity decay rates, we reveal that laser frequency detunings of minimum second-order autocorrelation function are discrete and can be divided into three regions. Moreover, the non-ideal situation where two QDs are not identical is discussed, indicating the robustness of the proposed scheme, which possesses sub-Poissonian character in a large QD difference variation range. Project supported by the National Natural Science Foundation of China (Grant Nos. 61372037 and 61401035), the Beijing Excellent Ph.D. Thesis Guidance Foundation, China (Grant No. 20131001301), and the Fund of State Key Laboratory of Information Photonics and Optical Communications (Beijing University of Posts and Telecommunications), China (Grant No. IPOC2015ZC05).
Influence of a phonon bath in a quantum dot cavity QED system: Dependence of the shape
We present a systematic analysis on the role of the quantum dot (QD) shape in the influence of the phonon bath on the dynamics of a QD cavity QED system. The spectral functions of the phonon bath in three representative QD shapes: spherical, ellipsoidal, and disk, are calculated from the carrier wave functions subjected to the confinement potential provided by the corresponding shape. The obtained spectral functions are used to calculate three main effects brought by the phonon bath, i.e., the coupling renormalization, the off-resonance assisted feeding rate and the pure dephasing rate. It is found that the spectral function of a disk QD has the widest distribution, hence the phonon bath in a disk QD can lead to the smallest renormalization factor, the largest dephasing rate in the short time domains(≤ 2 ps), and the off-resonance assisted feeding can support the widest detuning. Except for the pure dephasing rate in the long time domains, all the influences brought by the phonon bath show serious shape dependence. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)
Rabi oscillations in a quantum dot-cavity system coupled to a nonzero temperature phonon bath
Larson, Jonas [ICFO-Institut de Ciencies Fotoniques, E-08860 Castelldefels, Barcelona (Spain); Moya-Cessa, Hector [INAOE, Coordinacion de Optica, Apdo. Postal 51 y 216, 72000 Puebla, Pue (Mexico)], E-mail: jolarson@kth.se
2008-06-15
We study a quantum dot strongly coupled to a single high-finesse optical microcavity mode. We use a rotating wave approximation (RWA) method, commonly used in ion-laser interactions, together with the Lamb-Dicke approximation to obtain an analytic solution of this problem. The decay of Rabi oscillations because of the electron-phonon coupling is studied at arbitrary temperature and analytical expressions for the collapse and revival times are presented. Analyses without the RWA are presented as means of investigating the energy spectrum.
Transport Spectroscopy of a Spin-Coherent Dot-Cavity System.
Rössler, C; Oehri, D; Zilberberg, O; Blatter, G; Karalic, M; Pijnenburg, J; Hofmann, A; Ihn, T; Ensslin, K; Reichl, C; Wegscheider, W
2015-10-16
Quantum engineering requires controllable artificial systems with quantum coherence exceeding the device size and operation time. This can be achieved with geometrically confined low-dimensional electronic structures embedded within ultraclean materials, with prominent examples being artificial atoms (quantum dots) and quantum corrals (electronic cavities). Combining the two structures, we implement a mesoscopic coupled dot-cavity system in a high-mobility two-dimensional electron gas, and obtain an extended spin-singlet state in the regime of strong dot-cavity coupling. Engineering such extended quantum states presents a viable route for nonlocal spin coupling that is applicable for quantum information processing. PMID:26550890
Quantum Dot Cavity-QED in the Presence of Strong Electron-Phonon Interactions
Wilson-Rae, I
2001-01-01
A quantum dot strongly coupled to a single high finesse optical microcavity mode constitutes a new fundamental system for quantum optics. Here, the effect of exciton-phonon interactions on reversible quantum-dot cavity coupling is analysed without making Born-Markov approximation. The analysis is based on techniques that have been used to study the ``spin boson'' Hamiltonian. Observability of vacuum-Rabi splitting depends on the strength and the frequency dependence of the spectral density function characterizing the interactions with phonons, both of which can be influenced by phonon confinement.
Rabi oscillations in a quantum dot-cavity system coupled to a non-zero temperature phonon bath
Larson, Jonas; Moya-Cessa, Hector
2007-01-01
We study a quantum dot strongly coupled to a single high-finesse optical microcavity mode. We use a rotating wave approximation method, commonly used in ion-laser interactions, tegether with the Lamb-Dicke approximation to obtain an analytic solution of this problem. The decay of Rabi oscillations because of the electron-phonon coupling are studied at arbitrary temperature and analytical expressions for the collapse and revival times are presented. Analyses without the rotating wave approxima...
Coupling and single-photon purity of a quantum dot-cavity system studied using hydrostatic pressure
Zhou, P. Y.; Wu, X. F.; Ding, K.; Dou, X. M.; Zha, G. W.; Ni, H. Q.; Niu, Z. C.; Zhu, H. J.; Jiang, D. S. [State Key Laboratory of Superlattices and Microstructures, Institute of Semiconductors, Chinese Academy of Sciences, Beijing 100083 (China); Zhao, C. L. [College of Physics and Electronic Information, Inner Mongolia University for Nationalities, Tongliao 028043 (China); Sun, B. Q., E-mail: bqsun@semi.ac.cn [State Key Laboratory of Superlattices and Microstructures, Institute of Semiconductors, Chinese Academy of Sciences, Beijing 100083 (China); College of Physics and Electronic Information, Inner Mongolia University for Nationalities, Tongliao 028043 (China)
2015-01-07
We propose an approach to tune the emission of a single semiconductor quantum dot (QD) to couple with a planar cavity using hydrostatic pressure without inducing temperature variation during the process of measurement. Based on this approach, we studied the influence of cavity mode on the single-photon purity of an InAs/GaAs QD. Our measurement demonstrates that the single-photon purity degrades when the QD emission resonates with the cavity mode. This negative influence of the planar cavity is mainly caused by the cavity feeding effect.
Quantum Dot Cavity Spin Entanglement at a Distance - A Theoretical Analysis
Full text: Measurement of conditional Faraday rotation has recently been proposed for entanglement generation at a distance. In this talk we present a theoretical analysis of entanglement formation at a distance between two electron spins, each sitting in one of two 'distant' quantum dot cavities. Entanglement is induced by measuring the conditional Faraday rotation of a non-resonant laser pulse which has propagated through the two cavities. The basis for this scheme are two 'identical' scatterers, such as an atom or a quantum dot, where each has two initial states, whereby only one of them is optically active, for example, by dipole selection rules. Here we investigate one-sided cavities which avoid unintentional measurement in the reflected beam. Frequency 'sweet-spots' are identified for which, in spite of dissipative action, good fidelity entanglement generation should be possible. We also predict that monitoring of the Faraday rotation allows the detection of single spin flips, similar to single non-demolition photo-emission monitoring in atom quantum cavity systems. The possibility of studying entanglement death and revival in this system is discussed. (author)
All-optical tailoring of single-photon spectra in a quantum-dot microcavity system
Breddermann, Dominik; Binder, Rolf; Zrenner, Artur; Schumacher, Stefan
2016-01-01
Semiconductor quantum-dot cavity systems are promising sources for solid-state based on-demand generation of single photons for quantum communication. Commonly, the spectral characteristics of the emitted single photon are fixed by system properties such as electronic transition energies and spectral properties of the cavity. In the present work we study single-photon generation from the quantum-dot biexciton through a partly stimulated non-degenerate two-photon emission. We show that frequency and linewidth of the single photon can be fully controlled by the stimulating laser pulse, ultimately allowing for efficient all-optical spectral shaping of the single photon.
Nysteen, Anders; Nielsen, Per Kær; Mørk, Jesper
2013-01-01
photoluminescence excitation spectroscopy of a single quantum dot. We also investigate the implications for cavity QED, i.e., a coupled quantum dot-cavity system, and demonstrate that the phonon scattering may be strongly quenched. The quenching is explained by a balancing between the deformation potential...
Complete Coherent Control of a Quantum Dot Strongly Coupled to a Nanocavity
Dory, Constantin; Fischer, Kevin A.; Müller, Kai; Lagoudakis, Konstantinos G.; Sarmiento, Tomas; Rundquist, Armand; Zhang, Jingyuan L.; Kelaita, Yousif; Vučković, Jelena
2016-01-01
Strongly coupled quantum dot-cavity systems provide a non-linear configuration of hybridized light-matter states with promising quantum-optical applications. Here, we investigate the coherent interaction between strong laser pulses and quantum dot-cavity polaritons. Resonant excitation of polaritonic states and their interaction with phonons allow us to observe coherent Rabi oscillations and Ramsey fringes. Furthermore, we demonstrate complete coherent control of a quantum dot-photonic crystal cavity based quantum-bit. By controlling the excitation power and phase in a two-pulse excitation scheme we achieve access to the full Bloch sphere. Quantum-optical simulations are in good agreement with our experiments and provide insight into the decoherence mechanisms. PMID:27112420
Pillet, Claude-Alain
2006-01-01
This notes are an expanded version of the lectures given by the author at the Grenoble "Open Quantum Systems" summer school in 2003. They provide a short introduction to quantum dynamical systems and their ergodic properties with particular emphasis on the quantum Koopman–von Neumann spectral theory.
Sorting quantum systems efficiently.
Ionicioiu, Radu
2016-01-01
Measuring the state of a quantum system is a fundamental process in quantum mechanics and plays an essential role in quantum information and quantum technologies. One method to measure a quantum observable is to sort the system in different spatial modes according to the measured value, followed by single-particle detectors on each mode. Examples of quantum sorters are polarizing beam-splitters (PBS) - which direct photons according to their polarization - and Stern-Gerlach devices. Here we propose a general scheme to sort a quantum system according to the value of any d-dimensional degree of freedom, such as spin, orbital angular momentum (OAM), wavelength etc. Our scheme is universal, works at the single-particle level and has a theoretical efficiency of 100%. As an application we design an efficient OAM sorter consisting of a single multi-path interferometer which is suitable for a photonic chip implementation. PMID:27142705
Sorting quantum systems efficiently
Ionicioiu, Radu
2016-01-01
Measuring the state of a quantum system is a fundamental process in quantum mechanics and plays an essential role in quantum information and quantum technologies. One method to measure a quantum observable is to sort the system in different spatial modes according to the measured value, followed by single-particle detectors on each mode. Examples of quantum sorters are polarizing beam-splitters (PBS) – which direct photons according to their polarization – and Stern-Gerlach devices. Here we propose a general scheme to sort a quantum system according to the value of any d-dimensional degree of freedom, such as spin, orbital angular momentum (OAM), wavelength etc. Our scheme is universal, works at the single-particle level and has a theoretical efficiency of 100%. As an application we design an efficient OAM sorter consisting of a single multi-path interferometer which is suitable for a photonic chip implementation. PMID:27142705
Interference effects in the emission spectra of quantum dots in high-quality cavities
Keldysh, L. V.; Kulakovskii, V. D.; Reitzenstein, S.; Makhonin, M. N.; Forchel, A.
2007-01-01
We have investigated theoretically and experimentally the emission of (quantum dot-cavity) systems for different coupling strength and a wide range of exciton-photon mode detunings controlled by temperature variation in the range 10 45 K. Under close to resonance conditions, the radiation spectrum from the cavity emission becomes essentially dependent on the primary excitation path, which can be either via resonant quantum-dot exciton or via cavity mode. Particularly, in the case of nonresonant cavity mode excitation, the emission line becomes split into two asymmetric lines already in the weak coupling regime.
Danilov, Viatcheslav; /Oak Ridge; Nagaitsev, Sergei; /Fermilab
2011-11-01
Many quantum integrable systems are obtained using an accelerator physics technique known as Ermakov (or normalized variables) transformation. This technique was used to create classical nonlinear integrable lattices for accelerators and nonlinear integrable plasma traps. Now, all classical results are carried over to a nonrelativistic quantum case. In this paper we have described an extension of the Ermakov-like transformation to the Schroedinger and Pauli equations. It is shown that these newly found transformations create a vast variety of time dependent quantum equations that can be solved in analytic functions, or, at least, can be reduced to time-independent ones.
Clark, J W; Tarn, T J; Clark, John W.; Lucarelli, Dennis G.; Tarn, Tzyh-Jong
2003-01-01
A quantum system subject to external fields is said to be controllable if these fields can be adjusted to guide the state vector to a desired destination in the state space of the system. Fundamental results on controllability are reviewed against the background of recent ideas and advances in two seemingly disparate endeavors: (i) laser control of chemical reactions and (ii) quantum computation. Using Lie-algebraic methods, sufficient conditions have been derived for global controllability on a finite-dimensional manifold of an infinite-dimensional Hilbert space, in the case that the Hamiltonian and control operators, possibly unbounded, possess a common dense domain of analytic vectors. Some simple examples are presented. A synergism between quantum control and quantum computation is creating a host of exciting new opportunities for both activities. The impact of these developments on computational many-body theory could be profound.
We generalize the classical notion of a K-system to a non-commutative dynamical system by requiring that an invariantly defined memory loss be 100%. We give some examples of quantum K-systems and show that they cannot contain any quasi-periodic subsystem. 13 refs. (Author)
Magmatic "Quantum-Like" Systems
Rosinger, Elemer E
2008-01-01
Quantum computation has suggested, among others, the consideration of "non-quantum" systems which in certain respects may behave "quantum-like". Here, what algebraically appears to be the most general possible known setup, namely, of {\\it magmas} is used in order to construct "quantum-like" systems. The resulting magmatic composition of systems has as a well known particular case the tensor products.
Micheli, Fiorenza de [Centro de Estudios Cientificos, Arturo Prat 514, Valdivia (Chile); Instituto de Fisica, Pontificia Universidad Catolica de Valparaiso, Casilla 4059, Valparaiso (Chile); Zanelli, Jorge [Centro de Estudios Cientificos, Arturo Prat 514, Valdivia (Chile); Universidad Andres Bello, Av. Republica 440, Santiago (Chile)
2012-10-15
A degenerate dynamical system is characterized by a symplectic structure whose rank is not constant throughout phase space. Its phase space is divided into causally disconnected, nonoverlapping regions in each of which the rank of the symplectic matrix is constant, and there are no classical orbits connecting two different regions. Here the question of whether this classical disconnectedness survives quantization is addressed. Our conclusion is that in irreducible degenerate systems-in which the degeneracy cannot be eliminated by redefining variables in the action-the disconnectedness is maintained in the quantum theory: there is no quantum tunnelling across degeneracy surfaces. This shows that the degeneracy surfaces are boundaries separating distinct physical systems, not only classically, but in the quantum realm as well. The relevance of this feature for gravitation and Chern-Simons theories in higher dimensions cannot be overstated.
Vourdas, A.
2005-09-01
A finite quantum system in which the position and momentum take values in the Galois field GF(pell) is constructed from a smaller quantum system in which the position and momentum take values in {\\cal Z}_p , using field extension. The Galois trace is used in the definition of the Fourier transform. The Heisenberg-Weyl group of displacements and the Sp(2, GF(pell)) group of symplectic transformations are studied. A class of transformations inspired by the Frobenius maps in Galois fields is introduced. The relationship of this 'Galois quantum system' with its subsystems in which the position and momentum take values in subfields of GF(pell) is discussed.
Vourdas, A [Department of Computing, University of Bradford, Bradford BD7 1DP (United Kingdom)
2005-09-30
A finite quantum system in which the position and momentum take values in the Galois field GF(p{sup l}) is constructed from a smaller quantum system in which the position and momentum take values in Z{sub p}, using field extension. The Galois trace is used in the definition of the Fourier transform. The Heisenberg-Weyl group of displacements and the Sp(2, GF(p{sup l})) group of symplectic transformations are studied. A class of transformations inspired by the Frobenius maps in Galois fields is introduced. The relationship of this 'Galois quantum system' with its subsystems in which the position and momentum take values in subfields of GF(p{sup l}) is discussed.
Hohenester, Ulrich
2010-04-01
For a semiconductor quantum dot strongly coupled to a microcavity, we theoretically investigate phonon-assisted transitions from the exciton to a cavity photon, where the energy mismatch is compensated by phonon emission or absorption. By means of a Schrieffer-Wolff transformation we derive an effective Hamiltonian, which describes the combined effect of exciton-cavity and exciton-phonon couplings, and compute the scattering rates within a Fermi-golden-rule approach. The results of this approach are compared with those of a recently reported description scheme based on the independent boson model [U. Hohenester , Phys. Rev. B 80, 201311(R) (2009)] and a numerical density-matrix approach. All description schemes are shown to give very similar results. This demonstrates that phonon-assisted cavity feeding can be described in terms of a simple scattering process and does not require a non-Markovian treatment as suggested elsewhere. We present results for the spontaneous emission lifetime of a quantum dot initially populated with a single exciton or biexciton and for the spectral properties of an optically driven dot-cavity system operating in the strong-coupling regime. Our results demonstrate that phonon-assisted feeding plays a dominant role for strongly coupled dot-cavity systems when the detuning is of the order of a few millielectron volts.
A degenerate dynamical system is characterized by a symplectic structure whose rank is not constant throughout phase space. Its phase space is divided into causally disconnected, nonoverlapping regions in each of which the rank of the symplectic matrix is constant, and there are no classical orbits connecting two different regions. Here the question of whether this classical disconnectedness survives quantization is addressed. Our conclusion is that in irreducible degenerate systems—in which the degeneracy cannot be eliminated by redefining variables in the action—the disconnectedness is maintained in the quantum theory: there is no quantum tunnelling across degeneracy surfaces. This shows that the degeneracy surfaces are boundaries separating distinct physical systems, not only classically, but in the quantum realm as well. The relevance of this feature for gravitation and Chern-Simons theories in higher dimensions cannot be overstated.
Scheme of thinking quantum systems
V.I. Yukalov; Sornette, D
2009-01-01
A general approach describing quantum decision procedures is developed. The approach can be applied to quantum information processing, quantum computing, creation of artificial quantum intelligence, as well as to analyzing decision processes of human decision makers. Our basic point is to consider an active quantum system possessing its own strategic state. Processing information by such a system is analogous to the cognitive processes associated to decision making by humans. The algebra of p...
Scheme of thinking quantum systems
Yukalov, V. I.; Sornette, D.
2009-11-01
A general approach describing quantum decision procedures is developed. The approach can be applied to quantum information processing, quantum computing, creation of artificial quantum intelligence, as well as to analyzing decision processes of human decision makers. Our basic point is to consider an active quantum system possessing its own strategic state. Processing information by such a system is analogous to the cognitive processes associated to decision making by humans. The algebra of probability operators, associated with the possible options available to the decision maker, plays the role of the algebra of observables in quantum theory of measurements. A scheme is advanced for a practical realization of decision procedures by thinking quantum systems. Such thinking quantum systems can be realized by using spin lattices, systems of magnetic molecules, cold atoms trapped in optical lattices, ensembles of quantum dots, or multilevel atomic systems interacting with electromagnetic field.
Scheme of thinking quantum systems
Yukalov, V I
2009-01-01
A general approach describing quantum decision procedures is developed. The approach can be applied to quantum information processing, quantum computing, creation of artificial quantum intelligence, as well as to analyzing decision processes of human decision makers. Our basic point is to consider an active quantum system possessing its own strategic state. Processing information by such a system is analogous to the cognitive processes associated to decision making by humans. The algebra of probability operators, associated with the possible options available to the decision maker, plays the role of the algebra of observables in quantum theory of measurements. A scheme is advanced for a practical realization of decision procedures by thinking quantum systems. Such thinking quantum systems can be realized by using spin lattices, systems of magnetic molecules, cold atoms trapped in optical lattices, ensembles of quantum dots, or multilevel atomic systems interacting with electromagnetic field.
Scheme of thinking quantum systems
A general approach describing quantum decision procedures is developed. The approach can be applied to quantum information processing, quantum computing, creation of artificial quantum intelligence, as well as to analyzing decision processes of human decision makers. Our basic point is to consider an active quantum system possessing its own strategic state. Processing information by such a system is analogous to the cognitive processes associated to decision making by humans. The algebra of probability operators, associated with the possible options available to the decision maker, plays the role of the algebra of observables in quantum theory of measurements. A scheme is advanced for a practical realization of decision procedures by thinking quantum systems. Such thinking quantum systems can be realized by using spin lattices, systems of magnetic molecules, cold atoms trapped in optical lattices, ensembles of quantum dots, or multilevel atomic systems interacting with electromagnetic field
Quantum Cybernetics and Complex Quantum Systems Science - A Quantum Connectionist Exploration
Gonçalves, Carlos Pedro
2014-01-01
Quantum cybernetics and its connections to complex quantum systems science is addressed from the perspective of complex quantum computing systems. In this way, the notion of an autonomous quantum computing system is introduced in regards to quantum artificial intelligence, and applied to quantum artificial neural networks, considered as autonomous quantum computing systems, which leads to a quantum connectionist framework within quantum cybernetics for complex quantum computing systems. Sever...
Weiss, Ulrich
2012-01-01
Starting from first principles, this book introduces the fundamental concepts and methods of dissipative quantum mechanics and explores related phenomena in condensed matter systems. Major experimental achievements in cooperation with theoretical advances have brightened the field and brought it to the attention of the general community in natural sciences. Nowadays, working knowledge of dissipative quantum mechanics is an essential tool for many physicists. This book - originally published in 1990 and republished in 1999 and and 2008 as enlarged second and third editions - delves significantl
Weiss, U
1999-01-01
Recent advances in the quantum theory of macroscopic systems have brightened up the field and brought it into the focus of a general community in natural sciences. The fundamental concepts, methods and applications including the most recent developments, previously covered for the most part only in the original literature, are presented here in a comprehensive treatment to an audience who is reasonably familiar with quantum-statistical mechanics and has had rudimentary contacts with the path integral formulation.This book deals with the phenomena and theory of decoherence and dissipation in qu
Transitionless quantum driving in open quantum systems
We extend the concept of superadiabatic dynamics, or transitionless quantum driving, to quantum open systems whose evolution is governed by a master equation in the Lindblad form. We provide the general framework needed to determine the control strategy required to achieve superadiabaticity. We apply our formalism to two examples consisting of a two-level system coupled to environments with time-dependent bath operators. (paper)
Quantum critical points in quantum impurity systems
The numerical renormalization group method is used to investigate zero-temperature phase transitions in quantum impurity systems, in particular in the soft-gap Anderson model, where an impurity couples to a non-trivial fermionic bath. In this case, zero-temperature phase transitions occur between two different phases whose fixed points can be built up of non-interacting single-particle states. However, the quantum critical point cannot be described by non-interacting fermionic or bosonic excitations
Decoherence in open quantum systems
In the framework of the theory of open quantum systems based on completely positive quantum dynamical semigroups we study the transition from quantum to classical behaviour of the system of a harmonic oscillator interacting with an environment (in particular with a thermal bath) by discussing the evolution of the density matrix and Wigner function of the system. The two necessary conditions for a system to become classical - quantum decoherence and classical correlations - are discussed and the degree of quantum decoherence and the degree of classical correlations are estimated in order to analyze the classicality of the considered system. (author)
Hybrid Quantum Systems with Circuit Quantum Electrodynamics
Schuster, David
2012-02-01
Quantum Information Processing presents daunting challenges, with competing requirements of fast manipulation, long storage, and long distance transport of fragile quantum states. In aggregate, many of the challenges quantum computation have been met with nanosecond manipulations (quantum circuits), coherence times measured in seconds (atomic ions/nuclear spins), and entanglement transported over kilometers (linear optics), yet thus far no system has achieved all of the necessary components simultaneously. One promising direction is to leverage the best aspects of each system in a hybrid system, much as is done in a conventional computer, where transistors provide fast processing, magnetic memory provides massive long term storage, and information is transmitted via microwaves or fiber optics. A review of the constituent quantum systems, and the types of couplings between them will be presented. The coupling of a superconducting cavity/qubit system to electrons floating on helium will be discussed as an example of how to construct a hybrid system. Recent results on trapping and detection of electrons on helium using a superconducting cavity will be presented.
Quantum systems as classical systems
Cassa, A
2001-01-01
A characteristical property of a classical physical theory is that the observables are real functions taking an exact outcome on every (pure) state; in a quantum theory, at the contrary, a given observable on a given state can take several values with only a predictable probability. However, even in the classical case, when an observer is intrinsically unable to distinguish between some distinct states he can convince himself that the measure of its ''observables'' can have several values in a random way with a statistical character. What kind of statistical theory is obtainable in this way? It is possible, for example, to obtain exactly the statistical previsions of quantum mechanics? Or, in other words, can a physical system showing a classical behaviour appear to be a quantum system to a confusing observer? We show that from a mathematical viewpoint it is not difficult to produce a theory with hidden variables having this property. We don't even try to justify in physical terms the artificial construction ...
Asymptotically open quantum systems
In the present thesis we investigate the structure of time-dependent equations of motion in quantum mechanics.We start from two coupled systems with an autonomous equation of motion. A limit, in which the dynamics of one of the two systems has a decoupled evolution and imposes a non-autonomous evolution for the second system is identified. A result due to K. Hepp that provides a classical limit for dynamics turns out to be part and parcel for this limit and is generalized in our work. The method introduced by J.S. Howland for the solution of the time-dependent Schroedinger equation is interpreted as such a limit. Moreover, we associate our limit with the modern theory of quantization. (orig.)
Quantum Effects in Biological Systems
2016-01-01
Since the last decade the study of quantum mechanical phenomena in biological systems has become a vibrant field of research. Initially sparked by evidence of quantum effects in energy transport that is instrumental for photosynthesis, quantum biology asks the question of how methods and models from quantum theory can help us to understand fundamental mechanisms in living organisms. This approach entails a paradigm change challenging the related disciplines: The successful framework of quantum theory is taken out of its low-temperature, microscopic regimes and applied to hot and dense macroscopic environments, thereby extending the toolbox of biology and biochemistry at the same time. The Quantum Effects in Biological Systems conference is a platform for researchers from biology, chemistry and physics to present and discuss the latest developments in the field of quantum biology. After meetings in Lisbon (2009), Harvard (2010), Ulm (2011), Berkeley (2012), Vienna (2013), Singapore (2014) and Florence (2015),...
Iqbal, A.; Toor, A. H.
2001-01-01
We investigate the role of quantum mechanical effects in the central stability concept of evolutionary game theory i.e. an Evolutionarily Stable Strategy (ESS). Using two and three-player symmetric quantum games we show how the presence of quantum phenomenon of entanglement can be crucial to decide the course of evolutionary dynamics in a population of interacting individuals.
Quantum Dynamics in Biological Systems
Shim, Sangwoo
2012-01-01
In the first part of this dissertation, recent efforts to understand quantum mechanical effects in biological systems are discussed. Especially, long-lived quantum coherences observed during the electronic energy transfer process in the Fenna-Matthews-Olson complex at physiological condition are studied extensively using theories of open quantum systems. In addition to the usual master equation based approaches, the effect of the protein structure is investigated in atomistic detail through t...
Quantum trajectories and open many-body quantum systems
Daley, Andrew J.
2014-01-01
The study of open quantum systems has become increasingly important in the past years, as the ability to control quantum coherence on a single particle level has been developed in a wide variety of physical systems. In quantum optics, the study of open systems goes well beyond understanding the breakdown of quantum coherence. There, the coupling to the environment is sufficiently well understood that it can be manipulated to drive the system into desired quantum states, or to project the syst...
Quantum Effects in Biological Systems
Roy, Sisir
2014-07-01
The debates about the trivial and non-trivial effects in biological systems have drawn much attention during the last decade or so. What might these non-trivial sorts of quantum effects be? There is no consensus so far among the physicists and biologists regarding the meaning of "non-trivial quantum effects". However, there is no doubt about the implications of the challenging research into quantum effects relevant to biology such as coherent excitations of biomolecules and photosynthesis, quantum tunneling of protons, van der Waals forces, ultrafast dynamics through conical intersections, and phonon-assisted electron tunneling as the basis for our sense of smell, environment assisted transport of ions and entanglement in ion channels, role of quantum vacuum in consciousness. Several authors have discussed the non-trivial quantum effects and classified them into four broad categories: (a) Quantum life principle; (b) Quantum computing in the brain; (c) Quantum computing in genetics; and (d) Quantum consciousness. First, I will review the above developments. I will then discuss in detail the ion transport in the ion channel and the relevance of quantum theory in brain function. The ion transport in the ion channel plays a key role in information processing by the brain.
Quantum technologies with hybrid systems.
Kurizki, Gershon; Bertet, Patrice; Kubo, Yuimaru; Mølmer, Klaus; Petrosyan, David; Rabl, Peter; Schmiedmayer, Jörg
2015-03-31
An extensively pursued current direction of research in physics aims at the development of practical technologies that exploit the effects of quantum mechanics. As part of this ongoing effort, devices for quantum information processing, secure communication, and high-precision sensing are being implemented with diverse systems, ranging from photons, atoms, and spins to mesoscopic superconducting and nanomechanical structures. Their physical properties make some of these systems better suited than others for specific tasks; thus, photons are well suited for transmitting quantum information, weakly interacting spins can serve as long-lived quantum memories, and superconducting elements can rapidly process information encoded in their quantum states. A central goal of the envisaged quantum technologies is to develop devices that can simultaneously perform several of these tasks, namely, reliably store, process, and transmit quantum information. Hybrid quantum systems composed of different physical components with complementary functionalities may provide precisely such multitasking capabilities. This article reviews some of the driving theoretical ideas and first experimental realizations of hybrid quantum systems and the opportunities and challenges they present and offers a glance at the near- and long-term perspectives of this fascinating and rapidly expanding field. PMID:25737558
The overview of recent developments in the theory of quantum chaos is presented with the special emphasis on a number of unsolved problems and current apparent contradictions. The relation between dynamical quantum chaos and statistical random matrix theory is discussed. 97 refs
Fault Tolerant Quantum Filtering and Fault Detection for Quantum Systems
Gao, Qing; Dong, Daoyi; Petersen, Ian R.
2015-01-01
This paper aims to determine the fault tolerant quantum filter and fault detection equation for a class of open quantum systems coupled to a laser field that is subject to stochastic faults. In order to analyze this class of open quantum systems, we propose a quantum-classical Bayesian inference method based on the definition of a so-called quantum-classical conditional expectation. It is shown that the proposed Bayesian inference approach provides a convenient tool to simultaneously derive t...
A prototype quantum cryptography system
In this work we have constructed a new secure quantum key distribution system based on the BB84 protocol. Many current state-of-the-art quantum cryptography systems encounter major problems concerning low bit rate, synchronization, and stabilization. Our quantum cryptography system utilizes only laser diodes and standard passive optical components, to enhance the stability and also to decrease the space requirements. The development of this demonstration for a practical quantum key distribution system is a consequence of our previous work on the quantum cryptographic system using optical fiber components for the transmitter and receiver. There we found that the optical fiber couplers should not be used due to the problems with space, stability and alignment. The goal of the synchronization is to use as little transmission capacities as possible. The experimental results of our quantum key distribution system show the feasibility of getting more than 90 % transmission capacities with the approaches developed in this work. Therefore it becomes feasible to securely establish a random key sequence at a rate of 1 to ∼ 5K bit/s by using our stable, compact, cheap, and user-friendly modules for quantum cryptography. (author)
Three Terminal Quantum Dot System
N. Chandrasekar
2012-01-01
Full Text Available In this study, the transmission rate for the three terminal quantum dot system is determined using Keldysh nonequilibrium Green’s function technique for interacting and non-interacting cases. The three terminal quantum dot systems consist of three leads and three quantum dots that are arranged in a triangular form. Each led is coupled with each dot. The lesser and retarded Green’s functions are used for the calculations of transmission rates and how the transmission rates vary for interacting and non-interacting system are studied is investigated.
Manipulation of single quantum systems
Full text: The founders of quantum theory assumed in thought experiments that they were manipulating isolated quantum systems obeying the counterintuitive laws which they had just discovered. Technological advances have recently turned these virtual experiments into real ones by making possible the actual control of isolated quantum particles. Many laboratories are realizing such experiments, in a research field at the frontier between physics and information science. Fundamentally, these studies explore the transition between the microscopic world ruled by quantum laws and our macroscopic environment which appears classical. Practically, physicists hope that these experiments will result in new technologies exploiting the strange quantum logic to compute, communicate or measure physical quantities better than was previously conceivable. In Paris, we perform such experiments by juggling with photons trapped between superconducting mirrors. I will give a simple description of these studies, compare them to similar ones performed on other systems and guess about possible applications. (author)
Quantum technologies with hybrid systems
Kurizki, Gershon; Bertet, Patrice; Kubo, Yuimaru; Mølmer, Klaus; Petrosyan, David; Rabl, Peter; Schmiedmayer, Jörg
2015-01-01
An extensively pursued current direction of research in physics aims at the development of practical technologies that exploit the effects of quantum mechanics. As part of this ongoing effort, devices for quantum information processing, secure communication, and high-precision sensing are being implemented with diverse systems, ranging from photons, atoms, and spins to mesoscopic superconducting and nanomechanical structures. Their physical properties make some of these systems better suited ...
Efficient Simulation of Quantum Systems by Quantum Computers
Zalka, Christof
1996-01-01
We show that the time evolution of the wave function of a quantum mechanical many particle system can be implemented very efficiently on a quantum computer. The computational cost of such a simulation is comparable to the cost of a conventional simulation of the corresponding classical system. We then sketch how results of interest, like the energy spectrum of a system, can be obtained. We also indicate that ultimately the simulation of quantum field theory might be possible on large quantum ...
Mechanism for quantum speedup in open quantum systems
Liu, Hai-Bin; Yang, W. L.; An, Jun-Hong; Xu, Zhen-Yu
2016-02-01
The quantum speed limit (QSL) time for open system characterizes the most efficient response of the system to the environmental influences. Previous results showed that the non-Markovianity governs the quantum speedup. Via studying the dynamics of a dissipative two-level system, we reveal that the non-Markovian effect is only the dynamical way of the quantum speedup, while the formation of the system-environment bound states is the essential reason for the quantum speedup. Our attribution of the quantum speedup to the energy-spectrum character can supply another vital path for experiments when the quantum speedup shows up without any dynamical calculations. The potential experimental observation of our quantum speedup mechanism in the circuit QED system is discussed. Our results may be of both theoretical and experimental interest in exploring the ultimate QSL in realistic environments, and may open new perspectives for devising active quantum speedup devices.
Quantum Dot Systems: a versatile platform for quantum simulations
Barthelemy, Pierre; Vandersypen, Lieven M.K. [Kavli Institute of Nanoscience, TU Delft, 2600 GA Delft (Netherlands)
2013-11-15
Quantum mechanics often results in extremely complex phenomena, especially when the quantum system under consideration is composed of many interacting particles. The states of these many-body systems live in a space so large that classical numerical calculations cannot compute them. Quantum simulations can be used to overcome this problem: complex quantum problems can be solved by studying experimentally an artificial quantum system operated to simulate the desired hamiltonian. Quantum dot systems have shown to be widely tunable quantum systems, that can be efficiently controlled electrically. This tunability and the versatility of their design makes them very promising quantum simulators. This paper reviews the progress towards digital quantum simulations with individually controlled quantum dots, as well as the analog quantum simulations that have been performed with these systems. The possibility to use large arrays of quantum dots to simulate the low-temperature Hubbard model is also discussed. The main issues along that path are presented and new ideas to overcome them are proposed. (copyright 2013 by WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Quantum walk public-key cryptographic system
Vlachou, C.; Rodrigues, J.; Mateus, P.; Paunković, N.; Souto, A.
2015-12-01
Quantum Cryptography is a rapidly developing field of research that benefits from the properties of Quantum Mechanics in performing cryptographic tasks. Quantum walks are a powerful model for quantum computation and very promising for quantum information processing. In this paper, we present a quantum public-key cryptographic system based on quantum walks. In particular, in the proposed protocol the public-key is given by a quantum state generated by performing a quantum walk. We show that the protocol is secure and analyze the complexity of public key generation and encryption/decryption procedures.
Design of coherent quantum observers for linear quantum systems
Vuglar, Shanon L.; Amini, Hadis
2014-12-01
Quantum versions of control problems are often more difficult than their classical counterparts because of the additional constraints imposed by quantum dynamics. For example, the quantum LQG and quantum {{H}? } optimal control problems remain open. To make further progress, new, systematic and tractable methods need to be developed. This paper gives three algorithms for designing coherent quantum observers, i.e., quantum systems that are connected to a quantum plant and their outputs provide information about the internal state of the plant. Importantly, coherent quantum observers avoid measurements of the plant outputs. We compare our coherent quantum observers with a classical (measurement-based) observer by way of an example involving an optical cavity with thermal and vacuum noises as inputs.
Design of coherent quantum observers for linear quantum systems
Quantum versions of control problems are often more difficult than their classical counterparts because of the additional constraints imposed by quantum dynamics. For example, the quantum LQG and quantum H∞ optimal control problems remain open. To make further progress, new, systematic and tractable methods need to be developed. This paper gives three algorithms for designing coherent quantum observers, i.e., quantum systems that are connected to a quantum plant and their outputs provide information about the internal state of the plant. Importantly, coherent quantum observers avoid measurements of the plant outputs. We compare our coherent quantum observers with a classical (measurement-based) observer by way of an example involving an optical cavity with thermal and vacuum noises as inputs. (paper)
Quantum energy teleportation in a quantum Hall system
Yusa, Go; Izumida, Wataru; Hotta, Masahiro [Department of Physics, Tohoku University, Sendai 980-8578 (Japan)
2011-09-15
We propose an experimental method for a quantum protocol termed quantum energy teleportation (QET), which allows energy transportation to a remote location without physical carriers. Using a quantum Hall system as a realistic model, we discuss the physical significance of QET and estimate the order of energy gain using reasonable experimental parameters.
Quantum systems as classical systems
Cassa, Antonio
2001-01-01
A characteristical property of a classical physical theory is that the observables are real functions taking an exact outcome on every (pure) state; in a quantum theory, at the contrary, a given observable on a given state can take several values with only a predictable probability. However, even in the classical case, when an observer is intrinsically unable to distinguish between some distinct states he can convince himself that the measure of its ''observables'' can have several values in ...
Hypothesis testing with open quantum systems
Molmer, Klaus
2014-01-01
Using a quantum circuit model we derive the maximal ability to distinguish which of several candidate Hamiltonians describe an open quantum system. This theory, in particular, provides the maximum information retrievable from continuous quantum measurement records, available when a quantum system is perturbatively coupled to a broadband quantized environment.
Information Flow in Entangled Quantum Systems
Deutsch, David; Hayden, Patrick
1999-01-01
All information in quantum systems is, notwithstanding Bell's theorem, localised. Measuring or otherwise interacting with a quantum system S has no effect on distant systems from which S is dynamically isolated, even if they are entangled with S. Using the Heisenberg picture to analyse quantum information processing makes this locality explicit, and reveals that under some circumstances (in particular, in Einstein-Podolski-Rosen experiments and in quantum teleportation) quantum information is...
Quantum Relativity: Physical Laws Must be Invariant Over Quantum Systems
Merriam, P
2005-01-01
Decoherence may not solve all of the measurement problems of quantum mechanics. A solution to these problems is to allow that superpositions describe physically real systems in the following sense. Each quantum system carries around a local spacetime in whose terms other quantum systems may take on unsharp values. Each quantum system forms a physically valid coordinate frame. The laws of physics should be formulated to be invariant under the group of allowed transformations among such frames. A transformation of relatively superposed spatial coordinates that allows an electron system to preserve the de Broglie Relation in describing a doubleslit laboratory system in analogy to a Minkowskian Transformation is given. In general, quantum relativity says h cross equals 1 is invariant over transformations among quantum reference frames. It is argued this impacts gravity and gauge invariance.
The quantum Hall effect in quantum dot systems
It is proposed to use quantum dots in order to increase the temperatures suitable for observation of the integer quantum Hall effect. A simple estimation using Fock-Darwin spectrum of a quantum dot shows that good part of carriers localized in quantum dots generate the intervals of plateaus robust against elevated temperatures. Numerical calculations employing local trigonometric basis and highly efficient kernel polynomial method adopted for computing the Hall conductivity reveal that quantum dots may enhance peak temperature for the effect by an order of magnitude, possibly above 77 K. Requirements to potentials, quality and arrangement of the quantum dots essential for practical realization of such enhancement are indicated. Comparison of our theoretical results with the quantum Hall measurements in InAs quantum dot systems from two experimental groups is also given
Entanglement within the Quantum Trajectory Description of Open Quantum Systems
Nha, Hyunchul; Carmichael, H J
2004-01-01
The degree of entanglement in an open quantum system varies according to how information in the environment is read. A measure of this contextual entanglement is introduced based on quantum trajectory unravelings of the open system dynamics. It is used to characterize the entanglement in a driven quantum system of dimension $2\\times\\infty$ where the entanglement is induced by the environmental interaction. A detailed mechanism for the environment-induced entanglement is given.
Dynamics of complex quantum systems
Akulin, Vladimir M
2014-01-01
This book gathers together a range of similar problems that can be encountered in different fields of modern quantum physics and that have common features with regard to multilevel quantum systems. The main motivation was to examine from a uniform standpoint various models and approaches that have been developed in atomic, molecular, condensed matter, chemical, laser and nuclear physics in various contexts. The book should help senior-level undergraduate, graduate students and researchers putting particular problems in these fields into a broader scientific context and thereby taking advantage of well-established techniques used in adjacent fields. This second edition has been expanded to include substantial new material (e.g. new sections on Dynamic Localization and on Euclidean Random Matrices and new chapters on Entanglement, Open Quantum Systems, and Coherence Protection). It is based on the author’s lectures at the Moscow Institute of Physics and Technology, at the CNRS Aimé Cotton Laboratory, and on ...
Entangled systems. New directions in quantum physics
Entangled Systems is an introductory textbook for advanced students of physics, chemistry and computer science which covers an area of physics that has lately witnessed rapid expansion. The topics treated here include foundations of quantum theory, quantum information, quantum communication, quantum computing, quantum teleportation and hidden variables, thus providing not only a solid basis for the study of quantum theory as such, but also a profound foundation of knowledge from which readers can follow the rapid development of the topic or start out into a more specialized branch of research. Commented recommendations for further reading as well as end-of-chapter problems help the reader to access quickly the basic theoretical concepts of future key technologies. Only a basic prior knowledge of quantum theory and the necessary mathematical foundations is assumed, as introductory chapters are provided to present these to the readers. Thus, 'Entangled Systems' can be used both as a course book and for self-study purposes. From the contents: - The Mathematical Framework - Basic Concepts of Quantum Theory - The Simplest Quantum Systems: Qubits - Mixed State and Density Operator - Shannon's Entropy and Classical Information - The von Neumann Entropy and Quantum Information - Composite Systems - Entanglement - Correlations and Non-Local Measurements - There is no (Local-Realistic) Alternative to the Quantum Theory - Working with Entanglement - The Quantum Computer - General Measurements, POVM - The General Evolution of an Open Quantum System and Special Quantum Channels - Decoherence and Approaches to the Description of the Quantum Measurement Process - Two Implementations of Quantum Operations. (orig.)
Perturbative approach to Markovian open quantum systems
Li, Andy C. Y.; F. Petruccione; Jens Koch
2013-01-01
Perturbation theory (PT) is a powerful and commonly used tool in the investigation of closed quantum systems. In the context of open quantum systems, PT based on the Markovian quantum master equation is much less developed. The investigation of open systems mostly relies on exact diagonalization of the Liouville superoperator or quantum trajectories. In this approach, the system size is rather limited by current computational capabilities. Analogous to closed-system PT, we develop a PT suitab...
Quantum Indeterminacy of Cosmic Systems
Hogan, Craig J. [Fermi National Accelerator Laboratory (FNAL), Batavia, IL (United States)
2013-12-30
It is shown that quantum uncertainty of motion in systems controlled mainly by gravity generally grows with orbital timescale $H^{-1}$, and dominates classical motion for trajectories separated by distances less than $\\approx H^{-3/5}$ in Planck units. For example, the cosmological metric today becomes indeterminate at macroscopic separations, $H_0^{-3/5}\\approx 60$ meters. Estimates suggest that entangled non-localized quantum states of geometry and matter may significantly affect fluctuations during inflation, and connect the scale of dark energy to that of strong interactions.
Quantum tomography and classical propagator for quadratic quantum systems
The classical propagator for tomographic probability (which describes the quantum state instead of wave function or density matrix) is presented for quadratic quantum systems and its relation to the quantum propagator is considered. The new formalism of quantum mechanics, based on the probability representation of the state, is applied to particular quadratic systems - the harmonic oscillator, particle's free motion, problems of an ion in a Paul trap and in asymmetric Penning trap, and to the process of stimulated Raman scattering. The classical propagator for these systems is written in an explicit form. (author)
Polygamy of Entanglement in Multipartite Quantum Systems
Kim, Jeong San
2009-01-01
We show that bipartite entanglement distribution (or entanglement of assistance) in multipartite quantum systems is by nature polygamous. We first provide an analytic upper bound for the concurrence of assistance in bipartite quantum systems, and derive a polygamy inequality of multipartite entanglement in arbitrary dimensional quantum systems.
QUANTUM AND CLASSICAL CORRELATIONS IN GAUSSIAN OPEN QUANTUM SYSTEMS
Aurelian ISAR
2015-01-01
Full Text Available In the framework of the theory of open systems based on completely positive quantum dynamical semigroups, we give a description of the continuous-variable quantum correlations (quantum entanglement and quantum discord for a system consisting of two noninteracting bosonic modes embedded in a thermal environment. We solve the Kossakowski-Lindblad master equation for the time evolution of the considered system and describe the entanglement and discord in terms of the covariance matrix for Gaussian input states. For all values of the temperature of the thermal reservoir, an initial separable Gaussian state remains separable for all times. We study the time evolution of logarithmic negativity, which characterizes the degree of entanglement, and show that in the case of an entangled initial squeezed thermal state, entanglement suppression takes place for all temperatures of the environment, including zero temperature. We analyze the time evolution of the Gaussian quantum discord, which is a measure of all quantum correlations in the bipartite state, including entanglement, and show that it decays asymptotically in time under the effect of the thermal bath. This is in contrast with the sudden death of entanglement. Before the suppression of the entanglement, the qualitative evolution of quantum discord is very similar to that of the entanglement. We describe also the time evolution of the degree of classical correlations and of quantum mutual information, which measures the total correlations of the quantum system.
Quantum Teleportation in One-Dimensional Quantum Dots System
Wang, H; Wang, Hefeng; Kais, Sabre
2006-01-01
We present a model of quantum teleportation protocol based on one-dimensional quantum dots system. Three quantum dots with three electrons are used to perform teleportation, the unknown qubit is encoded using one electron spin on quantum dot A, the other two dots B and C are coupled to form a mixed space-spin entangled state. By choosing the Hamiltonian for the mixed space-spin entangled system, we can filter the space (spin) entanglement to obtain pure spin (space) entanglement and after a Bell measurement, the unknown qubit is transfered to quantum dot B. Selecting an appropriate Hamiltonian for the quantum gate allows the spin-based information to be transformed into a charge-based information. The possibility of generalizing this model to N-electrons is discussed.
Eigenfunctions in chaotic quantum systems
The structure of wavefunctions of quantum systems strongly depends on the underlying classical dynamics. In this text a selection of articles on eigenfunctions in systems with fully chaotic dynamics and systems with a mixed phase space is summarized. Of particular interest are statistical properties like amplitude distribution and spatial autocorrelation function and the implication of eigenfunction structures on transport properties. For systems with a mixed phase space the separation into regular and chaotic states does not always hold away from the semiclassical limit, such that chaotic states may completely penetrate into the region of the regular island. The consequences of this flooding are discussed and universal aspects highlighted. (orig.)
Eigenfunctions in chaotic quantum systems
Baecker, Arnd
2007-07-01
The structure of wavefunctions of quantum systems strongly depends on the underlying classical dynamics. In this text a selection of articles on eigenfunctions in systems with fully chaotic dynamics and systems with a mixed phase space is summarized. Of particular interest are statistical properties like amplitude distribution and spatial autocorrelation function and the implication of eigenfunction structures on transport properties. For systems with a mixed phase space the separation into regular and chaotic states does not always hold away from the semiclassical limit, such that chaotic states may completely penetrate into the region of the regular island. The consequences of this flooding are discussed and universal aspects highlighted. (orig.)
Software-defined Quantum Communication Systems
Humble, Travis S.; Sadlier, Ronald J.
2014-01-01
Quantum communication systems harness modern physics through state-of-the-art optical engineering to provide revolutionary capabilities. An important concern for quantum communication engineering is designing and prototyping these systems to evaluate proposed capabilities. We apply the paradigm of software-defined communication for engineering quantum communication systems to facilitate rapid prototyping and prototype comparisons. We detail how to decompose quantum communication terminals int...
Settnes, Mikkel; Kaer, Per; Moelbjerg, Anders; Mork, Jesper
2013-08-01
We show that Auger processes involving wetting layer transitions mediate emission from a cavity that is detuned from a quantum dot by even tens of meV. The wetting layer thus acts as a reservoir, which by Coulomb scattering can supply or absorb the energy difference between emitter and cavity. We perform microscopic calculations of the effect treating the wetting layer as a non-Markovian reservoir interacting with the coupled quantum dot-cavity system through Coulomb interactions. Experimentally, cavity feeding has been observed in the asymmetric detuning range of -10 to +45??meV. We show that this asymmetry arises naturally from the quasiequilibrium properties of the wetting layer reservoir. Furthermore, we present numerical calculations of both photoluminescence spectra and photon correlations, demonstrating good qualitative agreement with experiments. PMID:23971611
Quantum Computing in Solid State Systems
Ruggiero, B; Granata, C
2006-01-01
The aim of Quantum Computation in Solid State Systems is to report on recent theoretical and experimental results on the macroscopic quantum coherence of mesoscopic systems, as well as on solid state realization of qubits and quantum gates. Particular attention has been given to coherence effects in Josephson devices. Other solid state systems, including quantum dots, optical, ion, and spin devices which exhibit macroscopic quantum coherence are also discussed. Quantum Computation in Solid State Systems discusses experimental implementation of quantum computing and information processing devices, and in particular observations of quantum behavior in several solid state systems. On the theoretical side, the complementary expertise of the contributors provides models of the various structures in connection with the problem of minimizing decoherence.
Logical entropy of quantum dynamical systems
Ebrahimzadeh Abolfazl
2016-01-01
Full Text Available This paper introduces the concepts of logical entropy and conditional logical entropy of hnite partitions on a quantum logic. Some of their ergodic properties are presented. Also logical entropy of a quantum dynamical system is dehned and ergodic properties of dynamical systems on a quantum logic are investigated. Finally, the version of Kolmogorov-Sinai theorem is proved.
Quantum chaos in open systems: a quantum state diffusion analysis
Brun, Todd A.; Percival, Ian C.; Schack, Rüdiger
1995-01-01
Except for the universe, all quantum systems are open, and according to quantum state diffusion theory, many systems localize to wave packets in the neighborhood of phase space points. This is due to decoherence from the interaction with the environment, and makes the quasiclassical limit of such systems both more realistic and simpler in many respects than the more familiar quasiclassical limit for closed systems. A linearized version of this theory leads to the correct classical dynamics in...
Quantum systems, channels, information. A mathematical introduction
Holevo, Alexander S.
2012-07-01
The subject of this book is theory of quantum system presented from information science perspective. The central role is played by the concept of quantum channel and its entropic and information characteristics. Quantum information theory gives a key to understanding elusive phenomena of quantum world and provides a background for development of experimental techniques that enable measuring and manipulation of individual quantum systems. This is important for the new efficient applications such as quantum computing, communication and cryptography. Research in the field of quantum informatics, including quantum information theory, is in progress in leading scientific centers throughout the world. This book gives an accessible, albeit mathematically rigorous and self-contained introduction to quantum information theory, starting from primary structures and leading to fundamental results and to exiting open problems.
Quantum systems, channels, information. A mathematical introduction
The subject of this book is theory of quantum system presented from information science perspective. The central role is played by the concept of quantum channel and its entropic and information characteristics. Quantum information theory gives a key to understanding elusive phenomena of quantum world and provides a background for development of experimental techniques that enable measuring and manipulation of individual quantum systems. This is important for the new efficient applications such as quantum computing, communication and cryptography. Research in the field of quantum informatics, including quantum information theory, is in progress in leading scientific centers throughout the world. This book gives an accessible, albeit mathematically rigorous and self-contained introduction to quantum information theory, starting from primary structures and leading to fundamental results and to exiting open problems.
Note on entropies for quantum dynamical systems.
Watanabe, Noboru
2016-05-28
Quantum entropy and channel are fundamental concepts for quantum information theory progressed recently in various directions. We will review the fundamental aspects of mean entropy and mean mutual entropy and calculate them for open system dynamics. PMID:27091165
Optimal Control for Open Quantum Systems: Qubits and Quantum Gates
Roloff, Robert; Pötz, Walter
2009-01-01
This article provides a review of recent developments in the formulation and execution of optimal control strategies for the dynamics of quantum systems. A brief introduction to the concept of optimal control, the dynamics of of open quantum systems, and quantum information processing is followed by a presentation of recent developments regarding the two main tasks in this context: state-specific and state-independent optimal control. For the former, we present an extension of conventional theory (Pontryagin's principle) to quantum systems which undergo a non-Markovian time-evolution. Owing to its importance for the realization of quantum information processing, the main body of the review, however, is devoted to state-independent optimal control. Here, we address three different approaches: an approach which treats dissipative effects from the environment in lowest-order perturbation theory, a general method based on the time--evolution superoperator concept, as well as one based on the Kraus representation ...
Quantum-information processing in disordered and complex quantum systems
We study quantum information processing in complex disordered many body systems that can be implemented by using lattices of ultracold atomic gases and trapped ions. We demonstrate, first in the short range case, the generation of entanglement and the local realization of quantum gates in a disordered magnetic model describing a quantum spin glass. We show that in this case it is possible to achieve fidelities of quantum gates higher than in the classical case. Complex systems with long range interactions, such as ions chains or dipolar atomic gases, can be used to model neural network Hamiltonians. For such systems, where both long range interactions and disorder appear, it is possible to generate long range bipartite entanglement. We provide an efficient analytical method to calculate the time evolution of a given initial state, which in turn allows us to calculate its quantum correlations
Maxwell's demons in multipartite quantum correlated systems
Braga, Helena C.; Rulli, Clodoaldo C.; de Oliveira, Thiago R.; Sarandy, Marcelo S.
2014-10-01
We investigate the extraction of thermodynamic work by a Maxwell's demon in a multipartite quantum correlated system. We begin by adopting the standard model of a Maxwell's demon as a Turing machine, either in a classical or quantum setup depending on its ability to implement classical or quantum conditional dynamics. Then, for an n -partite system (A1,A2,⋯,An) , we introduce a protocol of work extraction that bounds the advantage of the quantum demon over its classical counterpart through the amount of multipartite quantum correlation present in the system, as measured by a thermal version of the global quantum discord. This result is illustrated for an arbitrary n -partite pure state of qubits with Schmidt decomposition, where it is shown that the thermal global quantum discord exactly quantifies the quantum advantage. Moreover, we also consider the work extraction via mixed multipartite states, where examples of tight upper bounds can be obtained.
Quantum state engineering in hybrid open quantum systems
Joshi, Chaitanya; Larson, Jonas; Spiller, Timothy P.
2016-04-01
We investigate a possibility to generate nonclassical states in light-matter coupled noisy quantum systems, namely, the anisotropic Rabi and Dicke models. In these hybrid quantum systems, a competing influence of coherent internal dynamics and environment-induced dissipation drives the system into nonequilibrium steady states (NESSs). Explicitly, for the anisotropic Rabi model, the steady state is given by an incoherent mixture of two states of opposite parities, but as each parity state displays light-matter entanglement, we also find that the full state is entangled. Furthermore, as a natural extension of the anisotropic Rabi model to an infinite spin subsystem, we next explored the NESS of the anisotropic Dicke model. The NESS of this linearized Dicke model is also an inseparable state of light and matter. With an aim to enrich the dynamics beyond the sustainable entanglement found for the NESS of these hybrid quantum systems, we also propose to combine an all-optical feedback strategy for quantum state protection and for establishing quantum control in these systems. Our present work further elucidates the relevance of such hybrid open quantum systems for potential applications in quantum architectures.
Could nanostructure be unspeakable quantum system?
Aristov, V V
2010-01-01
Heisenberg, Bohr and others were forced to renounce on the description of the objective reality as the aim of physics because of the paradoxical quantum phenomena observed on the atomic level. The contemporary quantum mechanics created on the base of their positivism point of view must divide the world into speakable apparatus which amplifies microscopic events to macroscopic consequences and unspeakable quantum system. Examination of the quantum phenomena corroborates the confidence expressed by creators of quantum theory that the renunciation of realism should not apply on our everyday macroscopic world. Nanostructures may be considered for the present as a boundary of realistic description for all phenomena including the quantum one.
Quantum Friction: Cooling Quantum Systems with Unitary Time Evolution
Bulgac, Aurel; Roche, Kenneth J; Wlaz?owski, Gabriel
2013-01-01
We introduce a type of quantum dissipation -- local quantum friction -- by adding to the Hamiltonian a local potential that breaks time-reversal invariance so as to cool the system. Unlike the Kossakowski-Lindblad master equation, local quantum friction directly effects unitary evolution of the wavefunctions rather than the density matrix: it may thus be used to cool fermionic many-body systems with thousands of wavefunctions that must remain orthogonal. In addition to providing an efficient way to simulate quantum dissipation and non-equilibrium dynamics, local quantum friction coupled with adiabatic state preparation significantly speeds up many-body simulations, making the solution of the time-dependent Schr\\"odinger equation significantly simpler than the solution of its stationary counterpart.
Entangling transformations in composite finite quantum systems
Vourdas, A [Department of Computing, University of Bradford, Bradford BD7 1DP (United Kingdom)
2003-12-01
Phase space methods are applied in the context of finite quantum systems. 'Galois quantum systems' (with a dimension which is a power of a prime number) are considered, and symplectic Sp(2,Z(d)) transformations are studied. Composite systems comprising two finite quantum systems are also considered. Symplectic Sp(4,Z(d)) transformations are classified into local and entangling ones and the necessary matrices which perform such transformations are calculated numerically.
Entangling transformations in composite finite quantum systems
Phase space methods are applied in the context of finite quantum systems. 'Galois quantum systems' (with a dimension which is a power of a prime number) are considered, and symplectic Sp(2,Z(d)) transformations are studied. Composite systems comprising two finite quantum systems are also considered. Symplectic Sp(4,Z(d)) transformations are classified into local and entangling ones and the necessary matrices which perform such transformations are calculated numerically
Entangling transformations in composite finite quantum systems
Vourdas, A.
2003-12-01
Phase space methods are applied in the context of finite quantum systems. 'Galois quantum systems' (with a dimension which is a power of a prime number) are considered, and symplectic Sp(2,{\\cal Z}(d)) transformations are studied. Composite systems comprising two finite quantum systems are also considered. Symplectic Sp(4,{\\cal Z}(d)) transformations are classified into local and entangling ones and the necessary matrices which perform such transformations are calculated numerically.
Could nanostructure be unspeakable quantum system?
Aristov, V. V.; Nikulov, A. V.
2010-01-01
Heisenberg, Bohr and others were forced to renounce on the description of the objective reality as the aim of physics because of the paradoxical quantum phenomena observed on the atomic level. The contemporary quantum mechanics created on the base of their positivism point of view must divide the world into speakable apparatus which amplifies microscopic events to macroscopic consequences and unspeakable quantum system. Examination of the quantum phenomena corroborates the confidence expresse...
Measures of macroscopicity for quantum spin systems
We investigate the notion of macroscopicity in the case of quantum spin systems and provide two main results. Firstly, we motivate the quantum Fisher information as a measure of the macroscopicity of quantum states. Secondly, we make a comparison with the existing literature on this topic. We report on a hierarchy among the measures and we conclude that one should carefully distinguish between macroscopic quantum states and macroscopic superpositions, which is a strict subclass of the former. (paper)
Quantum probabilities and entanglement for multimode quantum systems
Quantum probabilities are defined for several important physical cases characterizing measurements with multimode quantum systems. These are the probabilities for operationally testable measurements, for operationally uncertain measurements, and for entangled composite events. The role of the prospect and state entanglement is emphasized. Numerical modeling is presented for a two-mode Bose-condensed system of trapped atoms. The interference factor is calculated by invoking the channel-state duality.
Thermodynamics of Weakly Measured Quantum Systems
Alonso, Jose Joaquin; Lutz, Eric; Romito, Alessandro
2016-02-01
We consider continuously monitored quantum systems and introduce definitions of work and heat along individual quantum trajectories that are valid for coherent superposition of energy eigenstates. We use these quantities to extend the first and second laws of stochastic thermodynamics to the quantum domain. We illustrate our results with the case of a weakly measured driven two-level system and show how to distinguish between quantum work and heat contributions. We finally employ quantum feedback control to suppress detector backaction and determine the work statistics.
Classical and quantum dissipative systems
Razavy, Mohsen
2006-01-01
This book discusses issues associated with the quantum mechanical formulation of dissipative systems. It begins with an introductory review of phenomenological damping forces, and the construction of the Lagrangian and Hamiltonian for the damped motion. It is shown, in addition to these methods, that classical dissipative forces can also be derived from solvable many-body problems. A detailed discussion of these derived forces and their dependence on dynamical variables is also presented. The second part of this book investigates the use of classical formulation in the quantization of dynamica
Quantum Heat Engine With Multi-Level Quantum Systems
Quan, H T; Sun, C P
2005-01-01
By reformulating the first law of thermodynamics in the fashion of quantum-mechanical operators on the parameter manifold, we propose a universal class of quantum heat engines (QHE) using the multi-level quantum system as the working substance. We obtain a general expression of work for the thermodynamic cycle with two thermodynamic adiabatic processes, which are microscopically quantum adiabatic processes. We also classify the conditions for a 3-level QHE to extract positive work from a heat bath. Our result is counter-intuitively different from that of a 2-level system. As a more realistic illustration, a 3-level atom system with dark state configuration manipulated by classical light is used to demonstrate our central idea.
Quantum mechanics in complex systems
Hoehn, Ross Douglas
This document should be considered in its separation; there are three distinct topics contained within and three distinct chapters within the body of works. In a similar fashion, this abstract should be considered in three parts. Firstly, we explored the existence of multiply-charged atomic ions by having developed a new set of dimensional scaling equations as well as a series of relativistic augmentations to the standard dimensional scaling procedure and to the self-consistent field calculations. Secondly, we propose a novel method of predicting drug efficacy in hopes to facilitate the discovery of new small molecule therapeutics by modeling the agonist-protein system as being similar to the process of Inelastic Electron Tunneling Spectroscopy. Finally, we facilitate the instruction in basic quantum mechanical topics through the use of quantum games; this method of approach allows for the generation of exercises with the intent of conveying the fundamental concepts within a first year quantum mechanics classroom. Furthermore, no to be mentioned within the body of the text, yet presented in appendix form, certain works modeling the proliferation of cells types within the confines of man-made lattices for the purpose of facilitating artificial vascular transplants. In Chapter 2, we present a theoretical framework which describes multiply-charged atomic ions, their stability within super-intense laser fields, also lay corrections to the systems due to relativistic effects. Dimensional scaling calculations with relativistic corrections for systems: H, H-, H 2-, He, He-, He2-, He3- within super-intense laser fields were completed. Also completed were three-dimensional self consistent field calculations to verify the dimensionally scaled quantities. With the aforementioned methods the system's ability to stably bind 'additional' electrons through the development of multiple isolated regions of high potential energy leading to nodes of high electron density is shown. These nodes are spaced far enough from each other to minimized the electronic repulsion of the electrons, while still providing adequate enough attraction so as to bind the excess elections into orbitals. We have found that even with relativistic considerations these species are stably bound within the field. It was also found that performing the dimensional scaling calculations for systems within the confines of laser fields to be a much simpler and more cost-effective method than the supporting D=3 SCF method. The dimensional scaling method is general and can be extended to include relativistic corrections to describe the stability of simple molecular systems in super-intense laser fields. Chapter 3, we delineate the model, and aspects therein, of inelastic electron tunneling and map this model to the protein environment. G protein-coupled receptors (GPCRs) constitute a large family of receptors that sense molecules outside of a cell and activate signal transduction pathways inside the cell. Modeling how an agonist activates such a receptor is important for understanding a wide variety of physiological processes and it is of tremendous value for pharmacology and drug design. Inelastic electron tunneling spectroscopy (IETS) has been proposed as the mechanism by which olfactory GPCRs are activated by an encapsulated agonist. In this note we apply this notion to GPCRs within the mammalian nervous system using ab initio quantum chemical modeling. We found that non-endogenous agonists of the serotonin receptor share a singular IET spectral aspect both amongst each other and with the serotonin molecule: a peak that scales in intensity with the known agonist activities. We propose an experiential validation of this model by utilizing lysergic acid dimethylamide (DAM-57), an ergot derivative, and its isotopologues in which hydrogen atoms are replaced by deuterium. If validated our theory may provide new avenues for guided drug design and better in silico prediction of efficacies. Our final chapter, explores methods which may be explored to assist in the early instruction in quantum mechanics. The learning of quantum mechanics is contingent upon an understanding of the physical significance of the mathematics that one must perform. Concepts such as normalization, superposition, interference, probability amplitude and entanglement can prove challenging for the beginning student. This paper outlines several class exercises that use a non-classical version of tic-tac-toe to instruct several topics in an undergraduate quantum mechanics course. Quantum tic-tac-toe (QTTT) is a quantum analogue of classical tic-tac-toe (CTTT) benefiting from the use of superposition in movement, qualitative (and later quantitative) displays of entanglement and state collapse due to observation. QTTT can be used for the benefit of the students understanding in several other topics with the aid of proper discussion.
Quantum Open System Theory: Bipartite Aspects
Yu, Ting; Eberly, J. H.
2006-01-01
We demonstrate in straightforward calculations that even under ideally weak noise the relaxation of bipartite open quantum systems contains elements not previously encountered in quantum noise physics. While additivity of decay rates is known to be generic for decoherence of a single system, we demonstrate that it breaks down for bipartite coherence of even the simplest composite systems.
Symplectic transformations and quantum tomography in finite quantum systems
Quantum systems where the position and momentum are in the ring Zd (d is an odd integer) are considered. Symplectic transformations are studied, and the order of Sp(2,Zd) is calculated. Quantum tomography is also discussed. It is shown that measurements (used in the inverse Radon transform) need to be made on J2(d) lines (where J2(d) is the Jordan totient function). (fast track communication)
Symplectic transformations and quantum tomography in finite quantum systems
Vourdas, A [Department of Computing, University of Bradford, Bradford BD7 1DP (United Kingdom); Banderier, C, E-mail: A.Vourdas@Braford.ac.u [Laboratoire d' informatique de Paris-Nord, UMR CNRS 7030, Universite Paris XIII, Villetaneuse (France)
2010-01-29
Quantum systems where the position and momentum are in the ring Z{sub d} (d is an odd integer) are considered. Symplectic transformations are studied, and the order of Sp(2,Z{sub d}) is calculated. Quantum tomography is also discussed. It is shown that measurements (used in the inverse Radon transform) need to be made on J{sub 2}(d) lines (where J{sub 2}(d) is the Jordan totient function). (fast track communication)
Hybrid quantum systems of atoms and ions
In recent years, ultracold atoms have emerged as an exceptionally controllable experimental system to investigate fundamental physics, ranging from quantum information science to simulations of condensed matter models. Here we go one step further and explore how cold atoms can be combined with other quantum systems to create new quantum hybrids with tailored properties. Coupling atomic quantum many-body states to an independently controllable single-particle gives access to a wealth of novel physics and to completely new detection and manipulation techniques. We report on recent experiments in which we have for the first time deterministically placed a single ion into an atomic Bose Einstein condensate. A trapped ion, which currently constitutes the most pristine single particle quantum system, can be observed and manipulated at the single particle level. In this single-particle/many-body composite quantum system we show sympathetic cooling of the ion and observe chemical reactions of single particles in situ.
Hybrid quantum systems of atoms and ions
Zipkes, Christoph; Palzer, Stefan; Sias, Carlo; Khl, Michael
2010-01-01
In recent years, ultracold atoms have emerged as an exceptionally controllable experimental system to investigate fundamental physics, ranging from quantum information science to simulations of condensed matter models. Here we go one step further and explore how cold atoms can be combined with other quantum systems to create new quantum hybrids with tailored properties. Coupling atomic quantum many-body states to an independently controllable single-particle gives access to a wealth of novel physics and to completely new detection and manipulation techniques. We report on recent experiments in which we have for the first time deterministically placed a single ion into an atomic Bose Einstein condensate. A trapped ion, which currently constitutes the most pristine single particle quantum system, can be observed and manipulated at the single particle level. In this single-particle/many-body composite quantum system we show sympathetic cooling of the ion and observe chemical reactions of single particles in situ...
Controlling quantum critical dynamics of isolated systems
Del Campo, A.; K. Sengupta
2014-01-01
Controlling the non adiabatic dynamics of isolated quantum systems driven through a critical point is of interest in a variety of fields ranging from quantum simulation to finite-time thermodynamics. We briefly review the different methods for designing protocols which minimize excitation (defect) production in a closed quantum critical system driven out of equilibrium. We chart out the role of specific driving schemes for this procedure, point out their experimental relevance, and discuss th...
Robust observer for uncertain linear quantum systems
Yamamoto, Naoki
2006-01-01
In the theory of quantum dynamical filtering, one of the biggest issues is that the underlying system dynamics represented by a quantum stochastic differential equation must be known exactly in order that the corresponding filter provides an optimal performance; however, this assumption is generally unrealistic. Therefore, in this paper, we consider a class of linear quantum systems subjected to time-varying norm-bounded parametric uncertainties and then propose a robust observer such that th...
On the geometry of quantum constrained systems
Corichi, Alejandro
2008-01-01
The use of geometric methods has proved useful in the hamiltonian description of classical constrained systems. In this note we provide the first steps toward the description of the geometry of quantum constrained systems. We make use of the geometric formulation of quantum theory in which unitary transformations (including time evolution) can be seen, just as in the classical case, as finite canonical transformations on the quantum state space. We compare from this perspective the classical ...
Tailoring superradiance to design artificial quantum systems
Longo, Paolo; Keitel, Christoph H.; Evers, Jörg
2016-01-01
Cooperative phenomena arising due to the coupling of individual atoms via the radiation field are a cornerstone of modern quantum and optical physics. Recent experiments on x-ray quantum optics added a new twist to this line of research by exploiting superradiance in order to construct artificial quantum systems. However, so far, systematic approaches to deliberately design superradiance properties are lacking, impeding the desired implementation of more advanced quantum optical schemes. Here, we develop an analytical framework for the engineering of single-photon superradiance in extended media applicable across the entire electromagnetic spectrum, and show how it can be used to tailor the properties of an artificial quantum system. This “reverse engineering” of superradiance not only provides an avenue towards non-linear and quantum mechanical phenomena at x-ray energies, but also leads to a unified view on and a better understanding of superradiance across different physical systems. PMID:27009604
Tailoring superradiance to design artificial quantum systems
Longo, Paolo; Keitel, Christoph H.; Evers, Jörg
2016-03-01
Cooperative phenomena arising due to the coupling of individual atoms via the radiation field are a cornerstone of modern quantum and optical physics. Recent experiments on x-ray quantum optics added a new twist to this line of research by exploiting superradiance in order to construct artificial quantum systems. However, so far, systematic approaches to deliberately design superradiance properties are lacking, impeding the desired implementation of more advanced quantum optical schemes. Here, we develop an analytical framework for the engineering of single-photon superradiance in extended media applicable across the entire electromagnetic spectrum, and show how it can be used to tailor the properties of an artificial quantum system. This “reverse engineering” of superradiance not only provides an avenue towards non-linear and quantum mechanical phenomena at x-ray energies, but also leads to a unified view on and a better understanding of superradiance across different physical systems.
Tailoring superradiance to design artificial quantum systems.
Longo, Paolo; Keitel, Christoph H; Evers, Jörg
2016-01-01
Cooperative phenomena arising due to the coupling of individual atoms via the radiation field are a cornerstone of modern quantum and optical physics. Recent experiments on x-ray quantum optics added a new twist to this line of research by exploiting superradiance in order to construct artificial quantum systems. However, so far, systematic approaches to deliberately design superradiance properties are lacking, impeding the desired implementation of more advanced quantum optical schemes. Here, we develop an analytical framework for the engineering of single-photon superradiance in extended media applicable across the entire electromagnetic spectrum, and show how it can be used to tailor the properties of an artificial quantum system. This "reverse engineering" of superradiance not only provides an avenue towards non-linear and quantum mechanical phenomena at x-ray energies, but also leads to a unified view on and a better understanding of superradiance across different physical systems. PMID:27009604
Dynamics of a multipartite system undergoing matter-state-photon conversions
We examine the entanglement dynamics of two initially entangled qubits coupled to independent photon reservoirs and undergoing continuous matter-state-photon population transitions. We represent the decay and replenishment of matter-based bit states via photons by time-dependent generalized conversion functions. For the specific case of a sinusoidal function, we show that sudden death events in qubit-qubit entanglement anti-correlate (correlate) exactly with sudden birth events in photon-photon entanglement for the symmetric (anti-symmetric) mode of quantum conversions. We show the invariance in dynamics of all possible bipartite concurrences for various configurations of qubit-reservoir systems and highlight its crucial role in identifying a global concurrence of the multipartite system. We study the coherently driven quantum dot-cavity system as a specific application of our approach, including an analysis of evolution of its Meyer-Wallach measure with time.
Geometric Phase in Open Quantum Systems
Banerjee, S; Banerjee, Subhashish
2006-01-01
Geometric phase of an open two-level quantum system with a squeezed, thermal environment is studied for various types of system-environment interactions, both non-dissipative and dissipative. In the former type, we consider quantum non-demolition interaction with a bath of harmonic oscillators as well as of that of two-level systems. In the latter type, we consider the system interacting with a bath of harmonic oscillators in the weak Born-Markov approximation, and further, a simplified Jaynes-Cummings model in a vacuum bath. Our results extend features of geometric phase in open systems reported in the literature to include effects due to squeezing. The Kraus operator representation is employed to connect the open-system effects to quantum noise processes familiar from quantum information theory. This study has some implications for a practical implementation of geometric quantum computation.
Linear response theory for quantum open systems
J. H. Wei; Yan, YiJing
2011-01-01
Basing on the theory of Feynman's influence functional and its hierarchical equations of motion, we develop a linear response theory for quantum open systems. Our theory provides an effective way to calculate dynamical observables of a quantum open system at its steady-state, which can be applied to various fields of non-equilibrium condensed matter physics.
Classical Equations for Quantum Systems
Gell-Mann, Murray; Gell-Mann, Murray; Hartle, James B.
1993-01-01
The origin of the phenomenological deterministic laws that approximately govern the quasiclassical domain of familiar experience is considered in the context of the quantum mechanics of closed systems such as the universe as a whole. We investigate the requirements for coarse grainings to yield decoherent sets of histories that are quasiclassical, i.e. such that the individual histories obey, with high probability, effective classical equations of motion interrupted continually by small fluctuations and occasionally by large ones. We discuss these requirements generally but study them specifically for coarse grainings of the type that follows a distinguished subset of a complete set of variables while ignoring the rest. More coarse graining is needed to achieve decoherence than would be suggested by naive arguments based on the uncertainty principle. Even coarser graining is required in the distinguished variables for them to have the necessary inertia to approach classical predictability in the presence of t...
Quantum information theory with Gaussian systems
This thesis applies ideas and concepts from quantum information theory to systems of continuous-variables such as the quantum harmonic oscillator. The focus is on three topics: the cloning of coherent states, Gaussian quantum cellular automata and Gaussian private channels. Cloning was investigated both for finite-dimensional and for continuous-variable systems. We construct a private quantum channel for the sequential encryption of coherent states with a classical key, where the key elements have finite precision. For the case of independent one-mode input states, we explicitly estimate this precision, i.e. the number of key bits needed per input state, in terms of these parameters. (orig.)
Quantum information theory with Gaussian systems
Krueger, O.
2006-04-06
This thesis applies ideas and concepts from quantum information theory to systems of continuous-variables such as the quantum harmonic oscillator. The focus is on three topics: the cloning of coherent states, Gaussian quantum cellular automata and Gaussian private channels. Cloning was investigated both for finite-dimensional and for continuous-variable systems. We construct a private quantum channel for the sequential encryption of coherent states with a classical key, where the key elements have finite precision. For the case of independent one-mode input states, we explicitly estimate this precision, i.e. the number of key bits needed per input state, in terms of these parameters. (orig.)
Measuring quantum systems with tunnel junctions
Full text: We present a formalism that allows to describe a quantum system modulating the transmission of a tunnel junction. The tunnel junction acts as an environment for the quantum system. Contrary to the conventional approach to open quantum systems we retain a degree of freedom of the environment, the charge passed through the junction, after averaging over the bath degrees of freedom, employing a projection operator technique. The resulting object characterizing the joint dynamics of the system and the charge is the charge specific density matrix. We derive a master equation describing the time evolution of the charge specific density matrix. We consider two examples of quantum systems coupled to the junction: a spin and a harmonic oscillator. In the spin case we are able to analyze a quantum measurement process in detail. For the oscillator we investigate the noise in the tunnel junction induced by the coupling. (author)
Dissipations in coupled quantum systems
We investigate the dynamics of a composite quantum system, comprised of coupled subsystems, of which only one is significantly interacting with the environment. The validity of the conventional ad hoc approach--assuming that relaxation terms can be extracted directly from the master equation of the subsystem interacting with the reservoir--was examined. We derived the equation of motion for the composite system's reduced density matrix--applying only the factorization approximation, but not the conventional sequence of Markoff, coarse grain, and secular approximations. From our analysis, we concluded that the conventional ad hoc approach is applicable to zero-temperature reservoir, but fails for finite temperatures. It is further shown that at finite temperatures, the standard procedure does not even yield a master equation for the composite system, and its dynamics has to be studied by the equations of motion which are developed here. For demonstration we considered a system of a three-level atom, the two excited states are coupled to each other, and only one of them communicates with the ground state via a radiation reservoir
Coherent Dynamics of Complex Quantum Systems
Akulin, Vladimir M
2006-01-01
A large number of modern problems in physics, chemistry, and quantum electronics require a consideration of population dynamics in complex multilevel quantum systems. The purpose of this book is to provide a systematic treatment of these questions and to present a number of exactly solvable problems. It considers the different dynamical problems frequently encountered in different areas of physics from the same perspective, based mainly on the fundamental ideas of group theory and on the idea of ensemble average. Also treated are concepts of complete quantum control and correction of decoherence induced errors that are complementary to the idea of ensemble average. "Coherent Dynamics of Complex Quantum Systems" is aimed at senior-level undergraduate students in the areas of Atomic, Molecular, and Laser Physics, Physical Chemistry, Quantum Optics and Quantum Informatics. It should help them put particular problems in these fields into a broader scientific context and thereby take advantage of the well-elabora...
Understanding electronic systems in semiconductor quantum dots
Ciftja, Orion
2013-11-01
Systems of confined electrons are found everywhere in nature in the form of atoms where the orbiting electrons are confined by the Coulomb attraction of the nucleus. Advancement of nanotechnology has, however, provided us with an alternative way to confine electrons by using artificial confining potentials. A typical structure of this nature is the quantum dot, a nanoscale system which consists of few confined electrons. There are many types of quantum dots ranging from self-assembled to miniaturized semiconductor quantum dots. In this work we are interested in electrostatically confined semiconductor quantum dot systems where the electrostatic confining potential that traps the electrons is generated by external electrodes, doping, strain or other factors. A large number of semiconductor quantum dots of this type are fabricated by applying lithographically patterned gate electrodes or by etching on two-dimensional electron gases in semiconductor heterostructures. Because of this, the whole structure can be treated as a confined two-dimensional electron system. Quantum confinement profoundly affects the way in which electrons interact with each other, and external parameters such as a magnetic field. Since a magnetic field affects both the orbital and the spin motion of the electrons, the interplay between quantum confinement, electron-electron correlation effects and the magnetic field gives rise to very interesting physical phenomena. Thus, confined systems of electrons in a semiconductor quantum dot represent a unique opportunity to study fundamental quantum theories in a controllable atomic-like setup. In this work, we describe some common theoretical models which are used to study confined systems of electrons in a two-dimensional semiconductor quantum dot. The main emphasis of the work is to draw attention to important physical phenomena that arise in confined two-dimensional electron systems under various quantum regimes.
Transmission and System Control in Quantum Cryptography
Anand Sharma,; Vibha Ojha; Ramesh Chandra Belwal; Gaurav Agarwal
2011-01-01
Quantum cryptography provides security using thelaws of quantum mechanics. Currently, several typesof protocols of quantum key distribution (QKD) havebeen established. Some QKD protocols have beencertified by proofs of unconditional security. QKDprotocols have been confirmed to be resistant to anypossible attack. Along with the progress in keytransmission and post processing, the system controlneeds to be integrated with some steps for the QKD.No future technology can break such security. The...
Non-perturbative description of quantum systems
Feranchuk, Ilya; Le, Van-Hoang; Ulyanenkov, Alexander
2015-01-01
This bookintroduces systematically the operator method for the solution of the Schrdinger equation.This method permits to describe the states of quantum systems in the entire range of parameters of Hamiltonian with a predefined accuracy. The operator method is unique comparedwith other non-perturbative methods due to its ability to deliver in zeroth approximation the uniformly suitable estimate for both ground and excited states of quantum system. The method has been generalized for the application to quantum statistics and quantum field theory. In this book, the numerous applications of operator method for various physical systems are demonstrated. Simple models are used to illustrate the basic principles of the method which are further used for the solution of complex problems of quantum theory for many-particle systems. The results obtained are supplemented by numerical calculations, presented as tables and figures.
Mixing and entropy increase in quantum systems
This paper attempts to explain the key feature of deterministic chaotic classical systems and how they can be translated to quantum systems. To do so we develop the appropriate algebraic language for the non-specialist. 22 refs. (Author)
Macroscopic quantum effects in nanomechanical systems
Werner, P
2003-01-01
We investigate quantum effects in the mechanical properties of elastic beams on the nanoscale. Transverse quantum and thermal fluctuations and the nonlinear excitation energies are calculated for beams compressed in longitudinal direction. Near the Euler instability, the system is described by a one dimensional Ginzburg-Landau model where the order parameter is the amplitude of the buckling mode. We show that in single wall carbon nanotubes the crossover from thermal activation to quantum tunnelling is accessible and discuss the possibility of observing macroscopic quantum coherence in nanobeams near the critical strain.
Quantum Dynamical Entropy of Spin Systems
Miyadera, Takayuki; Ohya, Masanori
2003-01-01
We investigate a quantum dynamical entropy of one-dimesional quantum spin systems. We show that the dynamical entropy is bounded from above by a quantity which is related with group velocity determined by the interaction and mean entropy of the state.
Limit cycles in quantum systems
In this thesis we investigate Limit Cycles in Quantum Systems. Limit cycles are a renormalization group (RG) topology. When degrees of freedom are integrated out, the coupling constants flow periodically in a closed curve. The presence of limit cycles is restricted by the necessary condition of discrete scale invariance. A signature of discrete scale invariance and limit cycles is log-periodic behavior. The first part of this thesis is concerned with the study of limit cycles with the similarity renormalization group (SRG). Limit cycles are mainly investigated within conventional renormalization group frameworks, where degrees of freedom, which are larger than a given cutoff, are integrated out. In contrast, in the SRG potentials are unitarily transformed and thereby obtain a band-diagonal structure. The width of the band structure can be regarded as an effective cutoff. We investigate the appearance of limit cycles in the SRG evolution. Our aim is to extract signatures as well as the scaling factor of the limit cycle. We consider the 1/R2-potential in a two-body system and a three-body system with large scattering lengths. Both systems display a limit cycle. Besides the frequently used kinetic energy generator we apply the exponential and the inverse generator. In the second part of this thesis, Limit Cycles at Finite Density, we examine the pole structure of the scattering amplitude for distinguishable fermions at zero temperature in the medium. Unequal masses and a filled Fermi sphere for each fermion species are considered. We focus on negative scattering lengths and the unitary limit. The properties of the three-body spectrum in the medium and implications for the phase structure of ultracold Fermi gases are discussed.
Sliding mode control of quantum systems
This paper proposes a new robust control method for quantum systems with uncertainties involving sliding mode control (SMC). SMC is a widely used approach in classical control theory and industrial applications. We show that SMC is also a useful method for robust control of quantum systems. In this paper, we define two specific classes of sliding modes (i.e. eigenstates and state subspaces) and propose two novel methods combining unitary control and periodic projective measurements for the design of quantum SMC systems. Two examples including a two-level system and a three-level system are presented to demonstrate the proposed SMC method. One of the main features of the proposed method is that the designed control laws can guarantee the desired control performance in the presence of uncertainties in the system Hamiltonian. This SMC approach provides a useful control theoretic tool for robust quantum information processing with uncertainties.
Finite Quantum Systems and Their Applications to Quantum Information Processing
Vourdas, A.
2003-07-01
Quantum mechanics for finite systems is briefly reviewed and used in the context of quantum information processing. In an angular momentum Hilbert space, the displacement operators play the role of SU(2j + 1) generators. Unitary transformations are expressed as a finite sum of the displacement operators with the Weyl function as coefficients. A factorization of large qudits in terms of smaller qudits is studied. All unitary transformations on large qudits can be performed through appropriate unitary transformations on the smaller qudits. Coding with these states is also considered. A concatenated code that introduces redundancy in both amplitude and phase, is studied.
Avoiding irreversible dynamics in quantum systems
Karasik, Raisa Iosifovna
2009-10-01
Devices that exploit laws of quantum physics offer revolutionary advances in computation and communication. However, building such devices presents an enormous challenge, since it would require technologies that go far beyond current capabilities. One of the main obstacles to building a quantum computer and devices needed for quantum communication is decoherence or noise that originates from the interaction between a quantum system and its environment, and which leads to the destruction of the fragile quantum information. Encoding into decoherence-free subspaces (DFS) provides an important strategy for combating decoherence effects in quantum systems and constitutes the focus of my dissertation. The theory of DFS relies on the existence of certain symmetries in the decoherence process, which allow some states of a quantum system to be completely decoupled from the environment and thus to experience no decoherence. In this thesis I describe various approaches to DFS that are developed in the current literature. Although the general idea behind various approaches to DFS is the same, I show that different mathematical definitions of DFS actually have different physical meaning. I provide a rigorous definition of DFS for every approach, explaining its physical meaning and relation to other definitions. I also examine the theory of DFS for Markovian systems. These are systems for which the environment has no memory, i.e., any change in the environment affects the quantum system instantaneously. Examples of such systems include many systems in quantum optics that have been proposed for implementation of a quantum computer, such as atomic and molecular gases, trapped ions, and quantum dots. Here I develop a rigorous theory that provides necessary and sufficient conditions for the existence of DFS. This theory allows us to identify a special new class of DFS that was not known before. Under particular circumstances, dynamics of a quantum system can connive together with the interactions between the system and its environment in a special way to reduce decoherence. This property is used to discover new DFS that rely on rather counterintuitive phenomenon, which I call an "incoherent generation of coherences." I also provide examples of physical systems that support such states. These DFS can be used to suppress & coherence, but may not be sufficient for performing full quantum computation. I also explore the possibility of physically generating the DFS that are useful for quantum computation. For quantum computation we need to preserve at least two quantum states to encode the quantum analogue of classical bits. Here I aim to generate DFS in a system composed from a large collection of atoms or molecules and I need to determine how one should position atoms or molecules in 3D space so that the overall system possesses a DFS with at least two states (i.e., non-trivial DFS). I show that for many Markovian systems, non-trivial DFS can exist only when particles are located in exactly the same position in space. This, of course, is not possible in the real world. For these systems, I also show that states in DFS are states with infinite lifetime. However, for all practical applications we just need long-lived states. Thus in reality, we do just need to bring quantum particles close together to generate an imperfect DFS, i.e. a collection of long-lived states. This can be achieved, for example, for atoms within a single molecule.
Path integrals for dimerized quantum spin systems
Foussats, Adriana; Greco, Andres; Muramatsu, Alejandro
2010-01-01
Dimerized quantum spin systems may appear under several circumstances, e.g\\ by a modulation of the antiferromagnetic exchange coupling in space, or in frustrated quantum antiferromagnets. In general, such systems display a quantum phase transition to a N\\'eel state as a function of a suitable coupling constant. We present here two path-integral formulations appropriate for spin $S=1/2$ dimerized systems. The first one deals with a description of the dimers degrees of freedom in an SO(4) manif...
Level shift operators for open quantum systems
Merkli, Marco
2006-01-01
Level shift operators describe the second order displacement of eigenvalues under perturbation. They play a central role in resonance theory and ergodic theory of open quantum systems at positive temperatures. We exhibit intrinsic properties of level shift operators, properties which stem from the structure of open quantum systems at positive temperatures and which are common to all such systems. They determine the geometry of resonances bifurcating from eigenvalues of positive temperature Ha...
Quantum statistics of charged particle systems
The monograph covers a certain part of the hitherto available results on charged particle systems under the following headings: introduction, quantum statistics of many-particle systems, application of the Green's function to Coulomb systems, equilibrium properties in classical and quasiclassical approximation, quantum-statistical calculations of equilibrium properties, transport properties, and Green's function approach to optical properties. A subject index is included. 555 references, 63 figures, 10 tables
Quantum Markov Semigroups (Product Systems and Subordination)
Muhly, Paul S.; Solel, Baruch
2005-01-01
We show that if a product system comes from a quantum Markov semigroup, then it carries a natural Borel structure with respect to which the semigroup may be realized in terms of a measurable representation. We show, too, that the dual product system of a Borel product system also carries a natural Borel structure. We apply our analysis to study the order interval consisting of all quantum Markov semigroups that are subordinate to a given one.
Intrinsic and extrinsic properties of quantum systems
Hajicek, P
2008-01-01
The paper attempts to convince that the orthodox interpretation of quantum mechanics does not contradict philosophical realism by throwing light onto certain properties of quantum systems that seem to have escaped attention as yet. The exposition starts with the philosophical notions of realism. Then, the quantum mechanics as it is usually taught is demoted to a mere part of the theory called phenomenology of observations, and the common impression about its contradiction to realism is explained. The main idea of the paper, the physical notion of intrinsic properties, is introduced and many examples thereof are given. It replaces the irritating dichotomy of quantum and classical worlds by a much softer difference between intrinsic and extrinsic properties, which concern equally microscopic and macroscopic systems. Finally, the classicality and the quantum measurement are analyzed and found to present some still unsolved problems. A possible way of dealing with the Schr\\"{o}dinger cat is suggested that is base...
Extended objects in quantum systems
A quantum field theoretical study of the properties of extended objects appearing in the quantum ordered state is carried out in the framework of boson theory. First the process of creation of the ordered state is studied, and then the creation of extended objects in quantum ordered states. It is found that the spontaneous creation of an ordered state is always caused by a symmetry rearrangement when the symmetry of the Heisenberg fields is global, and that in quantum electrodynamics the dynamic rearrangement of symmetry takes place even when no ordered state is created. The c-number field phi sup(f)(chi) constructed by the boson method becomes the soliton solution of the Euler equations when the Planck constant is ignored, implying that the soliton solution can be regarded as an extended object with quantum origin. Finally the relations between the basic symmetry of the theory and topological charge is analyzed. Although basic symmetry does not restrict the shape of extended objects appearing in the ordered state, it influences which object can be classified by topological quantum number. The condition for topological quantization of an extended object is expressed in terms of the asymptotic behaviour of the boson function
Characterizing the entanglement of bipartite quantum systems
We derive a separability criterion for bipartite quantum systems which generalizes the already known criteria. It is based on observables having generic commutation relations. We then discuss in detail the relation among these criteria
Characterizing the entanglement of bipartite quantum systems
Giovannetti, Vittorio; Mancini, Stefano; Vitali, David; Tombesi, Paolo
2002-01-01
We derive a separability criterion for bipartite quantum systems which generalizes the already known criteria. It is based on observables having generic commutation relations. We then discuss in detail the relation among these criteria.
The Frobenius formalism in Galois quantum systems
Vourdas, A
2006-01-01
Quantum systems in which the position and momentum take values in the ring ${\\cal Z}_d$ and which are described with $d$-dimensional Hilbert space, are considered. When $d$ is the power of a prime, the position and momentum take values in the Galois field $GF(p^ \\ell)$, the position-momentum phase space is a finite geometry and the corresponding `Galois quantum systems' have stronger properties. The study of these systems uses ideas from the subject of field extension in the context of quantum mechanics. The Frobenius automorphism in Galois fields leads to Frobenius subspaces and Frobenius transformations in Galois quantum systems. Links between the Frobenius formalism and Riemann surfaces, are discussed.
Ground states of quantum spin systems
The authors prove that ground states of quantum spin systems are characterized by a principle of minimum local energy and that translationally invariant ground states are characterized by the principle of minimum energy per unit volume
Hamiltonian tomography: the quantum (system) measurement problem
Cole, Jared H.
2015-10-01
To harness the power of controllable quantum systems for information processing or quantum simulation, it is essential to be able to accurately characterise the system's Hamiltonian. Although in principle this requires determining less parameters than full quantum process tomography, a general and extendable method for reconstructing a general Hamiltonian has been elusive. In their recent paper, Wang et al (2015 New J. Phys. 17 093017) apply dynamical decoupling to the problem of Hamiltonian tomography and show how to reconstruct a general many-body Hamiltonian comprised of arbitrary interactions between qubits.
Thermal rectification in quantum graded mass systems
We show the existence of thermal rectification in the graded mass quantum chain of harmonic oscillators with self-consistent reservoirs. Our analytical study allows us to identify the ingredients leading to the effect. The presence of rectification in this effective, simple model (representing graded mass materials, systems that may be constructed in practice) indicates that rectification in graded mass quantum systems may be an ubiquitous phenomenon. Moreover, as the classical version of this model does not present rectification, our results show that, here, rectification is a direct result of the quantum statistics.
Correlation Function Bootstrapping in Quantum Chaotic Systems
Kaplan, L.
2005-01-01
We discuss a general and efficient approach for "bootstrapping" short-time correlation data in chaotic or complex quantum systems to obtain information about long-time dynamics and stationary properties, such as the local density of states. When the short-time data is sufficient to identify an individual quantum system, we obtain a systematic approximation for the spectrum and wave functions. Otherwise, we obtain statistical properties, including wave function intensity distributions, for an ...
Thermal rectification in quantum graded mass systems
Pereira, Emmanuel
2010-01-01
We show the existence of thermal rectification in the graded mass quantum chain of harmonic oscillators with self-consistent reservoirs. Our analytical study allows us to identify the ingredients leading to the effect. The presence of rectification in this effective, simple model (representing graded mass materials, systems that may be constructed in practice) indicates that rectification in graded mass quantum systems may be an ubiquitous phenomenon. Moreover, as the classical version of thi...
Relativistic Quantum Metrology in Open System Dynamics
Tian, Zehua; Fan, Heng; Jing, Jiliang
2015-01-01
Quantum metrology studies the ultimate limit of precision in estimating a physical quantity if quantum strategies are exploited. Here we investigate the evolution of a two-level atom as a detector which interacts with a massless scalar field using the master equation approach for open quantum system. We employ local quantum estimation theory to estimate the Unruh temperature when probed by a uniformly accelerated detector in the Minkowski vacuum. In particular, we evaluate the Fisher information (FI) for population measurement, maximize its value over all possible detector preparations and evolution times, and compare its behavior with that of the quantum Fisher information (QFI). We find that the optimal precision of estimation is achieved when the detector evolves for a long enough time. Furthermore, we find that in this case the FI for population measurement is independent of initial preparations of the detector and is exactly equal to the QFI, which means that population measurement is optimal. This resul...
Combinatorial Approach to Modeling Quantum Systems
Kornyak, Vladimir V.
2016-02-01
Using the fact that any linear representation of a group can be embedded into permutations, we propose a constructive description of quantum behavior that provides, in particular, a natural explanation of the appearance of complex numbers and unitarity in the formalism of the quantum mechanics. In our approach, the quantum behavior can be explained by the fundamental impossibility to trace the identity of the indistinguishable objects in their evolution. Any observation only provides information about the invariant relations between such objects. The trajectory of a quantum system is a sequence of unitary evolutions interspersed with observations—non-unitary projections. We suggest a scheme to construct combinatorial models of quantum evolution. The principle of selection of the most likely trajectories in such models via the large numbers approximation leads in the continuum limit to the principle of least action with the appropriate Lagrangians and deterministic evolution equations
Quantum electro-mechanical system (QEMS)
Full text: Recent development in Nano Electro-Mechanical Systems (NEMS) has yield oscillators with resonant frequencies above Giga Hertz with quality factors above 100,000. At this scale a NEMS oscillator becomes a quantum device capable of operating at the atomic level with extraordinary sensitivity to small forces or molecular masses. With this motivation, we study the phonon-electron interaction in several quantum electromechanical systems (QEMS). First, a system comprising a single quantum dot harmonically bound between two electrodes which facilitates a tunneling current between them and secondly the electron shuttle system firstly introduced by Gorelik. We describe the system via quantum master equation for the density operator of the electronic and vibrational degrees of freedom and thus incorporates the dynamics of both diagonal (population) and off diagonal (coherence) terms. We derive coupled equations of motion for the electron occupation number of the dot and the vibrational degrees of freedom, including damping of the vibration and thermo-mechanical noise. This dynamical description is related to observable features of the system including the stationary current as a function of bias voltage. A number of possible applications are explored for feasibility including molecular QEMS devices as quantum limited nanoscale detectors and as elements in quantum computer architectures. Copyright (2005) Australian Institute of Physics
Noise in quantum systems: facts and fantasies
Full text: We present a critical review of recent developments on quantum noise in a variety of mesoscopic conductors including ballistic, diffusive and tunnelling systems. We begin with a microscopic approach that describes quantum transport and fluctuations for correlated electrons at high external field taking the system beyond the linear response regime. We discuss two commonly believed results that (a) shot noise in diffusive systems is suppressed by '1/3' universally and (b) there is a 'crossover' of shot noise to thermal noise at finite temperature and applied field. Our analysis reveals contradictions based on fundamental physics and its logical implications. We examine another issue of measuring fractional charges in fractional quantum Hall effect (FQHE) experiments. It is believed that shot noise spectral density reveals the charge quantum of the current carriers as a Schottky phenomenon. Here again we analyse a number of unverified assumptions beyond the myth
Variational Principle for Classical-Quantum Systems
Grigorescu, M
2006-01-01
The evolution of a quantum particle interacting with a classical system is described by a generalized variational principle. The dynamical variable is a quantum state vector which includes the classical action as a phase factor, and the common time is treated as a collective variable. Combined with the model of bilinear coupling, the variational principle is applied to the problem of a quantum system in a thermal environment. It is shown that the statistical ensemble of Brownian state vectors is described by the solution of a nonlinear quantum Fokker-Planck equation for the density matrix. Exact solutions of this equation are obtained for the case of a two-level system, considering both stationary and nonstationary initial states.
Superconducting circuitry for quantum electromechanical systems
LaHaye, Matthew D.; Rouxinol, Francisco; Hao, Yu; Shim, Seung-Bo; Irish, Elinor K.
2015-05-01
Superconducting systems have a long history of use in experiments that push the frontiers of mechanical sensing. This includes both applied and fundamental research, which at present day ranges from quantum computing research and e orts to explore Planck-scale physics to fundamental studies on the nature of motion and the quantum limits on our ability to measure it. In this paper, we first provide a short history of the role of superconducting circuitry and devices in mechanical sensing, focusing primarily on efforts in the last decade to push the study of quantum mechanics to include motion on the scale of human-made structures. This background sets the stage for the remainder of the paper, which focuses on the development of quantum electromechanical systems (QEMS) that incorporate superconducting quantum bits (qubits), superconducting transmission line resonators and flexural nanomechanical elements. In addition to providing the motivation and relevant background on the physical behavior of these systems, we discuss our recent efforts to develop a particular type of QEMS that is based upon the Cooper-pair box (CPB) and superconducting coplanar waveguide (CPW) cavities, a system which has the potential to serve as a testbed for studying the quantum properties of motion in engineered systems.
Robust observer for uncertain linear quantum systems
In the theory of quantum dynamical filtering, one of the biggest issues is that the underlying system dynamics represented by a quantum stochastic differential equation must be known exactly in order that the corresponding filter provides an optimal performance; however, this assumption is generally unrealistic. Therefore, in this paper, we consider a class of linear quantum systems subjected to time-varying norm-bounded parametric uncertainties and then propose a robust observer such that the variance of the estimation error is guaranteed to be within a certain bound. Although in the linear case much of classical control theory can be applied to quantum systems, the quantum robust observer obtained in this paper does not have a classical analog due to the system's specific structure with respect to the uncertainties. Moreover, by considering a typical quantum control problem, we show that the proposed robust observer is fairly robust against a parametric uncertainty of the system even when the other estimators--the optimal Kalman filter and risk-sensitive observer--fail in the estimation
Molecular controlled of quantum nano systems
Paltiel, Yossi
2014-03-01
A century ago quantum mechanics created a conceptual revolution whose fruits are now seen in almost any aspect of our day-to-day life. Lasers, transistors and other solid state and optical devices represent the core technology of current computers, memory devices and communication systems. However, all these examples do not exploit fully the quantum revolution as they do not take advantage of the coherent wave-like properties of the quantum wave function. Controlled coherent system and devices at ambient temperatures are challenging to realize. We are developing a novel nano tool box with control coupling between the quantum states and the environment. This tool box that combines nano particles with organic molecules enables the integration of quantum properties with classical existing devices at ambient temperatures. The nano particles generate the quantum states while the organic molecules control the coupling and therefore the energy, charge, spin, or quasi particle transfer between the layers. Coherent effects at ambient temperatures can be measured in the strong coupling regime. In the talk I will present our nano tool box and show studies of charge transfer, spin transfer and energy transfer in the hybrid layers as well as collective transfer phenomena. These enable the realization of room temperature operating quantum electro optical devices. For example I will present in details, our recent development of a new type of chiral molecules based magnetless universal memory exploiting selective spin transfer.
Dicke model for quantum Hall systems
Hama, Y.; Fauzi, M. H.; Nemoto, K.; Hirayama, Y.; Ezawa, Z. F.
2016-02-01
In GaAs quantum Hall (QH) systems, electrons are coupled with nuclear spins through the hyperfine interaction, which is normally not strong enough to change the dynamics of electrons and nuclear spins. The dynamics of the QH systems, however, may drastically change when the nuclear spins interact with low-energy collective excitation modes of the electron spins. We theoretically investigate the nuclear-electron spin interaction in the QH systems as hybrid quantum systems driven by the hyperfine interaction. In particular, we study the interaction between the nuclear spins and the NambuGoldstone (NG) mode with the linear dispersion relation associated with the U(1) spin rotational symmetry breaking. We show that such an interaction is described as nuclear spins collectively coupled to the NG mode, and can be effectively described by the Dicke model. Based on the model we suggest that various collective spin phenomena realized in quantum optical systems can also emerge in the QH systems.
Quantum optical properties in plasmonic systems
Ooi, C. H. Raymond [Department of Physics, University of Malaya, 50603, Kuala Lumpur (Malaysia)
2015-04-24
Plasmonic metallic particle (MP) can affect the optical properties of a quantum system (QS) in a remarkable way. We develop a general quantum nonlinear formalism with exact vectorial description for the scattered photons by the QS. The formalism enables us to study the variations of the dielectric function and photon spectrum of the QS with the particle distance between QS and MP, exciting laser direction, polarization and phase in the presence of surface plasmon resonance (SPR) in the MP. The quantum formalism also serves as a powerful tool for studying the effects of these parameters on the nonclassical properties of the scattered photons. The plasmonic effect of nanoparticles has promising possibilities as it provides a new way for manipulating quantum optical properties of light in nanophotonic systems.
Ideal continuous measurement in open quantum systems
It is shown that in open quantum systems the so-called Zeno paradox is not valid. The equations of ideal continuous measurement for Markovian open systems are elaborated and applied to Pauli's simple open system the actual energy level of which is shown to be monitorable by continuous nondemolition measurement. (author)
Open quantum systems approach to atomtronics
Pepino, R. A.; Cooper, J.; Meiser, D.; Anderson, D. Z.; Holland, M J
2010-01-01
We derive a quantum master equation to treat quantum systems interacting with multiple reservoirs. The formalism is used to investigate atomic transport across a variety of lattice configurations. We demonstrate how the behavior of an electronic diode, a field-effect transistor, and a bipolar junction transistor can be realized with neutral, ultracold atoms trapped in optical lattices. An analysis of the current fluctuations is provided for the case of the atomtronic diode. Finally, we show t...
Modeling of quantum transport in open systems
Proietti Zaccaria, Remo
2003-01-01
Whereas classical transport physics is based on the concept of a probability distribution which is defined over the phase space of the system, the concept of a phase-space distribution function in the quantum formulation of transport is difficult, since the non-commutation of the position and momentum operators (the Heisenberg uncertainty principle) precludes the precise specification of a point in phase space. However, within the formulation of quantum mechanics, various formalisms based on ...
Note on quantum groups and integrable systems
Popolitov, A.
2016-01-01
The free-field formalism for quantum groups [preprint ITEP-M3/94, CRM-2202 hep-th/9409093] provides a special choice of coordinates on a quantum group. In these coordinates the construction of associated integrable system [arXiv:1207.1869] is especially simple. This choice also fits into general framework of cluster varieties [math.AG/0311245]—natural changes in coordinates are cluster mutations.
Scattering Theory for Open Quantum Systems
Behrndt, J.; Malamud, M. M.; Neidhardt, H.
2006-01-01
Quantum systems which interact with their environment are often modeled by maximal dissipative operators or so-called Pseudo-Hamiltonians. In this paper the scattering theory for such open systems is considered. First it is assumed that a single maximal dissipative operator $A_D$ in a Hilbert space $\\sH$ is used to describe an open quantum system. In this case the minimal self-adjoint dilation $\\widetilde K$ of $A_D$ can be regarded as the Hamiltonian of a closed system which contains the ope...
Open quantum systems far from equilibrium
Schaller, Gernot
2014-01-01
This monograph provides graduate students and also professional researchers aiming to understand the dynamics of open quantum systems with a valuable and self-contained toolbox. Special focus is laid on the link between microscopic models and the resulting open-system dynamics. This includes how to derive the celebrated Lindblad master equation without applying the rotating wave approximation. As typical representatives for non-equilibrium configurations it treats systems coupled to multiple reservoirs (including the description of quantum transport), driven systems, and feedback-controlled quantum systems. Each method is illustrated with easy-to-follow examples from recent research. Exercises and short summaries at the end of every chapter enable the reader to approach the frontiers of current research quickly and make the book useful for quick reference.
Complex quantum systems analysis of large Coulomb systems
Siedentop, Heinz
2013-01-01
This volume is based on lectures given during the program Complex Quantum Systems held at the National University of Singapore's Institute for Mathematical Sciences from 17 February to 27 March 2010. It guides the reader through two introductory expositions on large Coulomb systems to five of the most important developments in the field: derivation of mean field equations, derivation of effective Hamiltonians, alternative high precision methods in quantum chemistry, modern many body methods originating from quantum information, and - the most complex - semirelativistic quantum electrodynamics.
Quantum discord in matrix product systems
We consider a class of quantum systems with spin-flip symmetry and derive the quantum correlation measured by the quantum discord (QD). As an illustration, we investigate the QD in a three-body interaction model and an XYZ interaction model, whose ground states can be expressed as matrix product states, and the QD is exactly soluble. We show that the QD behaves differently than the quantum entanglement (QE) in many ways; for example, they may show opposite monotonicity and completely different finite-size effects. Furthermore, we compare the capability of the QD and the QE to detect quantum phase transitions (QPTs) and find that the QD is more reliable than the QE for signaling QPTs in these models: In the three-body interaction model, the QE is singular at the quantum critical point, however, it exhibits an additional singularity in the noncritical region, while the analyticity of the QD can be used to identify the quantum critical point perfectly; and in the XYZ interaction model, the QE vanishes in the thermodynamic limit, thus losing its ability to detect QPTs, while the QD still functions very well.
The Frobenius formalism in Galois quantum systems
Vourdas, A.
2006-01-01
Quantum systems in which the position and momentum take values in the ring ${\\cal Z}_d$ and which are described with $d$-dimensional Hilbert space, are considered. When $d$ is the power of a prime, the position and momentum take values in the Galois field $GF(p^ \\ell)$, the position-momentum phase space is a finite geometry and the corresponding `Galois quantum systems' have stronger properties. The study of these systems uses ideas from the subject of field extension in the context of quantu...
Quantum systems with finite Hilbert space
Quantum systems with finite Hilbert space are considered, and phase-space methods like the Heisenberg-Weyl group, symplectic transformations and Wigner and Weyl functions are discussed. A factorization of such systems in terms of smaller subsystems, based on the Chinese remainder theorem, is studied. The general formalism is applied to the case of angular momentum. In this context, SU(2) coherent states are used for analytic representations. Links between the theory of finite quantum systems and other fields of research are discussed
Quantum systems with finite Hilbert space
Vourdas, A [Department of Computing, University of Bradford, Bradford BD7 1DP (United Kingdom)
2004-03-01
Quantum systems with finite Hilbert space are considered, and phase-space methods like the Heisenberg-Weyl group, symplectic transformations and Wigner and Weyl functions are discussed. A factorization of such systems in terms of smaller subsystems, based on the Chinese remainder theorem, is studied. The general formalism is applied to the case of angular momentum. In this context, SU(2) coherent states are used for analytic representations. Links between the theory of finite quantum systems and other fields of research are discussed.
Scattering theory for open quantum systems
Behrndt, Jussi [Technische Univ. Berlin (Germany). Inst. fuer Mathematik; Malamud, Mark M. [Donetsk National University (Ukraine). Dept. of Mathematics; Neidhardt, Hagen [Weierstrass-Institut fuer Angewandte Analysis und Stochastik (WIAS) im Forschungsverbund Berlin e.V. (Germany)
2006-07-01
Quantum systems which interact with their environment are often modeled by maximal dissipative operators or so-called Pseudo-Hamiltonians. In this paper the scattering theory for such open systems is considered. First it is assumed that a single maximal dissipative operator A{sub D} in a Hilbert space H is used to describe an open quantum system. In this case the minimal self-adjoint dilation K of A{sub D} can be regarded as the Hamiltonian of a closed system which contains the open system {l_brace}A{sub D},h{r_brace}, but since K is necessarily not semibounded from below, this model is difficult to interpret from a physical point of view. In the second part of the paper an open quantum system is modeled with a family {l_brace}A({mu}){r_brace} of maximal dissipative operators depending on energy {mu}, and it is shown that the open system can be embedded into a closed system where the Hamiltonian is semibounded. Surprisingly it turns out that the corresponding scattering matrix can be completely recovered from scattering matrices of single Pseudo-Hamiltonians as in the first part of the paper. The general results are applied to a class of Sturm-Liouville operators arising in dissipative and quantum transmitting Schroedinger-Poisson systems. (orig.)
Statistical thermodynamics of polymer quantum systems
Chacón-Acosta, Guillermo; Dagdug, Leonardo; Morales-Técotl, Hugo A
2011-01-01
Polymer quantum systems are mechanical models quantized similarly as loop quantum gravity. It is actually in quantizing gravity that the polymer term holds proper as the quantum geometry excitations yield a reminiscent of a polymer material. In such an approach both non-singular cosmological models and a microscopic basis for the entropy of some black holes have arisen. Also important physical questions for these systems involve thermodynamics. With this motivation, in this work, we study the statistical thermodynamics of two one dimensional {\\em polymer} quantum systems: an ensemble of oscillators that describe a solid and a bunch of non-interacting particles in a box, which thus form an ideal gas. We first study the spectra of these polymer systems. It turns out useful for the analysis to consider the length scale required by the quantization and which we shall refer to as polymer length. The dynamics of the polymer oscillator can be given the form of that for the standard quantum pendulum. Depending on the...
Effective operator formalism for open quantum systems
Reiter, Florentin; Sørensen, Anders Søndberg
2012-01-01
We present an effective operator formalism for open quantum systems. Employing perturbation theory and adiabatic elimination of excited states for a weakly driven system, we derive an effective master equation which reduces the evolution to the ground-state dynamics. The effective evolution...
Recent advances in quantum integrable systems
Amico, L.; Belavin, A.; Buffenoir, E.; Castro Alvaredo, A.; Caudrelier, V.; Chakrabarti, A.; Corrig, E.; Crampe, N.; Deguchi, T.; Dobrev, V.K.; Doikou, A.; Doyon, B.; Feher, L.; Fioravanti, D.; Gohmann, F.; Hallnas, M.; Jimbo, M.; Konno, N.C.H.; Korchemsky, G.; Kulish, P.; Lassalle, M.; Maillet, J.M.; McCoy, B.; Mintchev, M.; Pakuliak, S.; Quano, F.Y.Z.; Ragnisco, R.; Ravanini, F.; Rittenberg, V.; Rivasseau, V.; Rossi, M.; Satta, G.; Sedrakyan, T.; Shiraishi, J.; Suzuki, N.C.J.; Yamada, Y.; Zamolodchikov, A.; Ishimoto, Y.; Nagy, Z.; Posta, S.; Sedra, M.B.; Zuevskiy, A.; Gohmann, F
2005-07-01
This meeting was dedicated to different aspects of the theory of quantum integrable systems. The organizers have intended to concentrate on topics related to the study of correlation functions, to systems with boundaries and to models at roots of unity. This document gathers the abstracts of 32 contributions, most of the contributions are accompanied by the set of transparencies.
Recent advances in quantum integrable systems
This meeting was dedicated to different aspects of the theory of quantum integrable systems. The organizers have intended to concentrate on topics related to the study of correlation functions, to systems with boundaries and to models at roots of unity. This document gathers the abstracts of 32 contributions, most of the contributions are accompanied by the set of transparencies
Coding with finite quantum systems
Coding using quantum states in an angular-momentum (2j+1)-dimensional Hilbert space H is considered in this paper. A concatenated code is studied in two steps. In the first step the space HN is considered and the code is its subspace HA spanned by the direct products of N angular-momentum states with the same m. In the second step the space HAM is considered and the code is its subspace HB spanned by the direct products of M angle states with the same m. It is shown that the code introduces redundancy with respect to any transformation
Coding with finite quantum systems
Vourdas, A.
2002-04-01
Coding using quantum states in an angular-momentum (2j+1)-dimensional Hilbert space H is considered in this paper. A concatenated code is studied in two steps. In the first step the space HN is considered and the code is its subspace HA spanned by the direct products of N angular-momentum states with the same m. In the second step the space HMA is considered and the code is its subspace HB spanned by the direct products of M angle states with the same m. It is shown that the code introduces redundancy with respect to any transformation.
Current in open quantum systems.
Gebauer, Ralph; Car, Roberto
2004-10-15
We show that a dissipative current component is present in the dynamics generated by a Liouville-master equation, in addition to the usual component associated with Hamiltonian evolution. The dissipative component originates from coarse graining in time, implicit in a master equation, and needs to be included to preserve current continuity. We derive an explicit expression for the dissipative current in the context of the Markov approximation. Finally, we illustrate our approach with a simple numerical example, in which a quantum particle is coupled to a harmonic phonon bath and dissipation is described by the Pauli master equation. PMID:15524960
Relativistic quantum metrology in open system dynamics.
Tian, Zehua; Wang, Jieci; Fan, Heng; Jing, Jiliang
2015-01-01
Quantum metrology studies the ultimate limit of precision in estimating a physical quantity if quantum strategies are exploited. Here we investigate the evolution of a two-level atom as a detector which interacts with a massless scalar field using the master equation approach for open quantum system. We employ local quantum estimation theory to estimate the Unruh temperature when probed by a uniformly accelerated detector in the Minkowski vacuum. In particular, we evaluate the Fisher information (FI) for population measurement, maximize its value over all possible detector preparations and evolution times, and compare its behavior with that of the quantum Fisher information (QFI). We find that the optimal precision of estimation is achieved when the detector evolves for a long enough time. Furthermore, we find that in this case the FI for population measurement is independent of initial preparations of the detector and is exactly equal to the QFI, which means that population measurement is optimal. This result demonstrates that the achievement of the ultimate bound of precision imposed by quantum mechanics is possible. Finally, we note that the same configuration is also available to the maximum of the QFI itself. PMID:25609187
Quantum temporal probabilities in tunneling systems
Anastopoulos, Charis; Savvidou, Ntina
2013-09-01
We study the temporal aspects of quantum tunneling as manifested in time-of-arrival experiments in which the detected particle tunnels through a potential barrier. In particular, we present a general method for constructing temporal probabilities in tunneling systems that (i) defines 'classical' time observables for quantum systems and (ii) applies to relativistic particles interacting through quantum fields. We show that the relevant probabilities are defined in terms of specific correlation functions of the quantum field associated with tunneling particles. We construct a probability distribution with respect to the time of particle detection that contains all information about the temporal aspects of the tunneling process. In specific cases, this probability distribution leads to the definition of a delay time that, for parity-symmetric potentials, reduces to the phase time of Bohm and Wigner. We apply our results to piecewise constant potentials, by deriving the appropriate junction conditions on the points of discontinuity. For the double square potential, in particular, we demonstrate the existence of (at least) two physically relevant time parameters, the delay time and a decay rate that describes the escape of particles trapped in the inter-barrier region. Finally, we propose a resolution to the paradox of apparent superluminal velocities for tunneling particles. We demonstrate that the idea of faster-than-light speeds in tunneling follows from an inadmissible use of classical reasoning in the description of quantum systems.
Heisenberg picture approach to the stability of quantum Markov systems
Quantum Markovian systems, modeled as unitary dilations in the quantum stochastic calculus of Hudson and Parthasarathy, have become standard in current quantum technological applications. This paper investigates the stability theory of such systems. Lyapunov-type conditions in the Heisenberg picture are derived in order to stabilize the evolution of system operators as well as the underlying dynamics of the quantum states. In particular, using the quantum Markov semigroup associated with this quantum stochastic differential equation, we derive sufficient conditions for the existence and stability of a unique and faithful invariant quantum state. Furthermore, this paper proves the quantum invariance principle, which extends the LaSalle invariance principle to quantum systems in the Heisenberg picture. These results are formulated in terms of algebraic constraints suitable for engineering quantum systems that are used in coherent feedback networks
Heisenberg picture approach to the stability of quantum Markov systems
Pan, Yu, E-mail: yu.pan@anu.edu.au, E-mail: zibo.miao@anu.edu.au; Miao, Zibo, E-mail: yu.pan@anu.edu.au, E-mail: zibo.miao@anu.edu.au [Research School of Engineering, Australian National University, Canberra, ACT 0200 (Australia); Amini, Hadis, E-mail: nhamini@stanford.edu [Edward L. Ginzton Laboratory, Stanford University, Stanford, California 94305 (United States); Gough, John, E-mail: jug@aber.ac.uk [Institute of Mathematics and Physics, Aberystwyth University, SY23 3BZ Wales (United Kingdom); Ugrinovskii, Valery, E-mail: v.ugrinovskii@gmail.com [School of Engineering and Information Technology, University of New South Wales at ADFA, Canberra, ACT 2600 (Australia); James, Matthew R., E-mail: matthew.james@anu.edu.au [ARC Centre for Quantum Computation and Communication Technology, Research School of Engineering, Australian National University, Canberra, ACT 0200 (Australia)
2014-06-15
Quantum Markovian systems, modeled as unitary dilations in the quantum stochastic calculus of Hudson and Parthasarathy, have become standard in current quantum technological applications. This paper investigates the stability theory of such systems. Lyapunov-type conditions in the Heisenberg picture are derived in order to stabilize the evolution of system operators as well as the underlying dynamics of the quantum states. In particular, using the quantum Markov semigroup associated with this quantum stochastic differential equation, we derive sufficient conditions for the existence and stability of a unique and faithful invariant quantum state. Furthermore, this paper proves the quantum invariance principle, which extends the LaSalle invariance principle to quantum systems in the Heisenberg picture. These results are formulated in terms of algebraic constraints suitable for engineering quantum systems that are used in coherent feedback networks.
Quons in a quantum dissipative system
Lee, Taejin
2016-03-01
String theory proves to be an imperative tool to explore the critical behavior of the quantum dissipative system. We discuss the quantum particles moving in two dimensions, in the presence of a uniform magnetic field, subject to a periodic potential and a dissipative force, which are described by the dissipative Wannier-Azbel-Hofstadter (DWAH) model. Using string theory formulation of the model, we find that the elementary excitations of the system at the generic points of the off-critical regions, in the zero temperature limit are quons, which satisfy q-deformed statistics.
Quantum spin glass in anisotropic dipolar systems
The spin-glass phase in the LiHoxY1-xF4 compound is considered. At zero transverse field this system is well described by the classical Ising model. At finite transverse field deviations from the transverse field quantum Ising model are significant, and one must take properly into account the hyperfine interactions, the off-diagonal terms in the dipolar interactions, and details of the full J = 8 spin Hamiltonian to obtain the correct physical picture. In particular, the system is not a spin glass at finite transverse fields and does not show quantum criticality
Quantum Hall effect in semiconductor systems with quantum dots and antidots
The integer quantum Hall effect in systems of semiconductor quantum dots and antidots is studied theoretically as a factor of temperature. It is established that the conditions for carrier localization in quantum-dot systems favor the observation of the quantum Hall effect at higher temperatures than in quantum-well systems. The obtained numerical results show that the fundamental plateau corresponding to the transition between the ground and first excited Landau levels can be retained up to a temperature of T ∼ 50 K, which is an order of magnitude higher than in the case of quantum wells. Implementation of the quantum Hall effect at such temperatures requires quantum-dot systems with controllable characteristics, including the optimal size and concentration and moderate geometrical and composition fluctuations. In addition, ordered arrangement is desirable, hence quantum antidots are preferable
Quantum temporal probabilities in tunneling systems
We study the temporal aspects of quantum tunneling as manifested in time-of-arrival experiments in which the detected particle tunnels through a potential barrier. In particular, we present a general method for constructing temporal probabilities in tunneling systems that (i) defines classical time observables for quantum systems and (ii) applies to relativistic particles interacting through quantum fields. We show that the relevant probabilities are defined in terms of specific correlation functions of the quantum field associated with tunneling particles. We construct a probability distribution with respect to the time of particle detection that contains all information about the temporal aspects of the tunneling process. In specific cases, this probability distribution leads to the definition of a delay time that, for parity-symmetric potentials, reduces to the phase time of Bohm and Wigner. We apply our results to piecewise constant potentials, by deriving the appropriate junction conditions on the points of discontinuity. For the double square potential, in particular, we demonstrate the existence of (at least) two physically relevant time parameters, the delay time and a decay rate that describes the escape of particles trapped in the inter-barrier region. Finally, we propose a resolution to the paradox of apparent superluminal velocities for tunneling particles. We demonstrate that the idea of faster-than-light speeds in tunneling follows from an inadmissible use of classical reasoning in the description of quantum systems. -- Highlights: Present a general methodology for deriving temporal probabilities in tunneling systems. Treatment applies to relativistic particles interacting through quantum fields. Derive a new expression for tunneling time. Identify new time parameters relevant to tunneling. Propose a resolution of the superluminality paradox in tunneling
Quantum temporal probabilities in tunneling systems
Anastopoulos, Charis, E-mail: anastop@physics.upatras.gr; Savvidou, Ntina, E-mail: ksavvidou@physics.upatras.gr
2013-09-15
We study the temporal aspects of quantum tunneling as manifested in time-of-arrival experiments in which the detected particle tunnels through a potential barrier. In particular, we present a general method for constructing temporal probabilities in tunneling systems that (i) defines classical time observables for quantum systems and (ii) applies to relativistic particles interacting through quantum fields. We show that the relevant probabilities are defined in terms of specific correlation functions of the quantum field associated with tunneling particles. We construct a probability distribution with respect to the time of particle detection that contains all information about the temporal aspects of the tunneling process. In specific cases, this probability distribution leads to the definition of a delay time that, for parity-symmetric potentials, reduces to the phase time of Bohm and Wigner. We apply our results to piecewise constant potentials, by deriving the appropriate junction conditions on the points of discontinuity. For the double square potential, in particular, we demonstrate the existence of (at least) two physically relevant time parameters, the delay time and a decay rate that describes the escape of particles trapped in the inter-barrier region. Finally, we propose a resolution to the paradox of apparent superluminal velocities for tunneling particles. We demonstrate that the idea of faster-than-light speeds in tunneling follows from an inadmissible use of classical reasoning in the description of quantum systems. -- Highlights: Present a general methodology for deriving temporal probabilities in tunneling systems. Treatment applies to relativistic particles interacting through quantum fields. Derive a new expression for tunneling time. Identify new time parameters relevant to tunneling. Propose a resolution of the superluminality paradox in tunneling.
System Design for a Long-Line Quantum Repeater
Van Meter, Rodney; Munro, W J; Nemoto, Kae
2007-01-01
We present a new control algorithm and system design for a network of quantum repeaters, and outline the end-to-end protocol architecture. Such a network will create long-distance quantum states, supporting quantum key distribution as well as distributed quantum computation. Quantum repeaters improve the reduction of quantum-communication throughput with distance from exponential to polynomial. Because a quantum state cannot be copied, a quantum repeater is not a signal amplifier, but rather executes algorithms for quantum teleportation in conjunction with a specialized type of quantum error correction called purification to raise the fidelity of the quantum states. We introduce our banded purification scheme, which is especially effective when the fidelity of coupled qubits is low, improving the prospects for experimental realization of such systems. The resulting throughput is calculated via detailed simulations of a long line composed of shorter hops. Our algorithmic improvements increase throughput by a f...
An exactly solvable system from quantum optics
Maciejewski, Andrzej J., E-mail: maciejka@astro.ia.uz.zgora.pl [J. Kepler Institute of Astronomy, University of Zielona Góra, Licealna 9, PL-65-417 Zielona Góra (Poland); Przybylska, Maria, E-mail: M.Przybylska@if.uz.zgora.pl [Institute of Physics, University of Zielona Góra, Licealna 9, 65-417 Zielona Góra (Poland); Stachowiak, Tomasz, E-mail: stachowiak@cft.edu.pl [Center for Theoretical Physics PAS, Al. Lotników 32/46, 02-668 Warsaw (Poland)
2015-07-31
We investigate a generalisation of the Rabi system in the Bargmann–Fock representation. In this representation the eigenproblem of the considered quantum model is described by a system of two linear differential equations with one independent variable. The system has only one irregular singular point at infinity. We show how the quantisation of the model is related to asymptotic behaviour of solutions in a vicinity of this point. The explicit formulae for the spectrum and eigenfunctions of the model follow from an analysis of the Stokes phenomenon. An interpretation of the obtained results in terms of differential Galois group of the system is also given. - Highlights: • New exactly solvable system from quantum optics is found. • Normalisation condition for system in Bargmann representation is used. • Formulae for spectrum and eigenfunctions from analysis of Stokes phenomenon are given.
EDITORIAL: CAMOP: Quantum Non-Stationary Systems CAMOP: Quantum Non-Stationary Systems
Dodonov, Victor V.; Man'ko, Margarita A.
2010-09-01
Although time-dependent quantum systems have been studied since the very beginning of quantum mechanics, they continue to attract the attention of many researchers, and almost every decade new important discoveries or new fields of application are made. Among the impressive results or by-products of these studies, one should note the discovery of the path integral method in the 1940s, coherent and squeezed states in the 1960-70s, quantum tunneling in Josephson contacts and SQUIDs in the 1960s, the theory of time-dependent quantum invariants in the 1960-70s, different forms of quantum master equations in the 1960-70s, the Zeno effect in the 1970s, the concept of geometric phase in the 1980s, decoherence of macroscopic superpositions in the 1980s, quantum non-demolition measurements in the 1980s, dynamics of particles in quantum traps and cavity QED in the 1980-90s, and time-dependent processes in mesoscopic quantum devices in the 1990s. All these topics continue to be the subject of many publications. Now we are witnessing a new wave of interest in quantum non-stationary systems in different areas, from cosmology (the very first moments of the Universe) and quantum field theory (particle pair creation in ultra-strong fields) to elementary particle physics (neutrino oscillations). A rapid increase in the number of theoretical and experimental works on time-dependent phenomena is also observed in quantum optics, quantum information theory and condensed matter physics. Time-dependent tunneling and time-dependent transport in nano-structures are examples of such phenomena. Another emerging direction of study, stimulated by impressive progress in experimental techniques, is related to attempts to observe the quantum behavior of macroscopic objects, such as mirrors interacting with quantum fields in nano-resonators. Quantum effects manifest themselves in the dynamics of nano-electromechanical systems; they are dominant in the quite new and very promising field of circuit QED. Another rapidly growing research field (although its origin can be traced to the beginning of the 1980s) is the quantum control of evolution at the microscopic level. These examples show that quantum non-stationary systems continue to be a living and very interesting part of quantum physics, uniting researchers from many different areas. Thus it is no mere chance that several special scientific meetings devoted to these topics have been organized recently. One was the international seminar 'Time-Dependent Phenomena in Quantum Mechanics' organized by Manfred Kleber and Tobias Kramer in 2007 at Blaubeuren, Germany. The proceedings of that event were published in 2008 as volume 99 of Journal of Physics: Conference Series. Another recent meeting was the International Workshop on Quantum Non-Stationary Systems, held on 19-23 October 2009 at the International Center for Condensed Matter Physics (ICCMP) in Brasilia, Brazil. It was organized and directed by Victor Dodonov (Institute of Physics, University of Brasilia, Brazil), Vladimir Man'ko (P N Lebedev Physical Institute, Moscow, Russia) and Salomon Mizrahi (Physics Department, Federal University of Sao Carlos, Brazil). This event was accompanied by a satellite workshop 'Quantum Dynamics in Optics and Matter', organized by Salomon Mizrahi and Victor Dodonov on 25-26 October 2009 at the Physics Department of the Federal University of Sao Carlos, Brazil. These two workshops, supported by the Brazilian federal agencies CAPES and CNPq and the local agencies FAP-DF and FAPESP, were attended by more than 120 participants from 16 countries. Almost 50 invited talks and 20 poster presentations covered a wide area of research in quantum mechanics, quantum optics and quantum information. This special issue of CAMOP/Physica Scripta contains contributions presented by some invited speakers and participants of the workshop in Brasilia. Although they do not cover all of the wide spectrum of problems related to quantum non-stationary systems, they nonetheless show some general trends. However, readers should remember that these comments represent the personal points of view of their authors. About a third of the comments are devoted to the evolution of quantum systems in the presence of dissipation or other sources of decoherence. This area, started by Landau in 1927, still contains many extremely interesting and unsolved problems. Here they are discussed in view of such different applications as the dynamics of quantum entanglement, cavity QED, optomechanics and the dynamical Casimir effect. Another group of comments deals with different (e.g. geometrical, tomographic, PT-symmetric) approaches to the dynamics of quantum systems, which have been developed in the past two decades. In particular, the problem of transition from quantum to classical description is considered and the inequalities generalizing the standard uncertainty relations are discussed in this connection. Three comments are devoted to the applications of nonclassical states, analytic representations and the algebraic techniques for resolving problems in quantum information and quantum statistical physics. The other contributions are related to different aspects of the dynamics of concrete physical systems, such as the wave-packet approach to the description of transport phenomena in mesoscopic systems, tunneling phenomena in low-dimensional semiconductor structures and resonance states of two-electron quantum dots. We thank all the authors and referees for their efforts in preparing this special issue. We hope that the comments in this collection will be useful for interested readers.
Quantum Transport in Strongly Correlated Systems
Bohr, Dan
2007-01-01
In the past decade there has been a trend towards studying ever smaller devices. Improved experimental techniques have made new experiments possible, one class of which is electron transport through molecules and artificially manufactured structures like quantum dots. In this type of systems...
Wigner quantum systems (Lie superalgebraic approach)
Palev, T D
2002-01-01
We present three groups of examples of Wigner Quantum Systems related to the Lie superalgebras $osp(1/6n)$, $sl(1/3n)$ and $sl(n/3)$ and discuss shortly their physical features. In the case of $sl(1/3n)$ we indicate that the underlying geometry is noncommutative.
System and method for making quantum dots
Bakr, Osman M.
2015-05-28
Embodiments of the present disclosure provide for methods of making quantum dots (QDs) (passivated or unpassivated) using a continuous flow process, systems for making QDs using a continuous flow process, and the like. In one or more embodiments, the QDs produced using embodiments of the present disclosure can be used in solar photovoltaic cells, bio-imaging, IR emitters, or LEDs.
Lithography system using quantum entangled photons
Williams, Colin (Inventor); Dowling, Jonathan (Inventor); della Rossa, Giovanni (Inventor)
2002-01-01
A system of etching using quantum entangled particles to get shorter interference fringes. An interferometer is used to obtain an interference fringe. N entangled photons are input to the interferometer. This reduces the distance between interference fringes by n, where again n is the number of entangled photons.
Quantum mechanics of a system with confinement
A study is made of the quantum mechanical model of confinement. The spectrum of a system with permanently confined channel is investiogated. A closed analytical expression is obtained for the S-matrix describing the scattering on N levels in the confined channel. The influence of the confined channel on the resonant and Coulomb states in the scattering channel is considered
Field-emission current from quantum system
Shpatakovskaya, G V, E-mail: shpagalya@yandex.r [Keldysh Institute of Applied Mathematics Russian Academy of Sciences, Miusskaya sq.4, 125047 Moscow (Russian Federation)
2010-11-01
A universal semiclassical approach is developed to calculate an emission current from a quantum system (atom, ion, metal cluster, metal surface, graphene ribbon, etc.) in a stationary electric field. The same expression is in use for a spherical emitter (atom, negative ion, metal cluster) and a plane metal surface. It is shown the results agree with those of other methods.
Nonseparability and noncommutativity in quantum systems
de La Torre, A. C.; Catuogno, P.; Ferrando, S.
1991-02-01
The quantum covariance function is calculated in some EPR-like systems for commuting observables in order to illustrate the nonseparability contribution to the incompatibility between commuting operators. It is shown that an attempt to eliminate the noncommutativity contribution to incompatibility fails in finite-dimensional cases and would require a nonseparable Hilbert space (nonseparable in the mathematical sense).
Quantum field theory and multiparticle systems
The use of quantum field theory methods for the investigation of the physical characteristics of the MANY-BODY SYSTEMS is discussed. Mainly discussed is the method of second quantization and the method of the Green functions. Briefly discussed is the method of calculating the Green functions at finite temperatures. (Z.J.)
Quantum mechanics classical results, modern systems, and visualized examples
Robinett, Richard W
2006-01-01
`Quantum Mechanics'' is a comprehensive introduction to quantum mechanics for advanced undergraduate students in physics. It provides the reader with a strong conceptual background in the subject, extensive experience with the necessary mathematical background, as well as numerous visualizations of quantum concepts and phenomena. - ;Quantum Mechanics: Classical Results, Modern Systems, and Visualized Examples is a comprehensive introduction to non-relativistic quantum mechanics for advanced undergraduate students in physics and related fields. It provides students with a strong conceptual background in the most important theoretical aspects of quantum mechanics, extensive experience with the mathematical tools required to solve problems, the opportunity to use quantum ideas to confront modern experimental. realizations of quantum systems, and numerous visualizations of quantum concepts and phenomena. Changes from the First Edition include many new discussions of modern quantum systems (such as Bose-Einstein c...
Open quantum systems approach to atomtronics
We derive a quantum master equation to treat quantum systems interacting with multiple reservoirs. The formalism is used to investigate the atomic transport of bosons across a variety of lattice configurations. We demonstrate how the behavior of an electronic diode, a field-effect transistor, and a bipolar junction transistor can be realized with neutral, ultracold atoms trapped in optical lattices. An analysis of the current fluctuations is provided for the case of the atomtronic diode. Finally, we show that it is possible to demonstrate and logic gate behavior in an optical lattice.
Open quantum systems approach to atomtronics
Pepino, R A; Meiser, D; Anderson, D Z; Holland, M J
2010-01-01
We derive a quantum master equation to treat quantum systems interacting with multiple reservoirs. The formalism is used to investigate atomic transport across a variety of lattice configurations. We demonstrate how the behavior of an electronic diode, a field-effect transistor, and a bipolar junction transistor can be realized with neutral, ultracold atoms trapped in optical lattices. An analysis of the current fluctuations is provided for the case of the atomtronic diode. Finally, we show that it is possible to demonstrate AND logic gate behavior in an optical lattice.
Energy Cost of Controlling Mesoscopic Quantum Systems
Horowitz, Jordan M.; Jacobs, Kurt
2015-09-01
We determine the minimum energy required to control the evolution of any mesoscopic quantum system in the presence of arbitrary Markovian noise processes. This result provides the mesoscopic equivalent of the fundamental cost of refrigeration, sets the minimum power consumption of mesoscopic devices that operate out of equilibrium, and allows one to calculate the efficiency of any control protocol, whether it be open-loop or feedback control. As examples, we calculate the energy cost of maintaining a qubit in the ground state and the efficiency of resolved-sideband cooling of nano-mechanical resonators, and discuss the energy cost of quantum information processing.
Scattering Theory for Open Quantum Systems
Behrndt, J; Neidhardt, H
2006-01-01
Quantum systems which interact with their environment are often modeled by maximal dissipative operators or so-called Pseudo-Hamiltonians. In this paper the scattering theory for such open systems is considered. First it is assumed that a single maximal dissipative operator $A_D$ in a Hilbert space $\\sH$ is used to describe an open quantum system. In this case the minimal self-adjoint dilation $\\widetilde K$ of $A_D$ can be regarded as the Hamiltonian of a closed system which contains the open system $\\{A_D,\\sH\\}$, but since $\\widetilde K$ is necessarily not semibounded from below, this model is difficult to interpret from a physical point of view. In the second part of the paper an open quantum system is modeled with a family $\\{A(\\mu)\\}$ of maximal dissipative operators depending on energy $\\mu$, and it is shown that the open system can be embedded into a closed system where the Hamiltonian is semibounded. Surprisingly it turns out that the corresponding scattering matrix can be completely recovered from sc...
Symmetry and stability of open quantum systems
The presentation of the thesis involves an introduction and six chapters. Chapter 1 presents notions and results used in the other chpaters. Chapters 2-6 present our results which are focused on two notions: generalized observable and dynamic semigroup. These notions characterize a specific research domain (set up during the last 10 years) which is currently called quantum mechanics of open systems. The two notions (generalized observable and dynamic semigroup) are mathematically correlated. They belong to the set of completely positive linear applications among observable algebras. This fact, associated with that formulation of quantum mechanics according to which it is a special case of quantum mechanics namely, that for which the observable algebra is commutative, help to understand the similar essence of the results presented in chapter 2-6. Thus, the natural mathematical background has been achieved for our results; it is represented by that category whose objects are the observable algebras and whose morphisms are completely positive linear contractions generating unity within unity. These ideas are extensively presented in the introduction. The fact that the relations between classical mechanics and quantum mechanics can be rigorously treated as positive linear applications between classical observable algebras commutative and quantum observable algebras non-commutative, which are automatically fully positive, has been initially shown in our paper. (author)
Simple quantum systems in the momentum representation
Núñez-Yépez, H N; Martínez y Romero, R P; Salas-Brito, A L
2000-01-01
The momentum representation is seldom used in quantum mechanics courses. Some students are thence surprised by the change in viewpoint when, in doing advanced work, they have to use the momentum rather than the coordinate representation. In this work, we give an introduction to quantum mechanics in momentum space, where the Schrödinger equation becomes an integral equation. To this end we discuss standard problems, namely, the free particle, the quantum motion under a constant potential, a particle interacting with a potential step, and the motion of a particle under a harmonic potential. What is not so standard is that they are all conceived from momentum space and hence they, with the exception of the free particle, are not equivalent to the coordinate space ones with the same names. All the problems are solved within the momentum representation making no reference to the systems they correspond to in the coordinate representation.
Ion-cavity system for quantum networks
Full text: A single atom interacting with a single mode of a cavity allows us to probe the quantum interaction between light and matter. In the context of quantum networks, such a system can provide an interface between stationary and flying qubits, making it possible for single photons to transport quantum information between the network nodes. We study a single 40Ca+ ion trapped inside a high-finesse optical resonator. First, we demonstrate and characterize a single-photon source, in which a vacuum-stimulated Raman process transfers atomic population between two Zeeman states of the ion, creating a single photon in the cavity. We evaluate the photon statistics by measuring the second-order correlation function. Moreover, we obtain the photon temporal profile and investigate the dynamics of the process. Secondly, we perform Raman spectroscopy using the cavity. Residual motion of the ion introduces motional sidebands in the Raman spectrum and thus offers prospects for cavity-assisted cooling. (author)
Quantum-mechanical aspects of classically chaotic driven systems
This paper treats atoms and molecules in laser fields as periodically driven quantum systems. The paper concludes by determining that stochastic excitation is possible in quantum systems with quasiperiodic driving. 17 refs
Cui, Ping
The thesis comprises two major themes of quantum statistical dynamics. One is the development of quantum dissipation theory (QDT). It covers the establishment of some basic relations of quantum statistical dynamics, the construction of several nonequivalent complete second-order formulations, and the development of exact QDT. Another is related to the applications of quantum statistical dynamics to a variety of research fields. In particular, unconventional but novel theories of the electron transfer in Debye solvents, quantum transport, and quantum measurement are developed on the basis of QDT formulations. The thesis is organized as follows. In Chapter 1, we present some background knowledge in relation to the aforementioned two themes of this thesis. The key quantity in QDT is the reduced density operator rho(t) ≡ trBrho T(t); i.e., the partial trace of the total system and bath composite rhoT(t) over the bath degrees of freedom. QDT governs the evolution of reduced density operator, where the effects of bath are treated in a quantum statistical manner. In principle, the reduced density operator contains all dynamics information of interest. However, the conventional quantum transport theory is formulated in terms of nonequilibrium Green's function. The newly emerging field of quantum measurement in relation to quantum information and quantum computing does exploit a sort of QDT formalism. Besides the background of the relevant theoretical development, some representative experiments on molecular nanojunctions are also briefly discussed. In chapter 2, we outline some basic (including new) relations that highlight several important issues on QDT. The content includes the background of nonequilibrium quantum statistical mechanics, the general description of the total composite Hamiltonian with stochastic system-bath interaction, a novel parameterization scheme for bath correlation functions, a newly developed exact theory of driven Brownian oscillator (DBO) systems, and its closely related solvation mode transformation of system-bath coupling Hamiltonian in general. The exact QDT of DBO systems is also used to clarify the validity of conventional QDT formulations that involve Markovian approximation. In Chapter 3, we develop three nonequivalent but all complete second-order QDT (CS-QDT) formulations. Two of them are of the conventional prescriptions in terms of time-local dissipation and memory kernel, respectively. The third one is called the correlated driving-dissipation equations of motion (CODDE). This novel CS-QDT combines the merits of the former two for its advantages in both the application and numerical implementation aspects. Also highlighted is the importance of correlated driving-dissipation effects on the dynamics of the reduced system. In Chapter 4, we construct an exact QDT formalism via the calculus on path integrals. The new theory aims at the efficient evaluation of non-Markovian dissipation beyond the weak system-bath interaction regime in the presence of time-dependent external field. By adopting exponential-like expansions for bath correlation function, hierarchical equations of motion formalism and continued fraction Liouville-space Green's function formalism are established. The latter will soon be used together with the Dyson equation technique for an efficient evaluation of non-perturbative reduced density matrix dynamics. The interplay between system-bath interaction strength, non-Markovian property, and the required level of hierarchy is also studied with the aid of simple spin-boson systems, together with the three proposed schemes to truncate the infinite hierarchy. In Chapter 5, we develop a nonperturbative theory of electron transfer (ET) in Debye solvents. The resulting exact and analytical rate expression is constructed on the basis of the aforementioned continued fraction Liouville-space Green's function formalism, together with the Dyson equation technique. Not only does it recover the celebrated Marcus' inversion and Kramers' turnover behaviors, the new theory also shows some distinct quantum solvation effects that can alter the ET mechanism. Moreover, the present theory predicts further for the ET reaction thermodynamics, such as equilibrium Gibbs free-energy and entropy, some interesting solvent-dependent features that are calling for experimental verification. In Chapter 6, we discuss the constructed QDTs, in terms of their unified mathematical structure that supports a linear dynamics space, and thus facilitates their applications to various physical problems. The involving details are exemplified with the CODDE form of QDT. As the linear space is concerned, we identify the Schrodinger versus Heisenberg picture and the forward versus backward propagation of the reduced, dissipative Liouville dynamics. For applications we discuss the reduced linear response theory and the optimal control problems, in which the correlated effects of non-Markovian dissipation and field driving are shown to be important. In Chapter 7, we turn to quantum transport, i.e., electric current through molecular or mesoscopic systems under finite applied voltage. By viewing the nonequilibrium transport setup as a quantum open system, we develop a reduced-density-matrix approach to quantum transport. The resulting current is explicitly expressed in terms of the molecular reduced density matrix by tracing out the degrees of freedom of the electrodes at finite bias and temperature. We propose a conditional quantum master equation theory, which is an extension of the conventional (or unconditional) QDT by tracing out the well-defined bath subsets individually, instead of the entire bath degrees of freedom. Both the current and the noise spectrum can be conveniently analyzed in terms of the conditional reduced density matrix dynamics. By far, the QDT (including the conditional one) has only been exploited in second-order form. A self-consistent Born approximation for the system-electrode coupling is further proposed to recover all existing nonlinear current-voltage behaviors including the nonequilibrium Kondo effect. Transport theory based on the exact QDT formalism will be developed in future. In Chapter 8, we study the quantum measurement of a qubit with a quantum-point-contact detector. On the basis of a unified quantum master equation (a form of QDT), we study the measurement-induced relaxation and dephasing of the qubit. Our treatment pays particular attention on the detailed-balance relation, which is a consequence of properly accounting for the energy exchange between the qubit and detector during the measurement process. We also derive a conditional quantum master equation for quantum measurement in general, and study the readout characteristics of the qubit measurement. Our theory is applicable to the quantum measurement at arbitrary voltage and temperature. A number of remarkable new features are found and highlighted in concern with their possible relevance to future experiments. In Chapter 9, we discuss the further development of QDT, aiming at an efficient evaluation of many-electron systems. This will be carried out by reducing the many-particle (Fermion or Boson) QDT to a single-particle one by exploring, e.g. the Wick's contraction theorem. It also results in a time-dependent density functional theory (TDDFT) for transport through complex large-scale (e.g. molecules) systems. Primary results of the TDDFT-QDT are reported. In Chapter 10, we summary the thesis, and comment and remark on the future work on both the theoretical and application aspects of QDT.
A Direct Coupling Coherent Quantum Observer for a Single Qubit Finite Level Quantum System
Petersen, Ian R.
2014-01-01
This paper considers the problem of constructing a direct coupling quantum observer for a single qubit finite level quantum system plant. The proposed observer is a single mode linear quantum system which is shown to be able to estimate one of the plant variables in a time averaged sense. A numerical example and simulations are included to illustrate the properties of the observer.
Security of practical quantum key distribution systems
Jain, Nitin
2015-02-24
This thesis deals with practical security aspects of quantum key distribution (QKD) systems. At the heart of the theoretical model of any QKD system lies a quantum-mechanical security proof that guarantees perfect secrecy of messages - based on certain assumptions. However, in practice, deviations between the theoretical model and the physical implementation could be exploited by an attacker to break the security of the system. These deviations may arise from technical limitations and operational imperfections in the physical implementation and/or unrealistic assumptions and insufficient constraints in the theoretical model. In this thesis, we experimentally investigate in depth several such deviations. We demonstrate the resultant vulnerabilities via proof-of-principle attacks on a commercial QKD system from ID Quantique. We also propose countermeasures against the investigated loopholes to secure both existing and future QKD implementations.
From classical to quantum theory of open systems
The paper presents a short survey of some results concerning the physical interpretation of the basic equations for quantum open systems. The concept of continuous medium for quantum systems is introduced. From this point of view, the question of completeness of a description and hidden parameters (scale) for quantum open systems are considered. The Heisenberg uncertainty principle in the physics of open quantum systems is represented
An impurity-induced gap system as a quantum data bus for quantum state transfer
We introduce a tight-binding chain with a single impurity to act as a quantum data bus for perfect quantum state transfer. Our proposal is based on the weak coupling limit of the two outermost quantum dots to the data bus, which is a gapped system induced by the impurity. By connecting two quantum dots to two sites of the data bus, the system can accomplish a high-fidelity and long-distance quantum state transfer. Numerical simulations for finite system show that the numerical and analytical results of the effective coupling strength agree well with each other. Moreover, we study the robustness of this quantum communication protocol in the presence of disorder in the couplings between the nearest-neighbor quantum dots. We find that the gap of the system plays an important role in robust quantum state transfer
Hybrid quantum systems of ions and atoms
Sias, Carlo
2014-01-01
In this chapter we review the progress in experiments with hybrid systems of trapped ions and ultracold neutral atoms. We give a theoretical overview over the atom-ion interactions in the cold regime and give a summary of the most important experimental results. We conclude with an overview of remaining open challenges and possible applications in hybrid quantum systems of ions and neutral atoms.
Chiral quantum mechanics (CQM) for antihydrogen systems
Van hooydonk, G.
2005-01-01
A first deception of QM on antiH already appears in one-center integrals for two-center systems (G. Van Hooydonk, physics/0511115). In reality, full QM is a theory for chiral systems but the QM establishment was wrong footed with a permutation of reference frames. With chiral quantum mechanics (CQM), the theoretical ban on natural antiH must be lifted as soon as possible.
Simulating open quantum systems by applying SU(4) to quantum master equations
Xu, Minghui; Tieri, D. A.; Holland, M J
2013-01-01
We show that open quantum systems of two-level atoms symmetrically coupled to a single-mode photon field can be efficiently simulated by applying a SU(4) group theory to quantum master equations. This is important since many foundational examples in quantum optics fall into this class. We demonstrate the method by finding exact solutions for many-atom open quantum systems such as lasing and steady state superradiance.
Irreversible processes in quantum mechanical systems
Although the information provided by the evolution of the density matrix of a quantum system is equivalent with the knowledge of all observables at a given time, it turns out ot be insufficient to answer certain questions in quantum optics or linear response theory where the commutator of certain observables at different space-time points is needed. In this doctoral thesis we prove the existence of density matrices for common probabilities at multiple times and discuss their properties and their characterization independent of a special representation. We start with a compilation of definitions and properties of classical common probabilities and correlation functions. In the second chapter we give the definition of a quantum mechanical Markov process and derive the properties of propagators, generators and conditional probabilities as well as their mutual relations. The third chapter is devoted to a treatment of quantum mechanical systems in thermal equilibrium for which the principle of detailed balance holds as a consequence of microreversibility. We work out the symmetry properties of the two-sided correlation functions which turn out to be analogous to those in classical processes. In the final chapter we use the Gaussian behavior of the stationary correlation function of an oscillator and determine a class of Markov processes which are characterized by dissipative Lionville operators. We succeed in obtaining the canonical representation in a purely algebraic way by means of similarity transformations. Starting from this representation it is particularly easy to calculate the propagator and the correlation function. (HJ) 891 HJ/HJ 892 MKO
Observable measure of quantum coherence in finite dimensional systems
Girolami, Davide
2014-01-01
Quantum coherence is the key resource for quantum technology, with applications in quantum optics, information processing, metrology and cryptography. Yet, there is no universally efficient method for quantifying coherence either in theoretical or in experimental practice. I introduce a framework for measuring quantum coherence in finite dimensional systems. I define a theoretical measure which satisfies the reliability criteria established in the context of quantum resource theories. Then, I...
Quantum Trajectory in Multi-Dimensional Non-Linear System
Kubotani, Hiroto
1999-01-01
We discuss quantum dynamics in multi-dimensional non-linear systems. It is well-known that wave functions are localized in a kicked rotor model. However, coupling with other degrees of freedom breaks the localization. In order to clarify the difference, we describe the quantum dynamics by deterministic rigid trajectories, which are accompanied with the de Broglie-Bohm interpretation of quantum mechanics, instead of wave functions. A bundle of quantum trajectories are repulsive through quantum...
Uncertainty relation for non-Hamiltonian quantum systems
Tarasov, Vasily E. [Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Moscow 119991 (Russian Federation)
2013-01-15
General forms of uncertainty relations for quantum observables of non-Hamiltonian quantum systems are considered. Special cases of uncertainty relations are discussed. The uncertainty relations for non-Hamiltonian quantum systems are considered in the Schroedinger-Robertson form since it allows us to take into account Lie-Jordan algebra of quantum observables. In uncertainty relations, the time dependence of quantum observables and the properties of this dependence are discussed. We take into account that a time evolution of observables of a non-Hamiltonian quantum system is not an endomorphism with respect to Lie, Jordan, and associative multiplications.
Uncertainty relation for non-Hamiltonian quantum systems
Tarasov, Vasily E.
2013-01-01
General forms of uncertainty relations for quantum observables of non-Hamiltonian quantum systems are considered. Special cases of uncertainty relations are discussed. The uncertainty relations for non-Hamiltonian quantum systems are considered in the Schrdinger-Robertson form since it allows us to take into account Lie-Jordan algebra of quantum observables. In uncertainty relations, the time dependence of quantum observables and the properties of this dependence are discussed. We take into account that a time evolution of observables of a non-Hamiltonian quantum system is not an endomorphism with respect to Lie, Jordan, and associative multiplications.
Mathematical Structure in Quantum Systems and applications
This volume contains most of the contributions presented at the Conference 'Mathematical Structures in Quantum Systems and applications', held at the Centro de Ciencias de Benasque 'Pedro Pascual', Benasque (Spain) from 8-14 July 2012. The aim of the Conference was to bring together physicists working on different applications of mathematical methods to quantum systems in order to enable the different communities to become acquainted with other approaches and techniques that could be used in their own fields of expertise. We concentrated on three main subjects: the geometrical description of Quantum Mechanics; the Casimir effect and its mathematical implications; the Quantum Zeno Effect and Open system dynamics. Each of these topics had a set of general lectures, aimed at presenting a global view on the subject, and other more technical seminars. We would like to thank all participants for their contribution to creating a wonderful scientific atmosphere during the Conference. We would especially like to thank the speakers and the authors of the papers contained in this volume, the members of the Scientific Committee for their guidance and support and, of course, the referees for their generous work. Special thanks are also due to the staff of the Centro de Ciencias de Benasque 'Pedro Pascual' who made this successful meeting possible. On behalf of the organising committee and the authors we would also like to acknowledge the partial support provided by the ESF-CASIMIR network ('New Trends and Applications of the Casimir Effect'), the QUITEMAD research Project (Quantum technologies at Madrid, Ref. Comunidad de Madrid P2009/ESP-1594), the MICINN Project (MTM2011-16027-E) and the Government from Aragon (DGA) (DGA, Department of Industry and Innovation and the European Social Fund, DGA-Grant 24/1) who made the Conference and this Proceedings volume possible.
Aberration-corrected quantum temporal imaging system
Zhu, Yunhui; Gauthier, Daniel J
2013-01-01
We describe the design of a temporal imaging system that simultaneously reshapes the temporal profile and converts the frequency of a photonic wavepacket, while preserving its quantum state. A field lens, which imparts a temporal quadratic phase modulation, is used to correct for the residual phase caused by field curvature in the image, thus enabling temporal imaging for phase-sensitive quantum applications. We show how this system can be used for temporal imaging of time-bin entangled photonic wavepackets and compare the field lens correction technique to systems based on a temporal telescope and far-field imaging. The field-lens approach removes the residual phase using four dispersive elements. The group delay dispersion (GDD) $D$ is constrained by the available bandwidth $\\Delta\
An E-payment system based on quantum group signature
Xiaojun, Wen
2010-12-01
Security and anonymity are essential to E-payment systems. However, existing E-payment systems will easily be broken into soon with the emergence of quantum computers. In this paper, we propose an E-payment system based on quantum group signature. In contrast to classical E-payment systems, our quantum E-payment system can protect not only the users' anonymity but also the inner structure of customer groups. Because of adopting the two techniques of quantum key distribution, a one-time pad and quantum group signature, unconditional security of our E-payment system is guaranteed.
Charge and momentum in quantum electromechanical systems
Bennett, Steven D.
We address theoretical questions in quantum nanoelectromechanical systems. These are systems where a mechanical oscillator is coupled to a conductor in which single electrons or the quantum coherence of electrons plays an important role. The interplay of quantum electronics with the motion of a relatively macroscopic object provides a way to probe both the mechanics and the electronics with extraordinary sensitivity. We address three problems based on monitoring either the electronic or mechanical component to measure quantum properties of the coupled system. First, we study the full charge transfer statistics and correlations in a tunnel junction coupled to a mechanical oscillator, viewing the current measured through the junction as a detector of the oscillator position. We find several surprising results that are not obtained in a study of only the average and variance of tunneled charge. Even when the oscillator is weakly coupled to the tunnel junction, it can lead to highly non-Gaussian tunneling statistics; moreover, non-Gaussian correlations between the oscillator motion and transferred charge show that the backaction of tunneling electrons on the oscillator cannot be fully described as coupling the oscillator to an effective thermal bath. Second, we use a general scattering approach to study the backaction of a quantum point contact position detector on a mechanical oscillator. Our results remain valid far from the tunneling limit, an important experimental regime and where previous calculations of backaction break down. We obtain the backaction damping and heating directly in terms of the scattering matrix, and find that not only the transmission but also the scattering phases play an important role. Finally, we study a quantum dot capacitively coupled to an oscillating cantilever. In this case, the damping of the mechanical oscillator is monitored to measure quantum electronic properties of the dot. For weak electromechanical coupling, we find an effective temperature-dependent level repulsion of Coulomb blockade peaks in the damping versus gate voltage, and show that this is a result of degenerate energy levels on the dot. We further consider the regime of strong coupling, where the cantilever motion strongly and nonlinearly affects the charge on the dot. In this regime, the lineshape asymmetry of Coulomb blockade peaks in the damping, also a result of degeneracy, is dramatically enhanced. These results are in excellent agreement with experimental observations.
Focus on coherent control of complex quantum systems
Whaley, Birgitta; Milburn, Gerard
2015-10-01
The rapid growth of quantum information sciences over the past few decades has fueled a corresponding rise in high profile applications in fields such as metrology, sensors, spintronics, and attosecond dynamics, in addition to quantum information processing. Realizing this potential of today’s quantum science and the novel technologies based on this requires a high degree of coherent control of quantum systems. While early efforts in systematizing methods for high fidelity quantum control focused on isolated or closed quantum systems, recent advances in experimental design, measurement and monitoring, have stimulated both need and interest in the control of complex or large scale quantum systems that may also be coupled to an interactive environment or reservoir. This focus issue brings together new theoretical and experimental work addressing the formulation and implementation of quantum control for a broad range of applications in quantum science and technology today.
Intertwining Symmetry Algebras of Quantum Superintegrable Systems
Calzada, Juan A; del Olmo, Mariano A; 10.3842/SIGMA.2009.039
2009-01-01
We present an algebraic study of a kind of quantum systems belonging to a family of superintegrable Hamiltonian systems in terms of shape-invariant intertwinig operators, that span pairs of Lie algebras like $(su(n),so(2n))$ or $(su(p,q),so(2p,2q))$. The eigenstates of the associated Hamiltonian hierarchies belong to unitary representations of these algebras. It is shown that these intertwining operators, related with separable coordinates for the system, are very useful to determine eigenvalues and eigenfunctions of the Hamiltonians in the hierarchy. An study of the corresponding superintegrable classical systems is also included for the sake of completness.
Quantum decoherence in the theory of open systems
Isar, A.
2007-01-01
In the framework of the Lindblad theory for open quantum systems, we determine the degree of quantum decoherence of a harmonic oscillator interacting with a thermal bath. It is found that the system manifests a quantum decoherence which is more and more significant in time. We calculate also the decoherence time scale and analyze the transition from quantum to classical behaviour of the considered system.
Simulating quantum systems on classical computers with matrix product states
Kleine, Adrian
2010-01-01
In this thesis, the numerical simulation of strongly-interacting many-body quantum-mechanical systems using matrix product states (MPS) is considered. Compared to classical systems, quantum many-body systems possess an exponentially enlarged number of degrees of freedom, significantly complicating a simulation on a classical computer. Matrix-Product-States are a novel representation of arbitrary quantum many-body states. Using quantum information theory, it is possible to show that Matrix-Pro...
Multiple-state quantum Otto engine, 1D box system
Quantum heat engines produce work using quantum matter as their working substance. We studied adiabatic and isochoric processes and defined the general force according to quantum system. The processes and general force are used to evaluate a quantum Otto engine based on multiple-state of one dimensional box system and calculate the efficiency. As a result, the efficiency depends on the ratio of initial and final width of system under adiabatic processes
Multiple-state quantum Otto engine, 1D box system
Latifah, E.; Purwanto, A.
2014-03-01
Quantum heat engines produce work using quantum matter as their working substance. We studied adiabatic and isochoric processes and defined the general force according to quantum system. The processes and general force are used to evaluate a quantum Otto engine based on multiple-state of one dimensional box system and calculate the efficiency. As a result, the efficiency depends on the ratio of initial and final width of system under adiabatic processes.
General System theory, Like-Quantum Semantics and Fuzzy Sets
Licata, Ignazio
2007-01-01
It is outlined the possibility to extend the quantum formalism in relation to the requirements of the general systems theory. It can be done by using a quantum semantics arising from the deep logical structure of quantum theory. It is so possible taking into account the logical openness relationship between observer and system. We are going to show how considering the truth-values of quantum propositions within the context of the fuzzy sets is here more useful for systemics . In conclusion we...
Construction of a quantum repeater based on a quantum dot in an optical microcavity system
We investigate an efficient quantum repeater protocol based on quantum dots (QDs) and optical microcavity coupled systems. The proposed system can be used for long-distance quantum entanglement distribution, exploiting the interaction between single photons and QDs embedded in optical microcavities. We present the entanglement generation and entanglement swapping modules with QDs in microcavity systems and generalize it to quantum repeaters. The utilization of QDs and coupled cavities leads to a high success probability for the generation of entanglement. By using current and near future technology, entanglement with a high fidelity can be achieved and robust quantum communication over long-distance channels is feasible. (letters)
Mixing properties of quantum systems
We generalize the classical notion of topological mixing for automorphisms of C*-algebras in two ways. We show that for Galilean invariant Fermi systems the weaker form of mixing is satisfied. With some additional requirement on the range of the interaction we can also demonstrate the stronger mixing property. (Author)
Quantum response of dephasing open systems
We develop a theory of adiabatic response for open systems governed by Lindblad evolutions. The theory determines the dependence of the response coefficients on the dephasing rates and allows for residual dissipation even when the ground state is protected by a spectral gap. We give the quantum response a geometric interpretation in terms of Hilbert space projections: for a two-level system and, more generally, for systems with a suitable functional form of the dephasing, the dissipative and non-dissipative parts of the response are linked to a metric and to a symplectic form. The metric is the Fubini-Study metric and the symplectic form is the adiabatic curvature. When the metric and symplectic structures are compatible, the non-dissipative part of the inverse matrix of response coefficients turns out to be immune to dephasing. We give three examples of physical systems whose quantum states induce compatible metric and symplectic structures on control space: qubit, coherent states and a model of the integer quantum Hall effect.
Nonequilibrium representative ensembles for isolated quantum systems
An isolated quantum system is considered, prepared in a nonequilibrium initial state. In order to uniquely define the system dynamics, one has to construct a representative statistical ensemble. From the principle of least action it follows that the role of the evolution generator is played by a grand Hamiltonian, but not merely by its energy part. A theorem is proved expressing the commutators of field operators with operator products through variational derivatives of these products. A consequence of this theorem is the equivalence of the variational equations for field operators with the Heisenberg equations for the latter. A finite quantum system cannot equilibrate in the strict sense. But it can tend to a quasi-stationary state characterized by ergodic averages and the appropriate representative ensemble depending on initial conditions. Microcanonical ensemble, arising in the eigenstate thermalization, is just a particular case of representative ensembles. Quasi-stationary representative ensembles are defined by the principle of minimal information. The latter also implies the minimization of an effective thermodynamic potential. -- Highlights: ? The evolution of a nonequilibrium isolated quantum system is considered. ? The grand Hamiltonian is shown to be the evolution generator. ? A theorem is proved connecting operator commutators with variational derivatives. ? Quasi-stationary states are described by representative ensembles. ? These ensembles, generally, depend on initial conditions.
Path integrals for dimerized quantum spin systems
Foussats, Adriana, E-mail: afoussats@gmail.co [Facultad de Ciencias Exactas, Ingenieria y Agrimensura and Instituto de Fisica Rosario (UNR-CONICET), Av. Pellegrini 250, 2000 Rosario (Argentina); Greco, Andres [Facultad de Ciencias Exactas, Ingenieria y Agrimensura and Instituto de Fisica Rosario (UNR-CONICET), Av. Pellegrini 250, 2000 Rosario (Argentina); Muramatsu, Alejandro [Institut fuer Theoretische Physik III, Universitaet Stuttgart, Pfaffenwaldring 57, D-70550 Stuttgart (Germany)
2011-01-11
Dimerized quantum spin systems may appear under several circumstances, e.g. by a modulation of the antiferromagnetic exchange coupling in space, or in frustrated quantum antiferromagnets. In general, such systems display a quantum phase transition to a Neel state as a function of a suitable coupling constant. We present here two path-integral formulations appropriate for spin S=1/2 dimerized systems. The first one deals with a description of the dimers degrees of freedom in an SO(4) manifold, while the second one provides a path-integral for the bond-operators introduced by Sachdev and Bhatt. The path-integral quantization is performed using the Faddeev-Jackiw symplectic formalism for constrained systems, such that the measures and constraints that result from the algebra of the operators is provided in both cases. As an example we consider a spin-Peierls chain, and show how to arrive at the corresponding field-theory, starting with both an SO(4) formulation and bond-operators.
Path integrals for dimerized quantum spin systems
Dimerized quantum spin systems may appear under several circumstances, e.g. by a modulation of the antiferromagnetic exchange coupling in space, or in frustrated quantum antiferromagnets. In general, such systems display a quantum phase transition to a Neel state as a function of a suitable coupling constant. We present here two path-integral formulations appropriate for spin S=1/2 dimerized systems. The first one deals with a description of the dimers degrees of freedom in an SO(4) manifold, while the second one provides a path-integral for the bond-operators introduced by Sachdev and Bhatt. The path-integral quantization is performed using the Faddeev-Jackiw symplectic formalism for constrained systems, such that the measures and constraints that result from the algebra of the operators is provided in both cases. As an example we consider a spin-Peierls chain, and show how to arrive at the corresponding field-theory, starting with both an SO(4) formulation and bond-operators.
Path integrals for dimerized quantum spin systems
Foussats, Adriana; Greco, Andrés; Muramatsu, Alejandro
2011-01-01
Dimerized quantum spin systems may appear under several circumstances, e.g. by a modulation of the antiferromagnetic exchange coupling in space, or in frustrated quantum antiferromagnets. In general, such systems display a quantum phase transition to a Néel state as a function of a suitable coupling constant. We present here two path-integral formulations appropriate for spin S=1/2 dimerized systems. The first one deals with a description of the dimers degrees of freedom in an SO(4) manifold, while the second one provides a path-integral for the bond-operators introduced by Sachdev and Bhatt. The path-integral quantization is performed using the Faddeev-Jackiw symplectic formalism for constrained systems, such that the measures and constraints that result from the algebra of the operators is provided in both cases. As an example we consider a spin-Peierls chain, and show how to arrive at the corresponding field-theory, starting with both an SO(4) formulation and bond-operators.
Multimode optomechanical system in the quantum regime
Nielsen, William H P; Møller, Christoffer B; Polzik, Eugene S; Schliesser, Albert
2016-01-01
We realise a simple and robust optomechanical system with a multitude of long-lived ($Q>10^7$) mechanical modes in a phononic-bandgap shielded membrane resonator. An optical mode of a compact Fabry-Perot resonator detects these modes' motion with a measurement rate ($96~\\mathrm{kHz}$) that exceeds the mechanical decoherence rates already at moderate cryogenic temperatures ($10\\,\\mathrm{K}$). Reaching this quantum regime entails, i.~a., quantum measurement backaction exceeding thermal forces, and thus detectable optomechanical quantum correlations. In particular, we observe ponderomotive squeezing of the output light mediated by a multitude of mechanical resonator modes, with quantum noise suppression up to -2.4 dB (-3.6 dB if corrected for detection losses) and bandwidths $\\lesssim 90\\,\\mathrm{ kHz}$. The multi-mode nature of the employed membrane and Fabry-Perot resonators lends itself to hybrid entanglement schemes involving multiple electromagnetic, mechanical, and spin degrees of freedom.
The Quantum as an Emergent System
Groessing, Gerhard; Pascasio, Johannes Mesa; Schwabl, Herbert; 10.1088/1742-6596/361/1/012008
2012-01-01
Double slit interference is explained with the aid of what we call "21stcentury classical physics". We model a particle as an oscillator ("bouncer") in a thermal context, which is given by some assumed "zero-point" field of the vacuum. In this way, the quantum is understood as an emergent system, i.e., a steady-state system maintained by a constant throughput of (vacuum) energy. To account for the particle's thermal environment, we introduce a "path excitation field", which derives from the thermodynamics of the zero-point vacuum and which represents all possible paths a particle can take via thermal path fluctuations. The intensity distribution on a screen behind a double slit is calculated, as well as the corresponding trajectories and the probability density current. Further, particular features of the relative phase are shown to be responsible for nonlocal effects not only in ordinary quantum theory, but also in our classical approach.
Decoherence in infinite quantum systems
Hellmich, Mario
2009-01-01
Die Quantenmechanik gilt heute als unsere grundlegendste physikalische Theorie. Als solche beschränkt sie sich nicht nur auf ihre ursprünglichen Anwendungsbereiche wie die Atomphysik, Elementarteilchenphysik und die Quantenfeldtheorie, sondern ihr Gegenstandsbereich sollte auch makroskopische Systeme einschließen, die den Gesetzen der klassischen Physik gehorchen. Hier stößt man jedoch auf ein fundamentales Problem: Wendet man die Gesetze der Quantenmechanik direkt auf die Objekte unserer All...
Controllability of multi-partite quantum systems and selective excitation of quantum dots
We consider the degrees of controllability of multi-partite quantum systems, as well as necessary and sufficient criteria for each case. The results are applied to the problem of simultaneous control of an ensemble of quantum dots with a single laser pulse. Finally, we apply optimal control techniques to demonstrate selective excitation of individual dots for a simultaneously controllable ensemble of quantum dots
Effective Equations of Motion for Quantum Systems
Bojowald, M.; A. Skirzewski
2006-01-01
In many situations, one can approximate the behavior of a quantum system, i.e. a wave function subject to a partial differential equation, by effective classical equations which are ordinary differential equations. A general method and geometrical picture is developed and shown to agree with effective action results, commonly derived through path integration, for perturbations around a harmonic oscillator ground state. The same methods are used to describe dynamical coherent states, which in ...
Quantum Statistical Mechanics for Nonextensive Systems II
Lenzi, E. K.; R. S. Mendes; Rajagopal, A. K.
1999-01-01
In this paper, the Green function theory of quantum many-particle systems recently presented is reworked within the framework of nonextensive statistical mechanics with a new normalized $q$-expectation values. This reformulation introduces a renormalization of temperature of the earlier theory and a self-consistency condition. The linear response theory is also presented, along with its two-particle Green function version. Finally, a Boltzmann transport-like equation is also developed here.
Classical and quantum chaos in atomic systems
Atomic systems played a major role in the birth and growth of quantum mechanics. One central idea was to relate the well-known classical motion of the electron of a hydrogen atom--an ellipsis around the nucleus--to the experimentally observed quantization of the energy levels. This is the aim of the Bohr and Bohr-Sommerfeld models. These simple semiclassical models were unable to make any reliable prediction on the energy spectrum of the next simplest atom, helium. Because of the great success of quantum mechanics, the problem of correspondence between the classical and the quantal dynamics has not received much attention in the last 60 years. The fundamental question is (Gutzwiller, 1990). How can classical mechanics be understood as a limiting case within quantum mechanics? For systems with time-independent one-dimensional dynamics like the harmonic oscillator and the hydrogen atom, the correspondence is well understood. The restriction to such simple cases creates the erroneous impression that the classical behavior of simple systems is entirely comprehensible and easily described. During the last 20 years it has been recognized that this in not true and that a complex behavior can be obtained from simple equations of motion. This usually happens when the motion is chaotic, that is, unpredictable on a long time scale although perfectly deterministic (Henon, 1983). A major problem is that of understanding how the regular or chaotic behavior of the classical system is manifest in its quantum properties, especially in the semiclassical limit. 53 refs., 15 figs., 1 tab
Open quantum systems and random matrix theory
A simple model for open quantum systems is analyzed with RMT. The system is coupled to the continuum in a minimal way. In this paper we see the effect of opening the system on the level statistics, in particular the level spacing, width distribution and Δ3(L) statistic are examined as a function of the strength of this coupling. The usual super-radiant state is observed, and it is seen that as it is formed, the level spacing and Δ3(L) statistic exhibit the signatures of missed levels
Open quantum systems and Random Matrix Theory
Mulhall, Declan
2014-01-01
A simple model for open quantum systems is analyzed with Random Matrix Theory. The system is coupled to the continuum in a minimal way. In this paper we see the effect of opening the system on the level statistics, in particular the $\\Delta_3(L)$ statistic, width distribution and level spacing are examined as a function of the strength of this coupling. A super-radiant transition is observed, and it is seen that as it is formed, the level spacing and $\\Delta_3(L)$ statistic exhibit the signat...
The quantum $H_3$ integrable system
Garca, Marcos A.G.(William I. Fine Theoretical Physics Institute, School of Physics and Astronomy, University of Minnesota, 116 Church Street SE, Minneapolis, MN 55455, U.S.A.); Turbiner, Alexander V.
2010-01-01
The quantum $H_3$ integrable system is a 3D system with rational potential related to the non-crystallographic root system $H_3$. It is shown that the gauge-rotated $H_3$ Hamiltonian as well as one of the integrals, when written in terms of the invariants of the Coxeter group $H_3$, is in algebraic form: it has polynomial coefficients in front of derivatives. The Hamiltonian has infinitely-many finite-dimensional invariant subspaces in polynomials, they form the infinite flag with the charact...
Nonlocal realistic theories and continuous quantum systems
Hauber, Anna; Freyberger, Matthias [Institut fuer Quantenphysik, Universitaet Ulm, D-89069 Ulm (Germany)
2009-07-01
Recently, a certain class of non-local, realistic theories (NLRT) has been formulated for two-particle systems with dichotomic observables and has been shown to be incompatible with quantum mechanics and with experimental data. The proof us es inequalities for correlation functions, as in the original Bell case. We study how to expand the formulation to systems with continuous variables and demonst rate how such systems can violate the predictions of the NLRT. Moreover, we analyze how violations of the NLRT-inequalities are related to violations of Bell-type inequalities.
Macroscopic models for quantum systems and computers
Aerts, Diederik [Center Leo Apostel, Vrije Universiteit Brussel, Krijgskundestraat 33, 1160 Brussels (Belgium); Czachor, Marek [Katedra Fizyki Teoretycznej i Metod Matematycznych, Politechnika Gdanska, 80-952 Gdansk (Poland); Dehaene, Jeroen [SISTA, Department of Electrical Engineering (ESAT), Faculty of Engineering, Katholieke Universiteit Leuven, 3000 Leuven (Belgium); Moor, Bart De [SISTA, Department of Electrical Engineering (ESAT), Faculty of Engineering, Katholieke Universiteit Leuven, 3000 Leuven (Belgium); D' Hooghe, Bart [Center Leo Apostel, Vrije Universiteit Brussel, Krijgskundestraat 33, 1160 Brussels (Belgium)
2007-05-15
We present examples of macroscopic systems entailing a quantum mechanical structure. One of our examples has a structure which is isomorphic to the spin structure for a spin 1/2 and another system entails a structure isomorphic to the structure of two spin 1/2 in the entangled singlet state. We elaborate this system by showing that an arbitrary tensor product state representing two entangled qubits can be described in a complete way by a specific internal constraint between the ray or density states of the two qubits, which describes the behavior of the state of one of the spins if measurements are executed on the other spin. Since any n-qubit unitary operation can be decomposed into 2-qubit gates and unary operations, we argue that our representation of 2-qubit entanglement contributes to a better understanding of the role of n-qubit entanglement in quantum computation. We illustrate our approach on two 2-qubit algorithms proposed by Deutsch, respectively Arvind et al. One of the advantages of the 2-qubit case besides its relative simplicity is that it allows for a nice geometrical representation of entanglement, which contributes to a more intuitive grasp of what is going on in a 2-qubit quantum computation.
Time fractional development of quantum systems
Ertik, Hüseyin; Demirhan, Doǧan; Şirin, Hüseyin; Büyükkılıç, Fevzi
2010-08-01
In this study, the effect of time fractionalization on the development of quantum systems is taken under consideration by making use of fractional calculus. In this context, a Mittag-Leffler function is introduced as an important mathematical tool in the generalization of the evolution operator. In order to investigate the time fractional evolution of the quantum (nano) systems, time fractional forms of motion are obtained for a Schrödinger equation and a Heisenberg equation. As an application of the concomitant formalism, the wave functions, energy eigenvalues, and probability densities of the potential well and harmonic oscillator are time fractionally obtained via the fractional derivative order α, which is a measure of the fractality of time. In the case α =1, where time becomes homogenous and continuous, traditional physical conclusions are recovered. Since energy and time are conjugate to each other, the fractional derivative order α is relevant to time. It is understood that the fractionalization of time gives rise to energy fluctuations of the quantum (nano) systems.
Time fractional development of quantum systems
In this study, the effect of time fractionalization on the development of quantum systems is taken under consideration by making use of fractional calculus. In this context, a Mittag-Leffler function is introduced as an important mathematical tool in the generalization of the evolution operator. In order to investigate the time fractional evolution of the quantum (nano) systems, time fractional forms of motion are obtained for a Schroedinger equation and a Heisenberg equation. As an application of the concomitant formalism, the wave functions, energy eigenvalues, and probability densities of the potential well and harmonic oscillator are time fractionally obtained via the fractional derivative order α, which is a measure of the fractality of time. In the case α=1, where time becomes homogenous and continuous, traditional physical conclusions are recovered. Since energy and time are conjugate to each other, the fractional derivative order α is relevant to time. It is understood that the fractionalization of time gives rise to energy fluctuations of the quantum (nano) systems.
Preparation of Quantum Gates for Open Quantum Systems by Lyapunov Control Method
Wen, Jie; Cong, Shuang
2016-03-01
In this paper the control laws of preparing quantum gates are designed based on Lyapunov stability theorem for two level open quantum systems. We propose a novel Lyapunov function according to the matrix logarithm function, which has higher accuracy and faster convergence speed by comparing them with those of the Lyapunov function of distance. Based on the proposed function, we design two types of control laws to prepare quantum gates for different systems including Markovian quantum systems with phase damping and amplitude damping, non-Markovian quantum systems and closed quantum systems. Furthermore, the system robustness when the Hamiltonian contains uncertainty is further investigated. In order to verify the superiorities of proposed function and control method, NOT gates are prepared by the designed control laws for different systems in the numerical experiments, and the results are comparatively analyzed.
Quantum coherence and correlations in cold atom systems
Szańkowski, Piotr
2015-01-01
Although the foundations of quantum and classical physics are much different, it is often difficult to pinpoint which features of a particular system are intrinsically "quantum". Perhapse, the most clear-cut distinction between "classical" and "quantum" can be made for systems composed of many particles when the properties of the ensemble are determined by the correlations between the constituents. The issue of grasping the nature of entanglement (i.e. quantum correlations) lies in its formal...
Zhou Ping; Deng Fuguo; Zhou Hongyu [The Key Laboratory of Beam Technology and Material Modification of Ministry of Education, and Institute of Low Energy Nuclear Physics, Beijing Normal University, Beijing 100875 (China)], E-mail: fgdeng@bnu.edu.cn
2009-03-15
We present a method for probabilistic quantum entanglement swapping between high-dimensional pure entangled systems by introducing only one auxiliary two-level particle. The probability of successful entanglement swapping is just the entanglement of the quantum channel. It can be used for practical long-distance quantum communication efficiently. We present a quantum secret sharing scheme based on quantum entanglement swapping with high-dimensional pure entangled systems. It has the advantage of having high intrinsic qubit efficiency and high capacity. Moreover, it greatly reduces the classical information exchanged for creating the private key.
Quantum Information Biology: From Theory of Open Quantum Systems to Adaptive Dynamics
Asano, Masanari; Basieva, Irina; Khrennikov, Andrei; Ohya, Masanori; Tanaka, Yoshiharu; Yamato, Ichiro
This chapter reviews quantum(-like) information biology (QIB). Here biology is treated widely as even covering cognition and its derivatives: psychology and decision making, sociology, and behavioral economics and finances. QIB provides an integrative description of information processing by bio-systems at all scales of life: from proteins and cells to cognition, ecological and social systems. Mathematically QIB is based on the theory of adaptive quantum systems (which covers also open quantum systems). Ideologically QIB is based on the quantum-like (QL) paradigm: complex bio-systems process information in accordance with the laws of quantum information and probability. This paradigm is supported by plenty of statistical bio-data collected at all bio-scales. QIB re ects the two fundamental principles: a) adaptivity; and, b) openness (bio-systems are fundamentally open). In addition, quantum adaptive dynamics provides the most generally possible mathematical representation of these principles.
Quantum entanglement in condensed matter systems
Laflorencie, Nicolas
2015-01-01
This review focuses on the field of quantum entanglement applied to condensed matter physics systems with strong correlations, a domain which has rapidly grown over the last decade. By tracing out part of the degrees of freedom of correlated quantum systems, useful and non-trivial informations can be obtained through the study of the reduced density matrix, whose eigenvalue spectrum (the entanglement spectrum) and the associated R\\'enyi entropies are now well recognized to contains key features. In particular, the celebrated area law for the entanglement entropy of ground-states will be discussed from the perspective of its subleading corrections which encode universal details of various quantum states of matter, e.g. symmetry breaking states or topological order. Going beyond entropies, the study of the low-lying part of the entanglement spectrum also allows to diagnose topological properties or give a direct access to the excitation spectrum of the edges, and may also raise significant questions about the u...
Quantum Spin Systems after DLS1978
Nachtergaele, B
2006-01-01
In their 1978 paper, Dyson, Lieb, and Simon (DLS) proved the existence of Ne'el order at positive temperature for the spin-S Heisenberg antiferromagnet on the d-dimensional hypercubic lattice when either S >= 1 and d >= 3 or S=1/2 and d is sufficiently large. This was the first proof of spontaneous breaking of a continuous symmetry in a quantum model at finite temperature. Since then the ideas of DLS have been extended and adapted to a variety of other problems. In this paper will present an overview of the most important developments in the study of the Heisenberg model and related quantum lattice systems since 1978, including but not restricted to those directly related to the paper by DLS.
Colloquium: Non-Markovian dynamics in open quantum systems
Breuer, Heinz-Peter; Laine, Elsi-Mari; Piilo, Jyrki; Vacchini, Bassano
2016-04-01
The dynamical behavior of open quantum systems plays a key role in many applications of quantum mechanics, examples ranging from fundamental problems, such as the environment-induced decay of quantum coherence and relaxation in many-body systems, to applications in condensed matter theory, quantum transport, quantum chemistry, and quantum information. In close analogy to a classical Markovian stochastic process, the interaction of an open quantum system with a noisy environment is often modeled phenomenologically by means of a dynamical semigroup with a corresponding time-independent generator in Lindblad form, which describes a memoryless dynamics of the open system typically leading to an irreversible loss of characteristic quantum features. However, in many applications open systems exhibit pronounced memory effects and a revival of genuine quantum properties such as quantum coherence, correlations, and entanglement. Here recent theoretical results on the rich non-Markovian quantum dynamics of open systems are discussed, paying particular attention to the rigorous mathematical definition, to the physical interpretation and classification, as well as to the quantification of quantum memory effects. The general theory is illustrated by a series of physical examples. The analysis reveals that memory effects of the open system dynamics reflect characteristic features of the environment which opens a new perspective for applications, namely, to exploit a small open system as a quantum probe signifying nontrivial features of the environment it is interacting with. This Colloquium further explores the various physical sources of non-Markovian quantum dynamics, such as structured environmental spectral densities, nonlocal correlations between environmental degrees of freedom, and correlations in the initial system-environment state, in addition to developing schemes for their local detection. Recent experiments addressing the detection, quantification, and control of non-Markovian quantum dynamics are also briefly discussed.
Low-rank driving in quantum systems
A new property of quantum systems called low-rank driving is introduced. Numerous simplifications in the solution of the time-dependent Schroedinger equation are pointed out for systems having this property. These simplifications are in the areas of finding eigenvalues, taking the Laplace transform, converting Schroedinger's equation to an integral form, discretizing the continuum, generalizing the Weisskopf-Wigner approximation, band-diagonalizing the Hamiltonian, finding new exact solutions to Schroedinger's equation, and so forth. The principal physical application considered is the phenomenon of coherent populations-trapping in continuum-continuum interactions
Many-body Wigner quantum systems
We present examples of many-body Wigner quantum systems. The position and the momentum operators RA and PA, A = 1, ..., n + 1, of the particles are noncanonical and are chosen so that Heisenberg and the Hamiltonian equations are identical. The spectrum of the energy with respect to the centre of mass is equidistant and has finite number of energy levels. The composite system is spread in a small volume around the centre of mass and within it the geometry is noncommutative. The underlying statistics is an exclusion statistics. (author). 23 refs
Geometric scaling in the quantum Hall system
The transitions between neighbouring plateaux in the quantum Hall system are observed to follow 'anti-holomorphic' scaling with 'superuniversal' scaling exponents, showing that the system contains an emergent sub-modular discrete symmetry and a holomorphic structure at low energies. We identify a class of effective scaling models consistent with this data, which is parametrized by the complex structure of a torus with a special spin structure, in which only the number of fermions (c) remains undetermined. For c=2 this gives the superuniversal anti-holomorphic scaling potential previously inferred from data, with scaling exponent ??2.6, in reasonable agreement with available scaling data
Parallel decoherence in composite quantum systems
M Dugići; J Jeknić-Dugić
2012-08-01
For the standard quantum Brownian motion (QBM) model, we point out the occurrence of simultaneous (parallel), mutually irreducible and autonomous decoherence processes. Besides the standard Brownian particle, we show that there is at least another system undergoing the dynamics described by the QBM model. We do this by selecting the two mutually irreducible, global structures (decompositions into subsystems) of the composite system of the QBM model. The generalization of this observation is a new, challenging task in the foundations of the decoherence theory. We do not place our findings in any interpretational context.
Quantum Optical Systems for the Implementation of Quantum Information Processing
Ralph, T. C.
2006-01-01
We review the field of Quantum Optical Information from elementary considerations through to quantum computation schemes. We illustrate our discussion with descriptions of experimental demonstrations of key communication and processing tasks from the last decade and also look forward to the key results likely in the next decade. We examine both discrete (single photon) type processing as well as those which employ continuous variable manipulations. The mathematical formalism is kept to the mi...
Propagation of Disturbances in Degenerate Quantum Systems
Chancellor, Nicholas
2011-01-01
Disturbances in gapless quantum many-body models are known to travel an unlimited distance throughout the system. Here, we explore this phenomenon in finite clusters with degenerate ground states. The specific model studied here is the one-dimensional J1-J2 Heisenberg Hamiltonian at and close to the Majumdar-Ghosh point. Both open and periodic boundary conditions are considered. Quenches are performed using a local magnetic field. The degenerate Majumdar-Ghosh ground state allows disturbances which carry quantum entanglement to propagate throughout the system, and thus dephase the entire system within the degenerate subspace. These disturbances can also carry polarization, but not energy, as all energy is stored locally. The local evolution of the part of the system where energy is stored drives the rest of the system through long-range entanglement. We also examine approximations for the ground state of this Hamiltonian in the strong field limit, and study how couplings away from the Majumdar-Ghosh point aff...
Description of an open quantum mechanical system
A model for the description of an open quantum mechanical many-particle system is formulated. It starts from the shell model and treats the continuous states by a coupled channels method. The mixing of the discrete shell model states via the continuum of decay channels results in the genuine decaying states of the system. These states are eigenstates of a non-Hermitean Hamilton operator the eigenvalues of which give both the energies and the widths of the states. All correlations between two particles which are caused by the two-particle residual interaction, are taken into account including those via the continuum. In the formalism describing the open quantum mechanical system, the coupling between the system and its environment appears nonlinearly. If the resonance states start to overlap, a redistribution of the spectroscopic values ('trapping effect') takes place. As a result, the complexity of the system is reduced at high level density, structures in space and time are formed. This redistribution describes, on the one hand, the transition from the well-known nuclear properties at low level density to those at high level density and fits, on the other hand, into the concept of selforganization. (orig.)
Integrable quantum Stäckel systems
The Stäckel separability of a Hamiltonian system is well known to ensure existence of a complete set of Poisson commuting integrals of motion quadratic in the momenta. We consider a class of Stäckel separable systems where the entries of the Stäckel matrix are monomials in the separation variables. We show that the only systems in this class for which the integrals of motion arising from the Stäckel construction keep commuting after quantization are, up to natural equivalence transformations, the so-called Benenti systems. Moreover, it turns out that the latter are the only quantum separable systems in the class under study.
Integrable quantum Stäckel systems
Błaszak, Maciej, E-mail: blaszakm@amu.edu.pl [Faculty of Physics, Adam Mickiewicz University, Umultowska 85, 61-614 Poznań (Poland); Domański, Ziemowit, E-mail: ziemowit@amu.edu.pl [Faculty of Physics, Adam Mickiewicz University, Umultowska 85, 61-614 Poznań (Poland); Sergyeyev, Artur, E-mail: Artur.Sergyeyev@math.slu.cz [Mathematical Institute, Silesian University in Opava, Na Rybníčku 1, 746 01 Opava (Czech Republic); Szablikowski, Błażej M., E-mail: bszablik@amu.edu.pl [Faculty of Physics, Adam Mickiewicz University, Umultowska 85, 61-614 Poznań (Poland)
2013-11-15
The Stäckel separability of a Hamiltonian system is well known to ensure existence of a complete set of Poisson commuting integrals of motion quadratic in the momenta. We consider a class of Stäckel separable systems where the entries of the Stäckel matrix are monomials in the separation variables. We show that the only systems in this class for which the integrals of motion arising from the Stäckel construction keep commuting after quantization are, up to natural equivalence transformations, the so-called Benenti systems. Moreover, it turns out that the latter are the only quantum separable systems in the class under study.
Topological entanglement entropy in bilayer quantum Hall systems
Chung, Myung-Hoon
2013-01-01
We calculate the topological entanglement entropy in bilayer quantum Hall systems, dividing the set of quantum numbers into four parts. This topological entanglement entropy allows us to draw a phase diagram in the parameter space of layer separation and tunneling amplitude. We perform the finite size scaling analysis of the topological entanglement entropy in order to see the quantum phase transition clearly.
A toy model of a macroscopic quantum coherent system
Muoz-Vega, R.; Flores-Godoy, J. J.; Fernndez-Anaya, G.; Salinas-Hernndez, E.
2013-03-01
This paper deals with macroscopic quantum coherence while using only basic quantum mechanics. A square double well is used to illustrate Leggett-Caldeira oscillations. The effect of thermal radiation on two-level systems is discussed. The concept of decoherence is introduced at an elementary level. Reference values are deduced for the energy, temperature and time scales involved in macroscopic quantum coherence.
A toy model of a macroscopic quantum coherent system
This paper deals with macroscopic quantum coherence while using only basic quantum mechanics. A square double well is used to illustrate Leggett–Caldeira oscillations. The effect of thermal radiation on two-level systems is discussed. The concept of decoherence is introduced at an elementary level. Reference values are deduced for the energy, temperature and time scales involved in macroscopic quantum coherence. (paper)
Comparison of quantum discord and relative entropy in some bipartite quantum systems
Mahdian, M.; Arjmandi, M. B.
2016-04-01
The study of quantum correlations in high-dimensional bipartite systems is crucial for the development of quantum computing. We propose relative entropy as a distance measure of correlations may be measured by means of the distance from the quantum state to the closest classical-classical state. In particular, we establish relations between relative entropy and quantum discord quantifiers obtained by means of orthogonal projection measurements. We show that for symmetrical X-states density matrices the quantum discord is equal to relative entropy. At the end of paper, various examples of X-states such as two-qubit and qubit-qutrit have been demonstrated.
Controlled Population Transfer in a Double Quantum Dot System
We study the potential for controlled population transfer between the ground states of two anharmonic coupled quantum dots. We propose a method based on the interaction of the quantum dot structure with external electromagnetic fields. The interaction of the quantum dot system with the electromagnetic fields is studied with the use of the time-dependent Schroedinger equation. We present numerical results for an asymmetric quantum dot structure
Controlled Population Transfer in a Double Quantum Dot System
Fountoulakis, Antonios; Terzis, Andreas F.; Paspalakis, Emmanuel
2007-12-01
We study the potential for controlled population transfer between the ground states of two anharmonic coupled quantum dots. We propose a method based on the interaction of the quantum dot structure with external electromagnetic fields. The interaction of the quantum dot system with the electromagnetic fields is studied with the use of the time-dependent Schrdinger equation. We present numerical results for an asymmetric quantum dot structure.
A neural-network-like quantum information processing system
Perus, Mitja; Bischof, Horst
2003-01-01
The Hopfield neural networks and the holographic neural networks are models which were successfully simulated on conventional computers. Starting with these models, an analogous fundamental quantum information processing system is developed in this article. Neuro-quantum interaction can regulate the "collapse"-readout of quantum computation results. This paper is a comprehensive introduction into associative processing and memory-storage in quantum-physical framework.
The transition to chaos conservative classical systems and quantum manifestations
Reichl, Linda E
2004-01-01
This book provides a thorough and comprehensive discussion of classical and quantum chaos theory for bounded systems and for scattering processes Specific discussions include • Noether’s theorem, integrability, KAM theory, and a definition of chaotic behavior • Area-preserving maps, quantum billiards, semiclassical quantization, chaotic scattering, scaling in classical and quantum dynamics, dynamic localization, dynamic tunneling, effects of chaos in periodically driven systems and stochastic systems • Random matrix theory and supersymmetry The book is divided into several parts Chapters 2 through 4 deal with the dynamics of nonlinear conservative classical systems Chapter 5 and several appendices give a thorough grounding in random matrix theory and supersymmetry techniques Chapters 6 and 7 discuss the manifestations of chaos in bounded quantum systems and open quantum systems respectively Chapter 8 focuses on the semiclassical description of quantum systems with underlying classical chaos, and Chapt...
Contemporary commercial quantum information security systems
Gnatyuk, Sergiy; Riabyi, Myroslav; Zhmurko, Tetiana
2013-01-01
Quantum cryptography has attracted considerable interest among specialists in information security. The overwhelming majority of research projects in quantum cryptography are related to the development of quantum key distribution protocols. Absence of generalized classification & systematization makes it difficult to estimate the level of the latest achievements and does not allow using quantum technologies with full efficiency. From this viewpoint the analysis of existed quantum key distr...
Corato, V [Seconda Universita di Napoli, Dipartimento di Ingegneria dell' Informazione and INFM, I-81031 Aversa (Italy); Rombetto, S [Seconda Universita di Napoli, Dipartimento di Ingegneria dell' Informazione and INFM, I-81031 Aversa (Italy); Silvestrini, P [Seconda Universita di Napoli, Dipartimento di Ingegneria dell' Informazione and INFM, I-81031 Aversa (Italy); Granata, C [Istituto di Cibernetica ' E. Caianiello' CNR, I-80078 Pozzuoli (Italy); Russo, R [Istituto di Cibernetica ' E. Caianiello' CNR, I-80078 Pozzuoli (Italy); Ruggiero, B [Istituto di Cibernetica ' E. Caianiello' CNR, I-80078 Pozzuoli (Italy)
2004-05-01
We present the experimental observation of the effects of macroscopic quantum tunnelling in a SQUID device, consisting of a rf SQUID coupled to a readout system based on a dc SQUID sensor. Data on the decay rate from the metastable flux states of a rf SQUID are reported, both in the classical and quantum regimes. The low dissipation level and the good insulation of the probe from external noise are encouraging in view of building a macroscopic quantum coherent system.
We present the experimental observation of the effects of macroscopic quantum tunnelling in a SQUID device, consisting of a rf SQUID coupled to a readout system based on a dc SQUID sensor. Data on the decay rate from the metastable flux states of a rf SQUID are reported, both in the classical and quantum regimes. The low dissipation level and the good insulation of the probe from external noise are encouraging in view of building a macroscopic quantum coherent system
On the notion of a macroscopic quantum system
Khrenikov, A Yu
2004-01-01
We analyse the notion of macroscopic quantum system from the point of view of the statistical structure of quantum theory. We come to conclusion that the presence of interference of probabilities should be used the main characteristic of quantumness (in the opposition to N. Bohr who permanently emphasized the crucial role of quantum action). In the light of recent experiments with statistical ensembles of people who produced interference of probabilities for special pairs of questions (which can be considered as measurements on people) human being should be considered as a macroscopic quantum system. There is also discussed relation with experiments of A. Zeilinger on interference of probabilities for macromoleculas.
Some aspects of quantum entanglement for CAR systems
Moriya, Hajime
2001-01-01
We study quantum entanglement for CAR systems. Since the subsystems of disjoint regions are not independent for CAR systems, there are some distinct features of quantum entanglement which cannot be observed in tensor product systems. We show the failure of triangle inequality of von Neumann and the possible increase of entanglement degree under operations done in a local region for a bipartite CAR system.
Quantum MIMO n-Systems and Conditions for Stability
Mansourbeigi, Seyed M H
2009-01-01
In this paper we present some conditions for the (strong) stabilizability of an n-D Quantum MIMO system P(X). It contains two parts. The first part is to introduce the n-D Quantum MIMO systems where the coefficients vary in the algebra of Q-meromorphic functions. Then we introduce some conditions for the stabilizability of these systems. The second part is to show that this Quantum system has the n-D system as its quantum limit and the results for the SISO,SIMO,MISO,MIMO are obtained again as special cases.
Superconducting system for adiabatic quantum computing
Corato, V [Dipartimento di Ingegneria dell' Informazione, Second University of Naples, 81031 Aversa (Italy); Roscilde, T [Department of Physics and Astronomy, University of Southern California, Los Angeles, CA 90089-0484 (Canada); Ruggiero, B [Istituto di Cibernetica ' E.Caianiello' del CNR, I-80078, Pozzuoli (Italy); Granata, C [Istituto di Cibernetica ' E.Caianiello' del CNR, I-80078, Pozzuoli (Italy); Silvestrini, P [Dipartimento di Ingegneria dell' Informazione, Second University of Naples, 81031 Aversa (Italy)
2006-06-01
We study the Hamiltonian of a system of inductively coupled flux qubits, which has been theoretically proposed for adiabatic quantum computation to handle NP problems. We study the evolution of a basic structure consisting of three coupled rf-SQUIDs upon tuning the external flux bias, and we show that the adiabatic nature of the evolution is guaranteed by the presence of the single-SQUID gap. We further propose a scheme and the first realization of an experimental device suitable for verifying the theoretical results.
Analytic Representation of Finite Quantum Systems
Zhang, S
2004-01-01
A transform between functions in R and functions in Zd is used to define the analogue of number and coherent states in the context of finite d-dimensional quantum systems. The coherent states are used to define an analytic representation in terms of theta functions. All states are represented by entire functions with growth of order 2, which have exactly d zeros in each cell. The analytic function of a state is constructed from its zeros. Results about the completeness of finite sets of coherent states within a cell are derived.
Analytic representation of finite quantum systems
Zhang, S.; Vourdas, A.
2004-08-01
A transform between functions in {\\bb R} and functions in {\\bb Z}_d is used to define the analogue of number and coherent states in the context of finite d-dimensional quantum systems. The coherent states are used to define an analytic representation in terms of theta functions. All states are represented by entire functions with growth of order 2, which have exactly d zeros in each cell. The analytic function of a state is constructed from its zeros. Results about the completeness of finite sets of coherent states within a cell are derived.
Analytic Representation of Finite Quantum Systems
Zhang, S.; Vourdas, A.
2005-01-01
A transform between functions in R and functions in Zd is used to define the analogue of number and coherent states in the context of finite d-dimensional quantum systems. The coherent states are used to define an analytic representation in terms of theta functions. All states are represented by entire functions with growth of order 2, which have exactly d zeros in each cell. The analytic function of a state is constructed from its zeros. Results about the completeness of finite sets of coher...
Analytic representation of finite quantum systems
Zhang, S; Vourdas, A [Department of Computing, University of Bradford, Bradford BD7 1DP (United Kingdom)
2004-08-27
A transform between functions in R and functions in Z{sub d} is used to define the analogue of number and coherent states in the context of finite d-dimensional quantum systems. The coherent states are used to define an analytic representation in terms of theta functions. All states are represented by entire functions with growth of order 2, which have exactly d zeros in each cell. The analytic function of a state is constructed from its zeros. Results about the completeness of finite sets of coherent states within a cell are derived.
Superconducting system for adiabatic quantum computing
We study the Hamiltonian of a system of inductively coupled flux qubits, which has been theoretically proposed for adiabatic quantum computation to handle NP problems. We study the evolution of a basic structure consisting of three coupled rf-SQUIDs upon tuning the external flux bias, and we show that the adiabatic nature of the evolution is guaranteed by the presence of the single-SQUID gap. We further propose a scheme and the first realization of an experimental device suitable for verifying the theoretical results
Scattering properties of an open quantum system
We study the scattering properties of an open quantum system, in terms of the complex poles of the analytically continued energy Green's function. We use a model for which many dynamical properties can be expressed analytically. We first study particle wave scattering and compute the Wigner delay times. Then, using perturbation theory, we compute the photodetachment rate due to a weak time-periodic electric field. In addition, we show that the model we use qualitatively reproduces several features of the experimentally obtained photodetachment cross section of H- ions and gives interesting insight into the mechanism underlying the photodetachment of H- ions. (c) 2000 The American Physical Society
Measuring entanglement entropy in a quantum many-body system
Islam, Rajibul; Ma, Ruichao; Preiss, Philipp M.; Eric Tai, M.; Lukin, Alexander; Rispoli, Matthew; Greiner, Markus
2015-12-01
Entanglement is one of the most intriguing features of quantum mechanics. It describes non-local correlations between quantum objects, and is at the heart of quantum information sciences. Entanglement is now being studied in diverse fields ranging from condensed matter to quantum gravity. However, measuring entanglement remains a challenge. This is especially so in systems of interacting delocalized particles, for which a direct experimental measurement of spatial entanglement has been elusive. Here, we measure entanglement in such a system of itinerant particles using quantum interference of many-body twins. Making use of our single-site-resolved control of ultracold bosonic atoms in optical lattices, we prepare two identical copies of a many-body state and interfere them. This enables us to directly measure quantum purity, Rnyi entanglement entropy, and mutual information. These experiments pave the way for using entanglement to characterize quantum phases and dynamics of strongly correlated many-body systems.
Measuring entanglement entropy in a quantum many-body system.
Islam, Rajibul; Ma, Ruichao; Preiss, Philipp M; Tai, M Eric; Lukin, Alexander; Rispoli, Matthew; Greiner, Markus
2015-12-01
Entanglement is one of the most intriguing features of quantum mechanics. It describes non-local correlations between quantum objects, and is at the heart of quantum information sciences. Entanglement is now being studied in diverse fields ranging from condensed matter to quantum gravity. However, measuring entanglement remains a challenge. This is especially so in systems of interacting delocalized particles, for which a direct experimental measurement of spatial entanglement has been elusive. Here, we measure entanglement in such a system of itinerant particles using quantum interference of many-body twins. Making use of our single-site-resolved control of ultracold bosonic atoms in optical lattices, we prepare two identical copies of a many-body state and interfere them. This enables us to directly measure quantum purity, Rényi entanglement entropy, and mutual information. These experiments pave the way for using entanglement to characterize quantum phases and dynamics of strongly correlated many-body systems. PMID:26632587
Spectra of nonlocally bound quantum systems
Sowa, A.
2011-06-01
We discuss a class of nonlinear and nonlocal models for the dynamics of a composite quantum system. The models in question depend on the following constituents: on two subsystem Hamiltonians (denoted by H and Ĥ), an analytic function ( f), and a real parameter ( s). As demonstrated elsewhere before, the stationary states can be described in these models fairly explicitly. In this article, we build upon that result, and discuss the topological as well as statistical characteristics of the spectra. Here, we concentrate on the special case f = log. It turns out that an energy spectrum of the nonlocally bound system substantially differs from that of its components. Indeed, we show rigorously that, if H is the harmonic oscillator and Ĥ is completely degenerate with one energy level, then the energy spectrum of the composite system has the topology of the Cantor set (for s > 2). In addition, we show that, if H is replaced by the logarithm of the harmonic oscillator, then the spectrum consists of finitely many intervals separated by gaps (for s sufficiently large). In the last case, the key analytic object is the series Σ n - s . In particular, as an interesting offshoot, this structure furnishes a nontautological immersion of fundamental number-theoretic functions into the quantum formalism.
Optimal dynamics for quantum-state and entanglement transfer through homogeneous quantum systems
The capability of faithfully transmit quantum states and entanglement through quantum channels is one of the key requirements for the development of quantum devices. Different solutions have been proposed to accomplish such a challenging task, which, however, require either an ad hoc engineering of the internal interactions of the physical system acting as the channel or specific initialization procedures. Here we show that optimal dynamics for efficient quantum-state and entanglement transfer can be attained in generic quantum systems with homogeneous interactions by tuning the coupling between the system and the two attached qubits. We devise a general procedure to determine the optimal coupling, and we explicitly implement it in the case of a channel consisting of a spin-(1/2)XY chain. The quality of quantum-state and entanglement transfer is found to be very good and, remarkably, almost independent of the channel length.
Quantum field theory of optical soliton constrained systems
The system of a optical soliton can be described by a singular Lagrangian. To our knowledge, the commutation relations and quantum equations of motion are given by using corresponding principle, it's not satisfactory since the constraints are ignored. In this paper, the commutation relations and quantum equations of motion are derived based on the Dirac theory of constrained systems. The conserved energy, momentum and the number of particles for this system are discussed at the quantum level
Quantum Field Induced Orderings in Fully Frustrated Ising Spin Systems
Tanaka, Shu; Hirano, Masaki; Miyashita, Seiji
2010-01-01
We study ordering mechanisms which are induced by the quantum fluctuation in fully frustrated Ising spin systems. Since there are many degenerated states in frustrated systems, "order by thermal disorder" often takes place due to a kind of entropy effect. To consider "order by quantum disorder" in fully frustrated Ising spin systems, we apply transverse field as quantum fluctuation. There exists a ferromagnetic correlation in each sublattice. The sublattice correlation at zero temperature is ...
Emergent kinetic constraints in open quantum systems
Everest, B; Garrahan, J P; Lesanovsky, I
2016-01-01
Kinetically constrained spin systems play an important role in understanding key properties of the dynamics of slowly relaxing materials, such as glasses. So far kinetic constraints have been introduced in idealised models aiming to capture specific dynamical properties of these systems. However, recently it has been experimentally shown by [M. Valado et al., arXiv:1508.04384 (2015)] that manifest kinetic constraints indeed govern the evolution of strongly interacting gases of highly excited atoms in a noisy environment. Motivated by this development we address and discuss the question concerning the type of kinetically constrained dynamics which can generally emerge in quantum spin systems subject to strong noise. We discuss an experimentally-realizable case which displays collective behavior, timescale separation and dynamical reducibility.
Level statistics for quantum Hall systems
Level statistics for two classes of disordered systems at criticality are analyzed in terms of different realizations of the Chalker-Coddington network model. These include: 1) Re-examination of the standard U(1) model describing dynamics of electrons on the lowest Landau level in the quantum Hall effect, where it is shown that after proper local unfolding the nearest-neighbor spacing distribution (NNSD) at the critical energy follows the Wigner surmise for Gaussian unitary ensembles (GUE). 2) Quasi-particles in disordered superconductors with broken time reversal and spin rotation invariance (in the language of random matrix theory this system is a representative of symmetry class D in the classification scheme of Altland and Zirnbauer). Here again the NNSD obeys the Wigner surmise for GUE, reflecting therefore only 'basic' discrete symmetries of the system (time reversal violation) and ignoring particle-hole symmetries and other finer details (criticality). In the localized regime level repulsion is suppressed
Asymptotically open quantum systems; Asymptotisch offene Quantensysteme
Westrich, M.
2008-04-15
In the present thesis we investigate the structure of time-dependent equations of motion in quantum mechanics.We start from two coupled systems with an autonomous equation of motion. A limit, in which the dynamics of one of the two systems has a decoupled evolution and imposes a non-autonomous evolution for the second system is identified. A result due to K. Hepp that provides a classical limit for dynamics turns out to be part and parcel for this limit and is generalized in our work. The method introduced by J.S. Howland for the solution of the time-dependent Schroedinger equation is interpreted as such a limit. Moreover, we associate our limit with the modern theory of quantization. (orig.)
Quantum Integrable Systems from Conformal Blocks
Chen, Heng-Yu
2016-01-01
In this note, we extend the striking connections between quantum integrable systems and conformal blocks recently found in http://arxiv.org/abs/1602.01858 in several directions. First, we explicitly demonstrate that the action of quartic conformal Casimir operator on general d-dimensional scalar conformal blocks, can be expressed in terms of certain combinations of commuting integrals of motions of the two particle hyperbolic BC2 Calogero-Sutherland system. The permutation and reflection properties of the underlying Dunkl operators play crucial roles in establishing such a connection. Next, we show that the scalar superconformal blocks in SCFTs with four and eight supercharges and suitable chirality constraints can also be identified with the eigenfunctions of the same Calogero-Sutherland system, this demonstrates the universality of such a connection. Finally, we observe that the so-called "seed" conformal blocks for constructing four point functions for operators with arbitrary space-time spins in four dime...
Quantum revivals and magnetization tunneling in effective spin systems
Krizanac, M.; Altwein, D.; Vedmedenko, E. Y.; Wiesendanger, R.
2016-03-01
Quantum mechanical objects or nano-objects have been proposed as bits for information storage. While time-averaged properties of magnetic, quantum-mechanical particles have been extensively studied experimentally and theoretically, experimental investigations of the real time evolution of magnetization in the quantum regime were not possible until recent developments in pump-probe techniques. Here we investigate the quantum dynamics of effective spin systems by means of analytical and numerical treatments. Particular attention is paid to the quantum revival time and its relation to the magnetization tunneling. The quantum revival time has been initially defined as the recurrence time of a total wave-function. Here we show that the quantum revivals of wave-functions and expectation values in spin systems may be quite different which gives rise to a more sophisticated definition of the quantum revival within the realm of experimental research. Particularly, the revival times for integer spins coincide which is not the case for half-integer spins. Furthermore, the quantum revival is found to be shortest for integer ratios between the on-site anisotropy and an external magnetic field paving the way to novel methods of anisotropy measurements. We show that the quantum tunneling of magnetization at avoided level crossing is coherent to the quantum revival time of expectation values, leading to a connection between these two fundamental properties of quantum mechanical spins.
On synthesis of linear quantum stochastic systems by pure cascading
Nurdin, Hendra I
2010-01-01
Recently, it has been demonstrated that an arbitrary linear quantum stochastic system can be realized as a cascade connection of simple one degree of freedom quantum harmonic oscillators together with a direct interaction Hamiltonian which is bilinear in the canonical operators of the oscillators. However, from an experimental point of view, realizations by pure cascading, without a direct interaction Hamiltonian, would be much simpler to implement and this raises the natural question of what class of linear quantum stochastic systems are realizable by cascading alone. This paper gives a precise characterization of this class of linear quantum stochastic systems and then it is proved that, in the weaker sense of transfer function realizability, all passive linear quantum stochastic systems belong to this class. A constructive example is given to show the transfer function realization of a two degrees of freedom passive linear quantum stochastic system by pure cascading.
Quantum Circuit Design for Solving Linear Systems of Equations
Cao, Yudong; Frankel, Steven; Kais, Sabre
2011-01-01
Recently, it has been demonstrated that quantum computers can be used for solving linear systems of algebraic equations with exponential speedup compared with classical computers. Here, we present a generic quantum circuit design for implementing the algorithm for solving linear systems. In particular, we show the detailed construction of a quantum circuit which solves a 4 by 4 linear system with 7 qubits. It consists of only the basic quantum gates that can be realized with present physical devices, implying great possibility for experimental implementation. Furthermore, the performance of the circuit is numerically simulated and its ability to solve the intended linear system is verified.
Probability representation of kinetic equation for open quantum system
Man'ko, V I; Shchukin, E V
2003-01-01
The tomographic probability distribution is used to decribe the kinetic equations for open quantum systems. Damped oscillator is studied. Purity parameter evolution for different damping regime is considered.
Kinetic equations for a nonideal quantum system
Bornath, Th.; Kremp, D.; Kraeft, W. D.; Schlanges, M.
1996-10-01
In the framework of real-time Green's functions, the general kinetic equations are investigated in a first-order gradient expansion. Within this approximation, the problem of the reconstruction of the two-time correlation functions from the one-time Wigner function was solved. For the Wigner function, a cluster expansion is found in terms of a quasiparticle distribution function. In equilibrium, this expansion leads to the well-known generalized Beth-Uhlenbeck expression of the second virial coefficient. As a special case, the T-matrix approximation for the self-energy is investigated. The quantum kinetic equation derived thus has, besides the (Markovian) Boltzmann collision integral, additional terms due to the retardation expansion which reflect memory effects. Special interest is paid to the case that bound states exist in the system. It is shown that the bound state contribution, which can be introduced via a bilinear expansion of the two-particle T matrix, follows from the first-order retardation term in the general kinetic equation. The full Wigner function is now a sum of one function describing the unbound particles and another one for the bound state contribution. The latter two functions have to be determined from a coupled set of kinetic equations. In contrast to the quantum Boltzmann equation, energy and density of a nonideal system are conserved.
Simple quantum system as a source of coherent information
The set of the simplest quantum systems is analyzed from the viewpoint of the coherent information volume, available by application of the corresponding information channels. It is shown, the coherent information for simple quantum models may be calculated and used for evaluating the potential possibilities of the corresponding quantum channels as a source of physical information in the experiments, related to the effects of the quantum states coherence. The following physical models: the two-level atom in the laser radiation fields; the combination of the two-level subsystems in the multilevel atom (hydrogen); the system of the two-level atoms in the process of combined quantum-determined evolution and under the effect of the quantum measurement and quantum duplication transformants; as well as one or two level atoms in the process of radiation, are considered
Correlations, quantum entanglement and interference in nanoscopic systems
Several of the most interesting quantum effects can or could be observed in nanoscopic systems. For example, the effect of strong correlations between electrons and of quantum interference can be measured in transport experiments through quantum dots, wires, individual molecules and rings formed by large molecules or arrays of quantum dots. In addition, quantum coherence and entanglement can be clearly observed in quantum corrals. In this paper we present calculations of transport properties through Aharonov–Bohm strongly correlated rings where the characteristic phenomenon of charge–spin separation is clearly observed. Additionally quantum interference effects show up in transport through π-conjugated annulene molecules producing important effects on the conductance for different source–drain configurations, leading to the possibility of an interesting switching effect. Finally, elliptic quantum corrals offer an ideal system to study quantum entanglement due to their focalizing properties. Because of an enhanced interaction between impurities localized at the foci, these systems also show interesting quantum dynamical behaviour and offer a challenging scenario for quantum information experiments
Quantum field theory in stationary coordinate systems
Quantum field theory is examined in stationary coordinate systems in Minkowski space. Preliminary to quantization of the scalar field, all of the possible stationary coordinate systems in flat spacetime are classified and explicitly constructed. Six distinct classes of such systems are found. Of these six, three have (identical) event horizons associated with them and five have Killing horizons. Two classes have distinct Killing and event horizons, with an intervening region analogous to the ergosphere in rotating black holes. Particular representatives of each class are selected for subsequent use in the quantum field theory. The scalar field is canonically quantized and a vacuum defined in each of the particular coordinate systems chosen. The vacuum states can be regarded as adapted to the six classes of stationary motions. There are only two vacuum states found, the Minkowski vacuum in those coordinate systems without event horizons and the Fulling vacuum in those with event horizons. The responses of monopole detectors traveling along stationary world lines are calculated in both the Minkowski and Fulling vacuums. The responses for each class of motions are distinct from those for every other class. A vacuum defined by the response of a detector must therefore not be equivalent in general to a vacuum defined by canonical quantization. Quantization of the scalar field within a rotating wedge is examined. It has not been possible to construct mode functions satisfying appropriate boundary conditions on the surface of the wedge. The asymptotic form of the renormalized stress tensor near the surfaces had been calculated and is found to include momentum terms which represent a circulation of energy within the wedge
Quantum and statistical mechanics in open systems: theory and examples
Zueco, David
2009-01-01
Using the system-bath model Hamiltonian this thesis covers the equilibrium and out of equilibrium properties of quantum open systems. Topics included are the calculation of thermodynamical quantities of open systems, derivation of quantum master equations, phase space and numerical methods and Linear and non Linear Response Theory. Applications are the transport in periodic potentials and the dynamics of spins.
Stationary states of two-level open quantum systems
A problem of finding stationary states of open quantum systems is addressed. We focus our attention on a generic type of open system: a qubit coupled to its environment. We apply the theory of block operator matrices and find stationary states of two-level open quantum systems under certain conditions applied on both the qubit and the surrounding.
Stationary states of two-level open quantum systems
Gardas, Bartlomiej; Puchala, Zbigniew
2010-01-01
A problem of finding stationary states of open quantum systems is addressed. We focus our attention on a generic type of open system: a qubit coupled to its environment. We apply the theory of block operator matrices and find stationary states of two--level open quantum systems under certain conditions applied both on the qubit and the surrounding.
Holonomic Quantum Control with Continuous Variable Systems
Albert, Victor V.; Shu, Chi; Krastanov, Stefan; Shen, Chao; Liu, Ren-Bao; Yang, Zhen-Biao; Schoelkopf, Robert J.; Mirrahimi, Mazyar; Devoret, Michel H.; Jiang, Liang
2016-04-01
Universal computation of a quantum system consisting of superpositions of well-separated coherent states of multiple harmonic oscillators can be achieved by three families of adiabatic holonomic gates. The first gate consists of moving a coherent state around a closed path in phase space, resulting in a relative Berry phase between that state and the other states. The second gate consists of "colliding" two coherent states of the same oscillator, resulting in coherent population transfer between them. The third gate is an effective controlled-phase gate on coherent states of two different oscillators. Such gates should be realizable via reservoir engineering of systems that support tunable nonlinearities, such as trapped ions and circuit QED.
On the kinetic theory of quantum systems
The contents of this thesis which deals with transport phenomena of specific gases, plasmas and fluids, can be separated into two distinct parts. In the first part a statistical way is suggested to estimate the neutrino mass. Herefore use is made of the fact that massive neutrinos possess a non-zero volume viscosity in contrast with massless neutrinos. The second part deals with kinetic theory of strongly condensed quantum systems of which examples in nature are: liquid Helium, heavy nuclei, electrons in a metal and the interior of stars. In degenerate systems fermions in general interact strongly so that ordinary kinetic theory is not directly applicable. For such cases Landau-Fermi-liquid theory, in which the strongly interacting particles are replaced by much weaker interacting quasiparticles, proved to be very useful. A method is developed in this theory to calculate transport coefficients. Applications of this method on liquid 3Helium yield surprisingly good agreement with experimental results for thermal conductivities. (Auth.)
Uncertainty relations, quantum and thermal fluctuations in Lindblad theory of open quantum systems
In the framework of the Lindblad theory for open quantum systems we derive closed analytical expressions of the uncertainty relation for a particle moving in a harmonic oscillator potential. The particle is in arbitrarily squeezed initial state and interacts with an environment at finite temperature. We examine how the quantum and thermal fluctuations of the environment contribute to the uncertainty in the canonical variables of the systems and study their relative importance in the evolution of the system towards equilibrium with be aim of clarifying the meaning of quantum, classical and thermal dissipation of energy. We show that upon contact with the bath the system evolves from a quantum-dominated state to a thermal-dominated state in a time which is of the same order as the decoherence time calculated before in similar models in the context of a transition from quantum mechanics to classical mechanics. (authors)
Constructing quantum games from a system of Bell's inequalities
We report constructing quantum games directly from a system of Bell's inequalities using Arthur Fine's analysis published in early 1980s. This analysis showed that such a system of inequalities forms a set of both necessary and sufficient conditions required to find a joint distribution function compatible with a given set of joint probabilities, in terms of which the system of Bell's inequalities is usually expressed. Using the setting of a quantum correlation experiment for playing a quantum game, and considering the examples of Prisoners' Dilemma and Matching Pennies, we argue that this approach towards constructing quantum games addresses some of their well-known criticisms.
On microstates counting in many body polymer quantum systems
Polymer quantum systems are mechanical models quantized in a similar way as loop quantum gravity but in which loops/graphs resembling polymers are replaced by discrete sets of points. Such systems have allowed to study in a simpler context some novel aspects of loop quantum gravity. Although thermal aspects play a crucial role in cosmology and black hole physics little attention has been given to the thermostatistics of many body polymer quantum systems. In this work we explore how the features of a one-dimensional effective polymer gas, affect its microstate counting and hence the corresponding thermodynamical quantities.
Concepts and methods in the theory of open quantum systems
Breuer, Heinz-Peter; Petruccione, Francesco
2003-01-01
The central physical concepts and mathematical techniques used in the theory of open quantum systems are reviewed. Particular emphasis is laid on the interrelations of apparently different approaches. Starting from the appropriate characterization of the quantum statistical ensembles naturally arising in the description of open quantum systems, the corresponding dynamical evolution equations are derived for the Markovian as well as for the non-Markovian case.
Optimal correlations in many-body quantum systems
Amico, Luigi; Rossini, Davide; Hamma, Alioscia; Korepin, Vladimir E.(International Institute of Physics, Universidade Federal do Rio Grande do Norte, Natal, RN, 59078-400, Brazil)
2011-01-01
Information and correlations in a quantum system are closely related through the process of measurement. We explore such relation in a many-body quantum setting, effectively bridging between quantum metrology and condensed matter physics. To this aim we adopt the information-theory view of correlations, and study the amount of correlations after certain classes of Positive-Operator-Valued Measurements are locally performed. As many-body system we consider a one-dimensional array of interactin...
Shrinked systems. Quantum physics on new paths
This introducing textbook for students of higher semesters of physics, chemistry, and informatics treats a in latest time dynamically expanding field of physics. This book deals among others with the themes quantum information theory, quantum communications, quantum computing, teleportation, hidden parameters, which-way-marking, quantum measuring process, POVM, quantum channels and mediates by this not only a deepened understanding of quantum theory but also basic science, in order to follow the fast development of the field respectively to enter a special field of research. Commented recommendations for further literature as well as exercise problems help the reader to find quickly a founded approach to the theoretical foundations of future key technologies. The book can be made to a base of courses and seminars. Because the required basic knowledge in mathematics and quantum theory is presented in introductory chapters, the book is also suited for the self-study
Computable measure of total quantum correlations of multipartite systems
Behdani, Javad; Akhtarshenas, Seyed Javad; Sarbishaei, Mohsen
2016-04-01
Quantum discord as a measure of the quantum correlations cannot be easily computed for most of density operators. In this paper, we present a measure of the total quantum correlations that is operationally simple and can be computed effectively for an arbitrary mixed state of a multipartite system. The measure is based on the coherence vector of the party whose quantumness is investigated as well as the correlation matrix of this part with the remainder of the system. Being able to detect the quantumness of multipartite systems, such as detecting the quantum critical points in spin chains, alongside with the computability characteristic of the measure, makes it a useful indicator to be exploited in the cases which are out of the scope of the other known measures.
Investigating non-Markovian dynamics of quantum open systems
Chen, Yusui
Quantum open system coupled to a non-Markovian environment has recently attracted widespread interest for its important applications in quantum information processing and quantum dissipative systems. New phenomena induced by the non-Markovian environment have been discovered in variety of research areas ranging from quantum optics, quantum decoherence to condensed matter physics. However, the study of the non-Markovian quantum open system is known a difficult problem due to its technical complexity in deriving the fundamental equation of motion and elusive conceptual issues involving non-equilibrium dynamics for a strong coupled environment. The main purpose of this thesis is to introduce several new techniques of solving the quantum open systems including a systematic approach to dealing with non-Markovian master equations from a generic quantum-state diffusion (QSD) equation. In the first part of this thesis, we briefly introduce the non-Markovian quantum-state diffusion approach, and illustrate some pronounced non-Markovian quantum effects through numerical investigation on a cavity-QED model. Then we extend the non-Markovian QSD theory to an interesting model where the environment has a hierarchical structure, and find out the exact non-Markovian QSD equation of this model system. We observe the generation of quantum entanglement due to the interplay between the non-Markovian environment and the cavity. In the second part, we show an innovative method to obtain the exact non-Markovian master equations for a set of generic quantum open systems based on the corresponding non-Markovian QSD equations. Multiple-qubit systems and multilevel systems are discussed in details as two typical examples. Particularly, we derive the exact master equation for a model consisting of a three-level atom coupled to an optical cavity and controlled by an external laser field. Additionally, we discuss in more general context the mathematical similarity between the multiple-qubit systems and multilevel systems. Based on our systematic method, we also show how to solve different types of models. In the last part, we use Heisenberg equations of motion and quantum trajectory approach to obtain the exact master equation for a quantum harmonic oscillator chains coupled to two finite temperature environments. The derived exact non-Markovian master equation is useful for exploration of quantum transport and quantum coherence dynamics.
Mechanical Systems that are both Classical and Quantum
Margolus, Norman
2008-01-01
Quantum dynamics can be regarded as a generalization of classical finite-state dynamics. This is a familiar viewpoint for workers in quantum computation, which encompasses classical computation as a special case. Here this viewpoint is extended to mechanics, where classical dynamics has traditionally been viewed as a macroscopic approximation of quantum behavior, not as a special case. When a classical dynamics is recast as a special case of quantum dynamics, the quantum description can be interpreted classically. For example, sometimes extra information is added to the classical state in order to construct the quantum description. This extra information is then eliminated by representing it in a superposition as if it were unknown information about a classical statistical ensemble. This usage of superposition leads to the appearance of Fermions in the quantum description of classical lattice-gas dynamics and turns continuous-space descriptions of finite-state systems into illustrations of classical sampling ...
Realization of quantum state privacy amplification in a nuclear magnetic resonance quantum system
Hao, Liang; Wang, Chuan; Long, Gui Lu, E-mail: gllong@tsinghua.edu.c [Key Laboratory for Atomic and Molecular NanoSciences and Department of Physics, Tsinghua University, Beijing 100084 (China)
2010-06-28
Quantum state privacy amplification (QSPA) is the quantum analogue of classical privacy amplification. If the state information of a series of single-particle states has some leakage, QSPA reduces this leakage by condensing the state information of two particles into the state of one particle. Recursive applications of the operations will eliminate the quantum state information leakage to a required minimum level. In this paper, we report the experimental implementation of a quantum state privacy amplification protocol in a nuclear magnetic resonance system. The density matrices of the states are constructed in the experiment, and the experimental results agree well with theory.
Realization of quantum state privacy amplification in a nuclear magnetic resonance quantum system
Quantum state privacy amplification (QSPA) is the quantum analogue of classical privacy amplification. If the state information of a series of single-particle states has some leakage, QSPA reduces this leakage by condensing the state information of two particles into the state of one particle. Recursive applications of the operations will eliminate the quantum state information leakage to a required minimum level. In this paper, we report the experimental implementation of a quantum state privacy amplification protocol in a nuclear magnetic resonance system. The density matrices of the states are constructed in the experiment, and the experimental results agree well with theory.
Correlation Functions in Open Quantum-Classical Systems
Chang-Yu Hsieh
2013-12-01
Full Text Available Quantum time correlation functions are often the principal objects of interest in experimental investigations of the dynamics of quantum systems. For instance, transport properties, such as diffusion and reaction rate coefficients, can be obtained by integrating these functions. The evaluation of such correlation functions entails sampling from quantum equilibrium density operators and quantum time evolution of operators. For condensed phase and complex systems, where quantum dynamics is difficult to carry out, approximations must often be made to compute these functions. We present a general scheme for the computation of correlation functions, which preserves the full quantum equilibrium structure of the system and approximates the time evolution with quantum-classical Liouville dynamics. Several aspects of the scheme are discussed, including a practical and general approach to sample the quantum equilibrium density, the properties of the quantum-classical Liouville equation in the context of correlation function computations, simulation schemes for the approximate dynamics and their interpretation and connections to other approximate quantum dynamical methods.
Automated drawing system of quantum energy levels
The purpose of this work is to derive an automated system that provides advantageous drawings of energy spectra for quantum systems (nuclei, atoms, molecules, etc.) required in various physical sciences. The automation involves the development of appropriate computational code and graphical imaging system based on raw data insertion, theoretical calculations and experimental or bibliographic data insertion. The system determines the appropriate scale to depict graphically with the best possible way in the available space. The presently developed code operates locally and the results are displayed on the screen and can be exported to a PostScript file. We note its main features to arrange and visualize in the available space the energy levels with their identity, taking care the existence in the final diagram the least auxiliary deviations. Future improvements can be the use of Java and the availability on the Internet. The work involves the automated plotting of energy levels in molecules, atoms, nuclei and other types of quantized energy spectra. The automation involves the development of an appropriate computational code and graphical imaging system
Automated drawing system of quantum energy levels
Stampoultzis, M.; Sinatkas, J.; Tsakstara, V.; Kosmas, T. S.
2014-03-01
The purpose of this work is to derive an automated system that provides advantageous drawings of energy spectra for quantum systems (nuclei, atoms, molecules, etc.) required in various physical sciences. The automation involves the development of appropriate computational code and graphical imaging system based on raw data insertion, theoretical calculations and experimental or bibliographic data insertion. The system determines the appropriate scale to depict graphically with the best possible way in the available space. The presently developed code operates locally and the results are displayed on the screen and can be exported to a PostScript file. We note its main features to arrange and visualize in the available space the energy levels with their identity, taking care the existence in the final diagram the least auxiliary deviations. Future improvements can be the use of Java and the availability on the Internet. The work involves the automated plotting of energy levels in molecules, atoms, nuclei and other types of quantized energy spectra. The automation involves the development of an appropriate computational code and graphical imaging system.
Maps for general open quantum systems and a theory of linear quantum error correction
We show that quantum subdynamics of an open quantum system can always be described by a linear, Hermitian map irrespective of the form of the initial total system state. Since the theory of quantum error correction was developed based on the assumption of completely positive (CP) maps, we present a generalized theory of linear quantum error correction, which applies to any linear map describing the open system evolution. In the physically relevant setting of Hermitian maps, we show that the CP-map-based version of quantum error correction theory applies without modifications. However, we show that a more general scenario is also possible, where the recovery map is Hermitian but not CP. Since non-CP maps have nonpositive matrices in their range, we provide a geometric characterization of the positivity domain of general linear maps. In particular, we show that this domain is convex and that this implies a simple algorithm for finding its boundary.
Quantum Liquid Crystal Phases in Strongly Correlated Fermionic Systems
Sun, Kai
2009-01-01
This thesis is devoted to the investigation of the quantum liquid crystal phases in strongly correlated electronic systems. Such phases are characterized by their partially broken spatial symmetries and are observed in various strongly correlated systems as being summarized in Chapter 1. Although quantum liquid crystal phases often involve
Quantum dissipative systems. 3. Definition and algebraic structure
It is shown that the operator for description of evolution of quantum dissipative systems leads to the fact that the Jacobi identity is not satisfied. In order to describe quantum dissipative systems it is necessary to use anti-commutative non-Lie algebra
On nonlinear evolution and supraluminal communication between finite quantum systems
Ferrero, M.; Salgado, D.; Sanchez-Gomez, J. L.
2005-01-01
We revise the 'no-signaling' condition for the supraluminal communication between two spatially separated finite quantum systems of arbitrary dimensions, thus generalizing a similar preceding approach for two-qubits: non-linear evolution does not necessarily imply the possibility of supraluminal communication between any sort of finite quantum systems.
Thermalization and pseudolocality in extended quantum systems
Doyon, Benjamin
2015-01-01
Recently, it was understood that extended concepts of locality played important roles in the study of extended quantum systems out of equilibrium, in particular in so-called generalized Gibbs ensembles. In this paper, we rigorously study pseudolocal charges and their involvement in time evolutions and in the thermalization process of arbitrary states with strong enough clustering properties. We show that the densities of pseudolocal charges form a Hilbert space, with inner product determined by response functions. Using this, we define the family of pseudolocal states: clustering states connected to the infinite-temperature state by paths whose tangents are actions of pseudolocal charges. This family includes thermal Gibbs states, as well as (a precise definition of) generalized Gibbs ensembles. We prove that the family of pseudolocal states is preserved by finite time evolution, and that, under certain conditions, the stationary state emerging at infinite time is a generalized Gibbs ensemble with respect to ...
Anions, quantum particles in planar systems
Our purpose here is to present a general review of the non-relativistic quantum-mechanical description of excitations that do not obey neither the Fermi-Dirac nor the Bose-Einstein statistics; they rather fulfill an intermediate statistics, the we called 'any-statistics'. As we shall see, this is a peculiarity of (1+1) and (1+2) dimensions, due to the fact that, in two space dimensions, the spin is not quantised, once the rotation group is Abelian. The relevance of studying theories in (1+2) dimensions is justified by the evidence that, in condensed matter physics, there are examples of planar systems, for which everything goes as if the third spatial dimension is frozen. (author)
Quantum integrable systems. Quantitative methods in biology
Feverati, Giovanni
2011-01-01
Quantum integrable systems have very strong mathematical properties that allow an exact description of their energetic spectrum. From the Bethe equations, I formulate the Baxter "T-Q" relation, that is the starting point of two complementary approaches based on nonlinear integral equations. The first one is known as thermodynamic Bethe ansatz, the second one as Kl\\"umper-Batchelor-Pearce-Destri- de Vega. I show the steps toward the derivation of the equations for some of the models concerned. I study the infrared and ultraviolet limits and discuss the numerical approach. Higher rank integrals of motion can be obtained, so gaining some control on the eigenvectors. After, I discuss the Hubbard model in relation to the N = 4 supersymmetric gauge theory. The Hubbard model describes hopping electrons on a lattice. In the second part, I present an evolutionary model based on Turing machines. The goal is to describe aspects of the real biological evolution, or Darwinism, by letting evolve populations of algorithms. ...
Experimental feedback control of quantum systems using weak measurements
Gillett, G G; Lanyon, B P; Almeida, M P; Barbieri, M; Pryde, G J; O'Brien, J L; Resch, K J; Bartlett, S D; White, A G
2009-01-01
A goal of the emerging field of quantum control is to develop methods for quantum technologies to function robustly in the presence of noise. Central issues are the fundamental limitations on the available information about quantum systems and the disturbance they suffer in the process of measurement. In the context of a simple quantum control scenario--the stabilization of non-orthogonal states of a qubit against dephasing--we experimentally explore the use of weak measurements in feedback control. We find that, despite the intrinsic difficultly of implementing them, weak measurements allow us to control the qubit better in practice than is even theoretically possible without them. Our work shows that these more general quantum measurements can play an important role for feedback control of quantum systems.
Hacking commercial quantum cryptography systems by tailored bright illumination
Lydersen, Lars; Wittmann, Christoffer; Elser, Dominique; Skaar, Johannes; Makarov, Vadim; 10.1038/NPHOTON.2010.214
2010-01-01
The peculiar properties of quantum mechanics allow two remote parties to grow a private, secret key, even if the eavesdropper can do anything permitted by the laws of nature. In quantum key distribution (QKD) the parties exchange non-orthogonal or entangled quantum states to generate quantum correlated classical data. Consequently, QKD implementations always rely on detectors to measure the relevant quantum property of the signal states. However, practical detectors are not only sensitive to quantum states. Here we show how an eavesdropper can exploit such deviations from the ideal behaviour: We demonstrate experimentally how the detectors in two commercially available QKD systems can be fully remote controlled using specially tailored bright illumination. This makes it possible to acquire the full secret key without leaving any trace; we propose an eavesdropping apparatus built of off-the-shelf components. The loophole is likely to be present in most QKD systems using avalanche photo diodes (APDs) to detect ...
Fate of classical solitons in one-dimensional quantum systems.
Pustilnik, M.; Matveev, K. A.
2015-11-23
We study one-dimensional quantum systems near the classical limit described by the Korteweg-de Vries (KdV) equation. The excitations near this limit are the well-known solitons and phonons. The classical description breaks down at long wavelengths, where quantum effects become dominant. Focusing on the spectra of the elementary excitations, we describe analytically the entire classical-to-quantum crossover. We show that the ultimate quantum fate of the classical KdV excitations is to become fermionic quasiparticles and quasiholes. We discuss in detail two exactly solvable models exhibiting such crossover, the Lieb-Liniger model of bosons with weak contact repulsion and the quantum Toda model, and argue that the results obtained for these models are universally applicable to all quantum one-dimensional systems with a well-defined classical limit described by the KdV equation.
The Geometric Phase in Quantum Systems
The discovery of the geometric phase is one of the most interesting and intriguing findings of the last few decades. It led to a deeper understanding of the concept of phase in quantum mechanics and motivated a surge of interest in fundamental quantum mechanical issues, disclosing unexpected applications in very diverse fields of physics. Although the key ideas underlying the existence of a purely geometrical phase had already been proposed in 1956 by Pancharatnam, it was Michael Berry who revived this issue 30 years later. The clarity of Berry's seminal paper, in 1984, was extraordinary. Research on the topic flourished at such a pace that it became difficult for non-experts to follow the many different theoretical ideas and experimental proposals which ensued. Diverse concepts in independent areas of mathematics, physics and chemistry were being applied, for what was (and can still be considered) a nascent arena for theory, experiments and technology. Although collections of papers by different authors appeared in the literature, sometimes with ample introductions, surprisingly, to the best of my knowledge, no specific and exhaustive book has ever been written on this subject. The Geometric Phase in Quantum Systems is the first thorough book on geometric phases and fills an important gap in the physical literature. Other books on the subject will undoubtedly follow. But it will take a fairly long time before other authors can cover that same variety of concepts in such a comprehensive manner. The book is enjoyable. The choice of topics presented is well balanced and appropriate. The appendices are well written, understandable and exhaustive - three rare qualities. I also find it praiseworthy that the authors decided to explicitly carry out most of the calculations, avoiding, as much as possible, the use of the joke 'after a straightforward calculation, one finds...' This was one of the sentences I used to dislike most during my undergraduate studies. A student is inexperienced in such matters and needs to look at details. This book is addressed to graduate physics and chemistry students and was written thinking of students. However, I would recommend it also to young and mature physicists, even those who are already 'into' the subject. It is a comprehensive work, jointly written by five researchers. After a simple introduction to the subject, the book gradually provides deeper concepts, more advanced theory and finally an interesting introduction and explanation of recent experiments. For its multidisciplinary features, this work could not have been written by one single author. The collaborative effort is undoubtedly one of its most interesting qualities. I would definitely recommend it to anyone who wants to learn more on the geometric phase, a topic that is both beautiful and intriguing. (book review)
Controlling open quantum systems: Tools, achievements, and limitations
Koch, Christiane P.
2016-01-01
The advent of quantum devices, which exploit the two essential elements of quantum physics, coherence and entanglement, has sparked renewed interest in the control of open quantum systems. Successful implementations face the challenge to preserve the relevant nonclassical features at the level of device operation. A major obstacle is decoherence which is caused by interaction with the environment. Optimal control theory is a tool that can be used to identify control strategies in the presence...
Quantum Circuit Design for Solving Linear Systems of Equations
Cao, Yudong; Daskin, Anmer; Frankel, Steven; Kais, Sabre
2011-01-01
Recently, it is shown that quantum computers can be used for obtaining certain information about the solution of a linear system Ax=b exponentially faster than what is possible with classical computation. Here we first review some key aspects of the algorithm from the standpoint of finding its efficient quantum circuit implementation using only elementary quantum operations, which is important for determining the potential usefulness of the algorithm in practical settings. Then we present a s...
Pole placement design for quantum systems via coherent observers
Miao, Zibo; James, Matthew R.; Ugrinovskii, Valery A.
2015-01-01
We previously extended Luenberger's approach for observer design to the quantum case, and developed a class of coherent observers which tracks linear quantum stochastic systems in the sense of mean values. In light of the fact that the Luenberger observer is commonly and successfully applied in classical control, it is interesting to investigate the role of coherent observers in quantum feedback. As the first step in exploring observer-based coherent control, in this paper we study pole-place...
Are quantum systems physical objects with physical properties ?
1999-01-01
Despite its power as the conceptual basis for a huge range of physical phenomena in atomic and subatomic physics, quantum mechanics still suffers from a lack of clarity regarding the physical meaning of its fundamental theoretical concepts such as those of quantum state and of quantum theoretical quantities or variables, dealt with by the known mathematical-theoretical rules. These concepts have generally been considered as not giving a direct description of physical systems, for they do not ...
Quantum Cost Efficient Reversible BCD Adder for Nanotechnology Based Systems
Islam, Md Saiful; Begum, Zerina
2011-01-01
Reversible logic allows low power dissipating circuit design and founds its application in cryptography, digital signal processing, quantum and optical information processing. This paper presents a novel quantum cost efficient reversible BCD adder for nanotechnology based systems using PFAG gate. It has been demonstrated that the proposed design offers less hardware complexity and requires minimum number of garbage outputs than the existing counterparts. The remarkable property of the proposed designs is that its quantum realization is given in NMR technology.
Entangled Systems New Directions in Quantum Physics
Audretsch, Jürgen
2007-01-01
An introductory textbook for advanced students of physics, chemistry and computer science, covering an area of physics that has lately witnessed rapid expansion. The topics treated here include quantum information, quantum communication, quantum computing, teleportation and hidden parameters, thus imparting not only a well-founded understanding of quantum theory as such, but also a solid basis of knowledge from which readers can follow the rapid development of the topic or delve deeper into a more specialized branch of research. Commented recommendations for further reading as well as end-of-chapter problems help the reader to quickly access the theoretical basics of future key technologies
Quantum-based electronic devices and systems selected topics in electronics and systems, v.14
Dutta, Mitra
1998-01-01
This volume includes highlights of the theories and experimental findings that underlie essential phenomena occurring in quantum-based devices and systems as well as the principles of operation of selected novel quantum-based electronic devices and systems. A number of the emerging approaches to creating new types of quantum-based electronic devices and systems are also discussed.
Classical and quantum simulations of many-body systems
Murg, Valentin
2008-04-07
This thesis is devoted to recent developments in the fields of classical and quantum simulations of many-body systems. We describe new classical algorithms that overcome problems apparent in conventional renormalization group and Monte Carlo methods. These algorithms make possible the detailed study of finite temperature properties of 2-D classical and 1-D quantum systems, the investigation of ground states of 2-D frustrated or fermionic systems and the analysis of time evolutions of 2-D quantum systems. Furthermore, we propose new 'analog' quantum simulators that are able to realize interesting models such as a Tonks-Girardeau gas or a frustrated spin-1/2 XY model on a trigonal lattice. These quantum simulators make use of optical lattices and trapped ions and are technically feasible. In fact, the Tonks-Girardeau gas has been realized experimentally and we provide a detailed comparison between the experimental data and the theoretical predictions. (orig.)
Classical and quantum simulations of many-body systems
This thesis is devoted to recent developments in the fields of classical and quantum simulations of many-body systems. We describe new classical algorithms that overcome problems apparent in conventional renormalization group and Monte Carlo methods. These algorithms make possible the detailed study of finite temperature properties of 2-D classical and 1-D quantum systems, the investigation of ground states of 2-D frustrated or fermionic systems and the analysis of time evolutions of 2-D quantum systems. Furthermore, we propose new ''analog'' quantum simulators that are able to realize interesting models such as a Tonks-Girardeau gas or a frustrated spin-1/2 XY model on a trigonal lattice. These quantum simulators make use of optical lattices and trapped ions and are technically feasible. In fact, the Tonks-Girardeau gas has been realized experimentally and we provide a detailed comparison between the experimental data and the theoretical predictions. (orig.)
Density matrix of strongly coupled quantum dot - microcavity system
Any two-level quantum system can be used as a quantum bit (qubit) - the basic element of all devices and systems for quantum information and quantum computation. Recently it was proposed to study the strongly coupled system consisting of a two-level quantum dot and a monoenergetic photon gas in a microcavity-the strongly coupled quantum dot-microcavity (QD-MC) system for short, with the Jaynes-Cumming total Hamiltonian, for the application in the quantum information processing. Different approximations were applied in the theoretical study of this system. In this work, on the basis of the exact solution of the Schrodinger equation for this system without dissipation we derive the exact formulae for its density matrix. The realization of a qubit in this system is discussed. The solution of the system of rate equation for the strongly coupled QD-MC system in the presence of the interaction with the environment was also established in the first order approximation with respect to this interaction.
Density matrix of strongly coupled quantum dot - microcavity system
Nguyen Van Hop [Hanoi National University of Education, 136 Xuan Thuy Road, Cau Giay Distr., Hanoi (Viet Nam)], E-mail: hopnvdhsp@yahoo.com
2009-09-01
Any two-level quantum system can be used as a quantum bit (qubit) - the basic element of all devices and systems for quantum information and quantum computation. Recently it was proposed to study the strongly coupled system consisting of a two-level quantum dot and a monoenergetic photon gas in a microcavity-the strongly coupled quantum dot-microcavity (QD-MC) system for short, with the Jaynes-Cumming total Hamiltonian, for the application in the quantum information processing. Different approximations were applied in the theoretical study of this system. In this work, on the basis of the exact solution of the Schrodinger equation for this system without dissipation we derive the exact formulae for its density matrix. The realization of a qubit in this system is discussed. The solution of the system of rate equation for the strongly coupled QD-MC system in the presence of the interaction with the environment was also established in the first order approximation with respect to this interaction.
Indirect control of quantum systems via an accessor: pure coherent control without system excitation
A pure indirect control of quantum systems via a quantum accessor is investigated. In this control scheme, we do not apply any external classical excitation fields on the controlled system and we control a quantum system via a quantum accessor and classical control fields control the accessor only. Complete controllability is investigated for arbitrary finite-dimensional quantum systems and exemplified by two- and three-dimensional systems. The scheme exhibits some advantages; it uses less qubits in the accessor and does not depend on the energy-level structure of the controlled system
Sliding Mode Control of Two-Level Quantum Systems
Dong, Daoyi; Petersen, Ian R
2010-01-01
This paper proposes a robust control method based on sliding mode design for two-level quantum systems with bounded uncertainties. An eigenstate of the two-level quantum system is identified as a sliding mode. The objective is to design a control law to steer the system's state into the sliding mode domain and then maintain it in that domain when bounded uncertainties exist in the system Hamiltonian. We propose a controller design method using the Lyapunov methodology and periodic projective ...
Trojan Horse attacks on Quantum Key Distribution systems
Gisin, Nicolas; Fasel, Sylvain; Kraus, Barbara; Zbinden, Hugo; Ribordy, Grégoire
2005-01-01
General Trojan-horse attacks on quantum-key-distribution systems, i.e., attacks on Alice or Bob’s system via the quantum channel, are analyzed. We illustrate the power of such attacks with today’s technology and conclude that all systems must implement active counter measures. In particular, all systems must include an auxiliary detector that monitors any incoming light. We show that such counter measures can be efficient, provided that enough additional privacy amplification is applied to th...
Quantum Anti-Zeno Effect in Artificial Quantum Systems
In this paper, we study a quantum anti-Zeno effect (QAZE) purely induced by repetitive measurements for an artificial atom interacting with a structured bath. This bath can be artificially realized with coupled resonators in one dimension and possesses photonic band structure like Bloch electron in a periodic potential. In the presence of repetitive measurements, the pure QAZE is discovered as the observable decay is not negligible even for the atomic energy level spacing outside of the energy band of the artificial bath. If there were no measurements, the decay would not happen outside of the band. In this sense, the enhanced decay is completely induced by measurements through the relaxation channels provided by the bath. Besides, we also discuss the controversial golden rule decay rates originated from the van Hove's singularities and the effects of the counter-rotating terms. (general)
Thermal and quantum noise in active systems
Courty, Jean-Michel; Grassia, Francesca; Reynaud, Serge
2001-01-01
We present a quantum network approach to the treatment of thermal and quantum fluctuations in measurement devices. The measurement is described as a scattering process of input fluctuations towards output ones. We present the results obtained with this method for the treatment of a cold damped capacitive accelerometer.
Adiabatic response and quantum thermoelectrics for ac-driven quantum systems
Ludovico, María Florencia; Battista, Francesca; von Oppen, Felix; Arrachea, Liliana
2016-02-01
We generalize the theory of thermoelectrics to include coherent electron systems under adiabatic ac driving, accounting for quantum pumping of charge and heat, as well as for the work exchanged between the electron system and driving potentials. We derive the relevant response coefficients in the adiabatic regime and show that they obey generalized Onsager reciprocity relations. We analyze the consequences of our generalized thermoelectric framework for quantum motors, generators, heat engines, and heat pumps, characterizing them in terms of efficiencies and figures of merit. We illustrate these concepts in a model for a quantum pump.
Quantum narrowing effect in a spin-Peierls system with quantum lattice fluctuation
We investigate a one-dimensional S=1/2 antiferromagnetic Heisenberg model coupled to quantum lattice vibration using a quantum Monte Carlo method. We study the ground-state lattice fluctuation where the system shows a characteristic structure factor. We also study the mass dependence of magnetic properties such as the magnetic susceptibility and the magnetic excitation spectrum. For heavy mass, the system shows the same behavior as the case of classical lattice vibration. On the other hand, for light mass, magnetic properties coincide with those of the static uniform chain. We investigate the physical mechanism of this behavior and propose the picture of quantum narrowing. (author)
Quantum groups, orthogonal polynomials and applications to some dynamical systems
The first part is concerned with the introduction of quantum groups as an extension of Lie groups. In particular, we study the case of unitary enveloping algebras in dimension 2. We then connect the quantum group formalism to the construction of g CGC recurrent relations. In addition, we construct g-deformed Krawtchouck and Meixner orthogonal polynomials and list their respective main characteristics. The second part deals with some dynamical systems from a classical, a quantum and a gp-analogue point of view. We investigate the Coulomb Kepler system by using the canonical namical systems which contain as special cases some interesting systems for nuclear of atomic physics and for quantum chemistry, such as the Hartmann system, the ring-shaped oscillator, the Smarodinsky-Winternitz system, the Aharonov-Bohen system and the dyania of Dirac and Schroedinger. (author)
Inequalities detecting quantum entanglement for 2 x d systems
We present a set of inequalities for detecting quantum entanglement of 2 x d quantum states. For 2 x 2 and 2 x 3 systems, the inequalities give rise to sufficient and necessary separability conditions for both pure and mixed states. For the case of d>3, these inequalities are necessary conditions for separability, which detect all entangled states that are not positive under partial transposition and even some entangled states with positive partial transposition. These inequalities are given by mean values of local observables and present an experimental way of detecting the quantum entanglement of 2 x d quantum states and even multiqubit pure states.
Attosecond neutron scattering from open quantum systems
Dreismann, C.; Aris, C. [Institute of Chemistry, Technical University of Berlin (Germany)
2010-07-01
Neutron Compton scattering (NCS) from single nuclei of atoms in molecules, e.g. H{sub 2} (and/or single atoms, e.g. He) is effectuated in the attosecond timescale. The related scattering time is considered in detail, in relation with the Uncertainty Relations. It is shown that the entity scattering time gives a statistical measure of the length of the time interval during which an elementary neutron-nucleus collision may occur, in the same way that the spatial extent of a particle wavefunction (or wavepacket) gives a statistical measure of the extent of the region in which the particle may be found. Consequently, the elementary neutron-nucleus scattering process represents a time-interference phenomenon over the sub-femtosecond ''scattering time'' window. Moreover, the very short-range strong interaction of the neutron-nucleus collision implies that the scattering system (e.g. a proton partically dressed'' with electrons) must be considered as an open quantum system. Experimental results from H{sub 2}, D{sub 2} and HD are mentioned and their anomalous scattering property in the attosecond timescale is qualitatively discussed, also in connection with the Schulman-Gaveau effect.
Chebyshev Expansion Applied to Dissipative Quantum Systems.
Popescu, Bogdan; Rahman, Hasan; Kleinekathöfer, Ulrich
2016-05-19
To determine the dynamics of a molecular aggregate under the influence of a strongly time-dependent perturbation within a dissipative environment is still, in general, a challenge. The time-dependent perturbation might be, for example, due to external fields or explicitly treated fluctuations within the environment. Methods to calculate the dynamics in these cases do exist though some of these approaches assume that the corresponding correlation functions can be written as a weighted sum of exponentials. One such theory is the hierarchical equations of motion approach. If the environment, however, is described by a complex spectral density or if its temperature is low, these approaches become very inefficient. Therefore, we propose a scheme based on a Chebyshev decomposition of the bath correlation functions and detail the respective quantum master equations within second-order perturbation theory in the environmental coupling. Similar approaches have recently been proposed for systems coupled to Fermionic reservoirs. The proposed scheme is tested for a simple two-level system and compared to existing results. Furthermore, the advantages and disadvantages of the present Chebyshev approach are discussed. PMID:26845380
Shushin, A. I.
2010-01-01
The manifestation of measurements, randomly distributed in time, on the evolution of quantum systems are analyzed in detail. The set of randomly distributed measurements (RDM) is modeled within the renewal theory, in which the distribution is characterized by the probability density function (PDF) W(t) of times t between successive events (measurements). The evolution of the quantum system affected by the RDM is shown to be described by the density matrix satisfying the stochastic Liouville e...
Scaling law and stability for a noisy quantum system
Sadgrove, Mark; Wimberger, Sandro; Parkins, Scott; Leonhardt, Rainer
2008-08-01
We show that a scaling law exists for the near-resonant dynamics of cold kicked atoms in the presence of a randomly fluctuating pulse amplitude. Analysis of a quasiclassical phase-space representation of the quantum system with noise allows a new scaling law to be deduced. The scaling law and associated stability are confirmed by comparison with quantum simulations and experimental data.
A note on quantum groups and integrable systems
Popolitov, Alexander
2015-01-01
Free-field formalism for quantum groups provides a special choice of coordinates on a quantum group. In these coordinates the construction of associated integrable system is especially simple. This choice also fits into general framework of cluster varieties -- natural changes of coordinates are cluster mutations.
Quantum-Classical Connection for Hydrogen Atom-Like Systems
Syam, Debapriyo; Roy, Arup
2011-01-01
The Bohr-Sommerfeld quantum theory specifies the rules of quantization for circular and elliptical orbits for a one-electron hydrogen atom-like system. This article illustrates how a formula connecting the principal quantum number "n" and the length of the major axis of an elliptical orbit may be arrived at starting from the quantum…
Quantum entanglement of unitary operators on bi-partite systems
Wang, X.; Zanardi, P.
2002-01-01
We study the entanglement of unitary operators on $d_1\\times d_2$ quantum systems. This quantity is closely related to the entangling power of the associated quantum evolutions. The entanglement of a class of unitary operators is quantified by the concept of concurrence.
System-free quantum mechanical description of particle decay processes
Jaroszkiewicz, G
2006-01-01
Using the formalism of system-free quantum mechanics, we show how quantum mechanical particle decay probabilities can be discussed rigorously within a framework that conserves total probability, requiring neither non-Hermitian Hamiltonians nor the ad-hoc introduction of complex energies. We apply our formalism to single channel decays, the ammonium molecule, and neutral Kaon decay processes.
Quantum dynamics simulation of a small quantum system embedded in a classical environment
The authors wish to consider quantum-dynamical processes that are not restricted to motion on a ground state Born-Oppenheimer surface, but may involve transitions between states. The authors interest is in such processes occurring in a complex environment that modulates the quantum process and interacts with it. In a system containing thousands degrees of freedom, the essential quantum behaviour is generally restricted to a small subsystem containing only a few degrees of freedom, while the environment can be treated classically. The challenge is threefold: 1) to treat the quantum subsystem correctly in a quantum-dynamical sense, 2) to treat the environment correctly in a classical dynamical sense, 3) to couple both systems in such a way that errors in the average or long-term behaviour are minimized. After an exposition of the theory, an insight into quantum-dynamical behaviour by using pictorial analogue, valid for a simple two-level system is given. Then, the authors give a short survey of applications related to collision processes involving quantum levels of one particle, and to proton transfer processes along hydrogen bonds in complex environments. Finally, they conclude with some general remarks on the validity of their approach. (N.T.)
Quantum Markov processes and applications in many-body systems
This thesis is concerned with the investigation of quantum as well as classical Markov processes and their application in the field of strongly correlated many-body systems. A Markov process is a special kind of stochastic process, which is determined by an evolution that is independent of its history and only depends on the current state of the system. The application of Markov processes has a long history in the field of statistical mechanics and classical many-body theory. Not only are Markov processes used to describe the dynamics of stochastic systems, but they predominantly also serve as a practical method that allows for the computation of fundamental properties of complex many-body systems by means of probabilistic algorithms. The aim of this thesis is to investigate the properties of quantum Markov processes, i.e. Markov processes taking place in a quantum mechanical state space, and to gain a better insight into complex many-body systems by means thereof. Moreover, we formulate a novel quantum algorithm which allows for the computation of the thermal and ground states of quantum many-body systems. After a brief introduction to quantum Markov processes we turn to an investigation of their convergence properties. We find bounds on the convergence rate of the quantum process by generalizing geometric bounds found for classical processes. We generalize a distance measure that serves as the basis for our investigations, the chi-square divergence, to non-commuting probability spaces. This divergence allows for a convenient generalization of the detailed balance condition to quantum processes. We then devise the quantum algorithm that can be seen as the natural generalization of the ubiquitous Metropolis algorithm to simulate quantum many-body Hamiltonians. By this we intend to provide further evidence, that a quantum computer can serve as a fully-fledged quantum simulator, which is not only capable of describing the dynamical evolution of quantum systems, but also gives access to the computation of their static properties. After this, we turn to an investigation of classical non-equilibrium steady states with methods derived from quantum information theory. We construct a special class of matrix product states that exhibit correlations which can best be understood in terms of classical Markov processes. Finally, we investigate the transport properties of non-equilibrium steady states. The dynamical equations are constructed in such a manner that they allow for both stochastic as well as coherent transport in the same formal framework. It is therefore possible to compare different forms of transport within the same model. (author)
Tartakovskii, Alexander
2012-07-01
Part I. Nanostructure Design and Structural Properties of Epitaxially Grown Quantum Dots and Nanowires: 1. Growth of III/V semiconductor quantum dots C. Schneider, S. Hofling and A. Forchel; 2. Single semiconductor quantum dots in nanowires: growth, optics, and devices M. E. Reimer, N. Akopian, M. Barkelid, G. Bulgarini, R. Heeres, M. Hocevar, B. J. Witek, E. Bakkers and V. Zwiller; 3. Atomic scale analysis of self-assembled quantum dots by cross-sectional scanning tunneling microscopy and atom probe tomography J. G. Keizer and P. M. Koenraad; Part II. Manipulation of Individual Quantum States in Quantum Dots Using Optical Techniques: 4. Studies of the hole spin in self-assembled quantum dots using optical techniques B. D. Gerardot and R. J. Warburton; 5. Resonance fluorescence from a single quantum dot A. N. Vamivakas, C. Matthiesen, Y. Zhao, C.-Y. Lu and M. Atature; 6. Coherent control of quantum dot excitons using ultra-fast optical techniques A. J. Ramsay and A. M. Fox; 7. Optical probing of holes in quantum dot molecules: structure, symmetry, and spin M. F. Doty and J. I. Climente; Part III. Optical Properties of Quantum Dots in Photonic Cavities and Plasmon-Coupled Dots: 8. Deterministic light-matter coupling using single quantum dots P. Senellart; 9. Quantum dots in photonic crystal cavities A. Faraon, D. Englund, I. Fushman, A. Majumdar and J. Vukovic; 10. Photon statistics in quantum dot micropillar emission M. Asmann and M. Bayer; 11. Nanoplasmonics with colloidal quantum dots V. Temnov and U. Woggon; Part IV. Quantum Dot Nano-Laboratory: Magnetic Ions and Nuclear Spins in a Dot: 12. Dynamics and optical control of an individual Mn spin in a quantum dot L. Besombes, C. Le Gall, H. Boukari and H. Mariette; 13. Optical spectroscopy of InAs/GaAs quantum dots doped with a single Mn atom O. Krebs and A. Lemaitre; 14. Nuclear spin effects in quantum dot optics B. Urbaszek, B. Eble, T. Amand and X. Marie; Part V. Electron Transport in Quantum Dots Fabricated by Lithographic Techniques: III-V Semiconductors and Carbon: 15. Electrically controlling single spin coherence in semiconductor nanostructures Y. Dovzhenko, K. Wang, M. D. Schroer and J. R. Petta; 16. Theory of electron and nuclear spins in III-V semiconductor and carbon-based dots H. Ribeiro and G. Burkard; 17. Graphene quantum dots: transport experiments and local imaging S. Schnez, J. Guettinger, F. Molitor, C. Stampfer, M. Huefner, T. Ihn and K. Ensslin; Part VI. Single Dots for Future Telecommunications Applications: 18. Electrically operated entangled light sources based on quantum dots R. M. Stevenson, A. J. Bennett and A. J. Shields; 19. Deterministic single quantum dot cavities at telecommunication wavelengths D. Dalacu, K. Mnaymneh, J. Lapointe, G. C. Aers, P. J. Poole, R. L. Williams and S. Hughes; Index.
Active optical clock based on four-level quantum system
Zhang, Tonggang; Yanfei WANG; Zang, Xiaorun; Zhuang, Wei; Chen, Jingbiao
2012-01-01
Active optical clock, a new conception of atomic clock, has been proposed recently. In this report, we propose a scheme of active optical clock based on four-level quantum system. The final accuracy and stability of two-level quantum system are limited by second-order Doppler shift of thermal atomic beam. To three-level quantum system, they are mainly limited by light shift of pumping laser field. These limitations can be avoided effectively by applying the scheme proposed here. Rubidium atom...
Model-Checking Linear-Time Properties of Quantum Systems
Ying, Mingsheng; Yu, Nengkun; Feng, Yuan
2011-01-01
We define a formal framework for reasoning about linear-time properties of quantum systems in which quantum automata are employed in the modeling of systems and certain closed subspaces of state (Hilbert) spaces are used as the atomic propositions about the behavior of systems. We provide an algorithm for verifying invariants of quantum automata. Then automata-based model-checking technique is generalized for the verification of safety properties recognizable by reversible automata and omega-properties recognizable by reversible Buechi automata.
Chaos and Relaxation in Classical and Quantum Spin Systems
Elsayed, Tarek A.
2013-01-01
The problems of chaos and relaxation have a fundamental importance in the study of many-body classical and quantum systems. We investigate some of the issues related to these problems numerically in classical and quantum spin systems. New results reported in this thesis include: (i) A remarkably simple algorithm for discriminating chaotic from nonchaotic behavior in classical systems using a time series of one macroscopic observable. The effectiveness of this algorithm stems from the qualitat...
Decoherence as irreversible dynamical process in open quantum systems
Full text: A framework for a general discussion in Heisenberg's representation of environmentally induced decoherence will be proposed. Example showing that classical properties do not have to be postulated as an independent ingredient will be given. It will be also shown that infinite open quantum systems in some case after decoherence behave like - simple classical dynamical systems; simples quantum mechanical systems representing one particle. (author)
Entangled Quantum State Discrimination using Pseudo-Hermitian System
Ghatak, Ananya
2012-01-01
We demonstrate how to discriminate two non-orthogonal, entangled quantum state which are slightly different from each other by using pseudo-Hermitian system. The positive definite metric operator which makes the pseudo-Hermitian systems fully consistent quantum theory is used for such a state discrimination. We further show that non-orthogonal states can evolve through a suitably constructed pseudo-Hermitian Hamiltonian to orthogonal states. Such evolution ceases at exceptional points of the pseudo-Hermitian system.
Quantum Measurement Problem and Systems Selfdescription in Operators Algebras Formalism
Mayburov, S.
2002-01-01
Quantum Measurement problem studied in Information Theory approach of systems selfdescription which exploits the information acquisition incompleteness for the arbitrary information system. The studied model of measuring system (MS) consist of measured state S environment E and observer $O$ processing input S signal. $O$ considered as the quantum object which interaction with S,E obeys to Schrodinger equation (SE). MS incomplete or restricted states for $O$ derived by the algebraic QM formali...
Effects of spacetime fluctuations on quantum systems
Spacetime can be understood as some kind of spacetime foam of fluctuating bubbles or loops which is expected to be an outcome of a theory of quantum gravity. This should lead to a fluctuating spacetime. In our approach we assume that spacetime fluctuations manifest as classical stochastic fluctuations of the metric. It will be shown how quantum dynamics is affected and we discuss the following effects: (i) an apparent violation of the weak equivalence principle, (ii) a modification of the spreading of wavepackets, and (iii) a loss of quantum coherence.
Certifying single-system steering for quantum-information processing
Li, Che-Ming; Chen, Yueh-Nan; Lambert, Neill; Chiu, Ching-Yi; Nori, Franco
2015-12-01
Einstein-Podolsky-Rosen (EPR) steering describes how different ensembles of quantum states can be remotely prepared by measuring one particle of an entangled pair. Here, we investigate quantum steering for single quantum d -dimensional systems (qudits) and devise efficient conditions to certify the steerability therein, which we find are applicable both to single-system steering and EPR steering. In the single-system case our steering conditions enable the unambiguous ruling out of generic classical means of mimicking steering. Ruling out "false-steering" scenarios has implications for securing channels against both cloning-based individual attack and coherent attacks when implementing quantum key distribution using qudits. We also show that these steering conditions also have applications in quantum computation, in that they can serve as an efficient criterion for the evaluation of quantum logic gates of arbitrary size. Finally, we describe how the nonlocal EPR variant of these conditions also function as tools for identifying faithful one-way quantum computation, secure entanglement-based quantum communication, and genuine multipartite EPR steering.
The Power of Quantum Systems on a Line
Aharonov, Dorit; Gottesman, Daniel; Irani, Sandy; Kempe, Julia
2009-04-01
We study the computational strength of quantum particles (each of finite dimensionality) arranged on a line. First, we prove that it is possible to perform universal adiabatic quantum computation using a one-dimensional quantum system (with 9 states per particle). This might have practical implications for experimentalists interested in constructing an adiabatic quantum computer. Building on the same construction, but with some additional technical effort and 12 states per particle, we show that the problem of approximating the ground state energy of a system composed of a line of quantum particles is QMA-complete; QMA is a quantum analogue of NP. This is in striking contrast to the fact that the analogous classical problem, namely, one-dimensional MAX-2-SAT with nearest neighbor constraints, is in P. The proof of the QMA-completeness result requires an additional idea beyond the usual techniques in the area: Not all illegal configurations can be ruled out by local checks, so instead we rule out such illegal configurations because they would, in the future, evolve into a state which can be seen locally to be illegal. Our construction implies (assuming the quantum Church-Turing thesis and that quantum computers cannot efficiently solve QMA-complete problems) that there are one-dimensional systems which take an exponential time to relax to their ground states at any temperature, making them candidates for being one-dimensional spin glasses.
A robust, scanning quantum system for nanoscale sensing and imaging
Maletinsky, P; Grinolds, M S; Hausmann, B; Lukin, M D; Walsworth, R -L; Loncar, M; Yacoby, A
2011-01-01
Controllable atomic-scale quantum systems hold great potential as sensitive tools for nanoscale imaging and metrology. Possible applications range from nanoscale electric and magnetic field sensing to single photon microscopy, quantum information processing, and bioimaging. At the heart of such schemes is the ability to scan and accurately position a robust sensor within a few nanometers of a sample of interest, while preserving the sensor's quantum coherence and readout fidelity. These combined requirements remain a challenge for all existing approaches that rely on direct grafting of individual solid state quantum systems or single molecules onto scanning-probe tips. Here, we demonstrate the fabrication and room temperature operation of a robust and isolated atomic-scale quantum sensor for scanning probe microscopy. Specifically, we employ a high-purity, single-crystalline diamond nanopillar probe containing a single Nitrogen-Vacancy (NV) color center. We illustrate the versatility and performance of our sc...
Open quantum spin systems in semiconductor quantum dots and atoms in optical lattices
In this Thesis, we study open quantum spin systems from different perspectives. The first part is motivated by technological challenges of quantum computation. An important building block for quantum computation and quantum communication networks is an interface between material qubits for storage and data processing and travelling photonic qubits for communication. We propose the realisation of a quantum interface between a travelling-wave light field and the nuclear spins in a quantum dot strongly coupled to a cavity. Our scheme is robust against cavity decay as it uses the decay of the cavity to achieve the coupling between nuclear spins and the travelling-wave light fields. A prerequiste for such a quantum interface is a highly polarized ensemble of nuclear spins. High polarization of the nuclear spin ensemble is moreover highly desirable as it protects the potential electron spin qubit from decoherence. Here we present the theoretical description of an experiment in which highly asymmetric dynamic nuclear spin pumping is observed in a single self-assembled InGaAs quantum dot. The second part of this Thesis is devoted to fundamental studies of dissipative spin systems. We study general one-dimensional spin chains under dissipation and propose a scheme to realize a quantum spin system using ultracold atoms in an optical lattice in which both coherent interaction and dissipation can be engineered and controlled. This system enables the study of non-equilibrium and steady state physics of open and driven spin systems. We find, that the steady state expectation values of different spin models exhibit discontinuous behaviour at degeneracy points of the Hamiltonian in the limit of weak dissipation. This effect can be used to dissipatively probe the spectrum of the Hamiltonian. We moreover study spin models under the aspect of state preparation and show that dissipation drives certain spin models into highly entangled state. Finally, we study a spin chain with subwavelength interatomic distances that exhibits long rage interactions. What lies at the heart of all these approaches is the endeavour to include the coupling to the environment into the description of the physical system with the aim of harnessing dissipative processes. While decoherence masks or destroys quantum effects and is considered as the main adversary of any quantum information application, we turn the existence of the dissipative coupling of spin systems to the environment into a fruitful resource.
Open quantum spin systems in semiconductor quantum dots and atoms in optical lattices
Schwager, Heike
2012-07-04
In this Thesis, we study open quantum spin systems from different perspectives. The first part is motivated by technological challenges of quantum computation. An important building block for quantum computation and quantum communication networks is an interface between material qubits for storage and data processing and travelling photonic qubits for communication. We propose the realisation of a quantum interface between a travelling-wave light field and the nuclear spins in a quantum dot strongly coupled to a cavity. Our scheme is robust against cavity decay as it uses the decay of the cavity to achieve the coupling between nuclear spins and the travelling-wave light fields. A prerequiste for such a quantum interface is a highly polarized ensemble of nuclear spins. High polarization of the nuclear spin ensemble is moreover highly desirable as it protects the potential electron spin qubit from decoherence. Here we present the theoretical description of an experiment in which highly asymmetric dynamic nuclear spin pumping is observed in a single self-assembled InGaAs quantum dot. The second part of this Thesis is devoted to fundamental studies of dissipative spin systems. We study general one-dimensional spin chains under dissipation and propose a scheme to realize a quantum spin system using ultracold atoms in an optical lattice in which both coherent interaction and dissipation can be engineered and controlled. This system enables the study of non-equilibrium and steady state physics of open and driven spin systems. We find, that the steady state expectation values of different spin models exhibit discontinuous behaviour at degeneracy points of the Hamiltonian in the limit of weak dissipation. This effect can be used to dissipatively probe the spectrum of the Hamiltonian. We moreover study spin models under the aspect of state preparation and show that dissipation drives certain spin models into highly entangled state. Finally, we study a spin chain with subwavelength interatomic distances that exhibits long rage interactions. What lies at the heart of all these approaches is the endeavour to include the coupling to the environment into the description of the physical system with the aim of harnessing dissipative processes. While decoherence masks or destroys quantum effects and is considered as the main adversary of any quantum information application, we turn the existence of the dissipative coupling of spin systems to the environment into a fruitful resource.
Does an onlooker stop an evolving quantum system?
The evolution of quantum mechanics has followed the critical analysis of 'gedanken' experiments. Many of these concrete speculations can become implemented today in the laboratory - thanks to now available techniques. A key experiment is concerned with the time evolution of a quantum system under repeated or continuing observation. Here, three problems overlap: 1. The microphysical measurement by a macroscopic device, 2. the system's temporal evolution, and 3. the emergence of macroscopic reality out of the microcosmos. A well-known calculation shows the evolution of a quantum system being slowed down, or even obstructed, when the system is merely observed.An experiment designed to demonstrate this 'quantum Zeno effect' and performed in the late eighties on an ensemble of identical atomic ions confirmed its quantum description, but turned out inconclusive with respect to the very origin of the impediment of evolution. During the past years, experiments on individualelectrodynamically stored and laser-cooled ions have been performed that unequivocally demonstrate the observed system's quantum evolution being impeded. Strategy and results exclude any physical reaction on the measured object, but reveal the effect of the gain of information as put forward by the particular correlation of the ion state with the detected signal. They shed light on the process of measurement as well as on the quantum evolution and allow an epistemological interpretation
Quantum-Classical System: Simple Harmonic Oscillator
Sulistiono, Tri
1997-01-01
Problems concerning with application of quantum rules on classical phenomena have been widely studied, for which lifted up the idea about quantization and uncertainty principle. Energy quantization on classical example of simple harmonic oscillator has been reviewed in this paper.
Quantum dot systems: artificial atoms with tunable properties
Full text: Quantum dots - also called zero-dimensional electron systems or artificial atoms - are physical objects where the constituent electrons are confined in a small spatial region, leading to discrete eigenvalues for the energies of the confined electrons. Large quantum dots offer a dense energy spectrum comparable to that of metallic grains, whereas small quantum dots more closely resemble atoms in their electronic properties. Quantum dots can be linked to leads by tunnel barriers, hence permitting electrical transport measurements: Coulomb blockade and single-electron charging effects are observed due to the repulsive electron electron interaction on the quantum dot site. Usually fabricated by conventional semiconductor growth and processing technology, the advantage is that both simple and also more complex quantum dot systems can be designed to purpose, acting as model systems with in-situ tunable parameters such as the number of confined electrons in the quantum dot and the strength of the tunnel coupling to the leads, electrostatically controlled by the applied voltages to gate electrodes. With increasing the tunnel coupling to the leads, the virtual occupation of the quantum dot from the leads becomes more and more important -- the simple description of electrical transport by single-electron tunneling events breaks down. The basic physics is described by the Kondo physics based on the Anderson impurity model. A system consisting of strongly electrostatically coupled quantum dots with separate leads to each quantum dot represent another realization of the Anderson impurity model. Experiments to verify the analogy are presented. The experimental data embedded within this tutorial have been obtained with Alexander Huebel, Matthias Keller, Joerg Schmid, David Quirion, Armin Welker, Ulf Wilhelm, and Klaus von Klitzing. (author)
Quantum systems that follow classical dynamics
Manfredi, G; Feix, M R
1993-01-01
For a special class of potentials, the dynamical evolution of any quantum wavepacket is entirely determined by the laws of classical mechanics. Here, the properties of this class are investigated both from the viewpoint of the Ehrenfest theorem (which provides the evolution of the average position and momentum), and the Wigner representation (which expresses quantum mechanics in a phase space formalism). Finally, these results are extended to the case of a charged particle in a uniform magnetic field. (author)
Dimensional loss in nonequilibrium quantum systems
Quantum steady state processes far from equilibrium can be characterized by wave functions whose coefficients (in a fixed basis) evolve onto a fractal set. This is explicitly shown for the prototypical situation of heat flow from hot to cold reservoirs, with two spin-1/2 particles in a thermal gradient. The resulting dimensional loss, induced by the nonequilibrium environment, is related to the quantum transport process
Closed-loop and robust control of quantum systems.
Chen, Chunlin; Wang, Lin-Cheng; Wang, Yuanlong
2013-01-01
For most practical quantum control systems, it is important and difficult to attain robustness and reliability due to unavoidable uncertainties in the system dynamics or models. Three kinds of typical approaches (e.g., closed-loop learning control, feedback control, and robust control) have been proved to be effective to solve these problems. This work presents a self-contained survey on the closed-loop and robust control of quantum systems, as well as a brief introduction to a selection of basic theories and methods in this research area, to provide interested readers with a general idea for further studies. In the area of closed-loop learning control of quantum systems, we survey and introduce such learning control methods as gradient-based methods, genetic algorithms (GA), and reinforcement learning (RL) methods from a unified point of view of exploring the quantum control landscapes. For the feedback control approach, the paper surveys three control strategies including Lyapunov control, measurement-based control, and coherent-feedback control. Then such topics in the field of quantum robust control as H(∞) control, sliding mode control, quantum risk-sensitive control, and quantum ensemble control are reviewed. The paper concludes with a perspective of future research directions that are likely to attract more attention. PMID:23997680
Vourdas, A.; Banderier, C.
2010-01-01
Quantum systems where the position and momentum are in the ring {\\bb Z}_d (d is an odd integer) are considered. Symplectic transformations are studied, and the order of Sp(2,{\\bb Z}_d) is calculated. Quantum tomography is also discussed. It is shown that measurements (used in the inverse Radon transform) need to be made on J2(d) lines (where J2(d) is the Jordan totient function).
Quantum railroads and directed localization at the juncture of quantum Hall systems
Nonoyama, Shinji; Kirczenow, George
2002-01-01
The integer quantum Hall effect (QHE) and one-dimensional Anderson localization (AL) are limiting special cases of a more general phenomenon, directed localization (DL), predicted to occur in disordered one-dimensional wave guides called "quantum railroads" (QRR). Here we explain the surprising results of recent measurements by Kang et al. [Nature 403, 59 (2000)] of electron transfer between edges of two-dimensional electron systems and identify experimental evidence of QRR's in the general, ...
Einstein-Podolsky-Rosen paradox and measurement of quantum system
Kladko, Konstantin
1999-01-01
Einstein-Podolsky-Rosen (EPR) paradox is considered in a relation to a measurement of an arbitrary quantum system . It is shown that the EPR paradox always appears in a gedanken experiment with two successively joined measuring devices.
Fidelity and entanglement fidelity for infinite-dimensional quantum systems
Instead of unitary freedom for finite-dimensional cases, bi-contractive freedom in the operator-sum representation for quantum channels of infinite-dimensional systems is established. Specifically, if the channel sends every pure state to a finite rank state, then the isometric freedom feature holds. Then, a method of computing entanglement fidelity and a relation between quantum fidelity and entanglement fidelity for infinite-dimensional systems are obtained. In addition, upper and lower bounds of the quantum fidelity, and their connection to the trace distance, are also provided. (paper)
Quantum beats in fluorescence for multi-level atomic system
For Λ-type three-level atomic systems we have clarified using diagram that (1) it is impossible to observe quantum beats due to the ground state sublevels by measuring the time dependence of the fluorescence intensity, and (2) why it is physically possible to observe and how we can observe quantum beats in the ground state sublevels by using fluorescence. Generalization of the results shows that we can determine from which state (the ground state or the excited state) the quantum beats are originated. Analytical result is shown for four-level atomic systems.
Equivalence relations between deterministic and quantum mechanical systems
Several quantum mechanical models are shown to be equivalent to certain deterministic systems because a basis can be found in terms of which the wave function does not spread. This suggests that apparently indeterministic behavior typical for a quantum mechanical world can be the result of locally deterministic laws of physics. We show how certain deterministic systems allow the construction of a Hilbert space and a Hamiltonian so that at long distance scales they may appear to behave as quantum field theories, including interactions but as yet no mass term. These observations are suggested to be useful for building theories at the Planck scale
Photonic reagent control of dynamically homologous quantum systems
The general objective of quantum control is the manipulation of atomic scale physical and chemical phenomena through the application of external control fields. These tailored fields, or photonic reagents, exhibit systematic properties analogous to those of ordinary laboratory reagents. This analogous behavior is explored further here by considering the controlled response of a family of homologous quantum systems to a single common photonic reagent. A level set of dynamically homologous quantum systems is defined as the family that produces the same value(s) for a target physical observable(s) when controlled by a common photonic reagent. This paper investigates the scope of homologous quantum system control using the level set exploration technique (L-SET). L-SET enables the identification of continuous families of dynamically homologous quantum systems. Each quantum system is specified by a point in a hypercube whose edges are labeled by Hamiltonian matrix elements. Numerical examples are presented with simple finite level systems to illustrate the L-SET concepts. Both connected and disconnected families of dynamically homologous systems are shown to exist
Information Systems Self-description and Quantum Measurement Problem
Mayburov, S.
2004-01-01
Information-Theoretical restrictions on the systems self-descriptions are applied to Quantum Measurements Theory. For the quantum object S measurement by information system O such restrictions are described by the restricted states formalism by Breuer. The analogous restrictions obtained in Algebraic QM from the analysis of Segal algebra U of O observables; O restricted states set is defined as U dual space. From Segal theorem for the associative subalgebra it's shown that such states describ...
Vertex Models and Quantum Spin Systems: a nonlocal approach
Evertz, H. G.; Marcu, M
1993-01-01
Within a general cluster framework, we discuss the loop-algorithm, a new type of cluster algorithm that reduces critical slowing down in vertex models and in quantum spin systems. We cover the example of the 6-vertex model in detail. For the F-model, we present numerical results that demonstrate the effectiveness of the loop algorithm. We discuss how to modify the original algorithm for some more complicated situations, especially for quantum spin systems in one and two dimensions.
Plausibility of quantum coherent states in biological systems
Salari, V [Institut de Mineralogie et de Physique des Milieux Condenses, Universite Pierre et Marie Curie-Paris 6, CNRS UMR7590 (France); Tuszynski, J [Department of Experimental Oncology, Cross Cancer Institute, 11560 University Avenue Edmonton, AB T6G 1Z2 (Canada); Rahnama, M [Department of Physics, Shahid Bahonar University of Kerman, Kerman (Iran, Islamic Republic of); Bernroider, G, E-mail: vahid.salari@impmc.upmc.fr [Department of Organismic Biology, University of Salzburg, Hellbrunnerstrasse 34, Salzburg (Austria)
2011-07-08
In this paper we briefly discuss the necessity of using quantum mechanics as a fundamental theory applicable to some key functional aspects of biological systems. This is especially relevant to three important parts of a neuron in the human brain, namely the cell membrane, microtubules (MT) and ion channels. We argue that the recently published papers criticizing the use of quantum theory in these systems are not convincing.
Plausibility of quantum coherent states in biological systems
In this paper we briefly discuss the necessity of using quantum mechanics as a fundamental theory applicable to some key functional aspects of biological systems. This is especially relevant to three important parts of a neuron in the human brain, namely the cell membrane, microtubules (MT) and ion channels. We argue that the recently published papers criticizing the use of quantum theory in these systems are not convincing.
Thermal Rectification in the Nonequilibrium Quantum-Dot-System
Chen, T; Wang, X. B.
2012-01-01
Quantum thermal transport in two-quantum-dot system with Dzyaloshinskii-Moriya interaction (DM interaction) has been studied. The sign of thermal rectification can be controlled through changing the energy splitting or the DM interaction strength. The anisotropic term in the system can also affect the sign of rectification. Compared with other proposals [Phys. Rev. B 80, 172301 (2009)], our model can offer larger rectification efficiency and show the potential application in designing the pol...
Entangled Quantum State Discrimination using Pseudo-Hermitian System
Ghatak, Ananya; Mandal, Bhabani Prasad(Department of Physics, Banaras Hindu University, Varanasi, 221005, India)
2012-01-01
We demonstrate how to discriminate two non-orthogonal, entangled quantum state which are slightly different from each other by using pseudo-Hermitian system. The positive definite metric operator which makes the pseudo-Hermitian systems fully consistent quantum theory is used for such a state discrimination. We further show that non-orthogonal states can evolve through a suitably constructed pseudo-Hermitian Hamiltonian to orthogonal states. Such evolution ceases at exceptional points of the ...
Quantum entropy of systems described by non-Hermitian Hamiltonians
Sergi, Alessandro; Zloshchastiev, Konstantin G.
2015-01-01
We study the quantum entropy of systems that are described by general non-Hermitian Hamiltonians, including those which can model the effects of sinks or sources. We generalize the von Neumann entropy to the non-Hermitian case and find that one needs both the normalized and non-normalized density operators in order to properly describe irreversible processes. It turns out that such a generalization monitors the onset of disorder in quantum dissipative systems. We give arguments for why one ca...
Theory and simulation of cavity quantum electro-dynamics in multi-partite quantum complex systems
Alidoosty Shahraki, Moslem; Khorasani, Sina; Aram, Mohammad Hasan [Sharif University of Technology, School of Electrical Engineering, Tehran (Iran, Islamic Republic of)
2014-05-15
The cavity quantum electrodynamics of various complex systems is here analyzed using a general versatile code developed in this research. Such quantum multi-partite systems normally consist of an arbitrary number of quantum dots in interaction with an arbitrary number of cavity modes. As an example, a nine-partition system is simulated under different coupling regimes, consisting of eight emitters interacting with one cavity mode. Two-level emitters (e.g. quantum dots) are assumed to have an arrangement in the form of a linear chain, defining the mutual dipole-dipole interactions. It was observed that plotting the system trajectory in the phase space reveals a chaotic behavior in the so-called ultrastrong-coupling regime. This result is mathematically confirmed by detailed calculation of the Kolmogorov entropy, as a measure of chaotic behavior. In order to study the computational complexity of our code, various multi-partite systems consisting of one to eight quantum dots in interaction with one cavity mode were solved individually. Computation run times and the allocated memory for each system were measured. (orig.)
Theory and simulation of cavity quantum electro-dynamics in multi-partite quantum complex systems
The cavity quantum electrodynamics of various complex systems is here analyzed using a general versatile code developed in this research. Such quantum multi-partite systems normally consist of an arbitrary number of quantum dots in interaction with an arbitrary number of cavity modes. As an example, a nine-partition system is simulated under different coupling regimes, consisting of eight emitters interacting with one cavity mode. Two-level emitters (e.g. quantum dots) are assumed to have an arrangement in the form of a linear chain, defining the mutual dipole-dipole interactions. It was observed that plotting the system trajectory in the phase space reveals a chaotic behavior in the so-called ultrastrong-coupling regime. This result is mathematically confirmed by detailed calculation of the Kolmogorov entropy, as a measure of chaotic behavior. In order to study the computational complexity of our code, various multi-partite systems consisting of one to eight quantum dots in interaction with one cavity mode were solved individually. Computation run times and the allocated memory for each system were measured. (orig.)
Contexts, Systems and Modalities: A New Ontology for Quantum Mechanics
Auffèves, Alexia; Grangier, Philippe
2016-02-01
In this article we present a possible way to make usual quantum mechanics fully compatible with physical realism, defined as the statement that the goal of physics is to study entities of the natural world, existing independently from any particular observer's perception, and obeying universal and intelligible rules. Rather than elaborating on the quantum formalism itself, we propose a new quantum ontology, where physical properties are attributed jointly to the system, and to the context in which it is embedded. In combination with a quantization principle, this non-classical definition of physical reality sheds new light on counter-intuitive features of quantum mechanics such as the origin of probabilities, non-locality, and the quantum-classical boundary.
Contexts, Systems and Modalities: A New Ontology for Quantum Mechanics
Auffves, Alexia; Grangier, Philippe
2015-09-01
In this article we present a possible way to make usual quantum mechanics fully compatible with physical realism, defined as the statement that the goal of physics is to study entities of the natural world, existing independently from any particular observer's perception, and obeying universal and intelligible rules. Rather than elaborating on the quantum formalism itself, we propose a new quantum ontology, where physical properties are attributed jointly to the system, and to the context in which it is embedded. In combination with a quantization principle, this non-classical definition of physical reality sheds new light on counter-intuitive features of quantum mechanics such as the origin of probabilities, non-locality, and the quantum-classical boundary.
Scavenging quantum information: Multiple observations of quantum systems
Rapcan, P. [Research Center for Quantum Information, Institute of Physics, Slovak Academy of Sciences, Dubravska cesta 9, 845 11 Bratislava (Slovakia); Calsamiglia, J.; Munoz-Tapia, R. [Fisica Teorica: Informacio i Fenomens Quantics, Edifici Cn, Universitat Autonoma de Barcelona, E-08193 Bellaterra (Barcelona) (Spain); Bagan, E. [Fisica Teorica: Informacio i Fenomens Quantics, Edifici Cn, Universitat Autonoma de Barcelona, E-08193 Bellaterra (Barcelona) (Spain); Department of Physics, Hunter College of the City University of New York, 695 Park Avenue, New York, New York 10021 (United States); Physics Department, Brookhaven National Laboratory, Upton, New York 11973 (United States); Buzek, V. [Research Center for Quantum Information, Institute of Physics, Slovak Academy of Sciences, Dubravska cesta 9, 845 11 Bratislava (Slovakia); Faculty of Informatics, Masaryk University, Botanicka 68a, CZ-602 00 Brno (Czech Republic)
2011-09-15
Given an unknown state of a qudit that has already been measured optimally, can one still extract any information about the original unknown state? Clearly, after a maximally informative measurement, the state of the system collapses into a postmeasurement state from which the same observer cannot obtain further information about the original state of the system. However, the system still encodes a significant amount of information about the original preparation for a second observer who is unaware of the actions of the first one. We study how a series of independent observers can obtain, or can scavenge, information about the unknown state of a system (quantified by the fidelity) when they sequentially measure it. We give closed-form expressions for the estimation fidelity when one or several qudits are available to carry information about the single-qudit state, and we study the classical limit when an arbitrarily large number of observers can obtain (nearly) complete information on the system. In addition to the case where all observers perform most informative measurements, we study the scenario where a finite number of observers estimates the state with equal fidelity, regardless of their position in the measurement sequence and the scenario where all observers use identical measurement apparatuses (up to a mutually unknown orientation) chosen so that a particular observer's estimation fidelity is maximized.
Scavenging quantum information: Multiple observations of quantum systems
Given an unknown state of a qudit that has already been measured optimally, can one still extract any information about the original unknown state? Clearly, after a maximally informative measurement, the state of the system collapses into a postmeasurement state from which the same observer cannot obtain further information about the original state of the system. However, the system still encodes a significant amount of information about the original preparation for a second observer who is unaware of the actions of the first one. We study how a series of independent observers can obtain, or can scavenge, information about the unknown state of a system (quantified by the fidelity) when they sequentially measure it. We give closed-form expressions for the estimation fidelity when one or several qudits are available to carry information about the single-qudit state, and we study the classical limit when an arbitrarily large number of observers can obtain (nearly) complete information on the system. In addition to the case where all observers perform most informative measurements, we study the scenario where a finite number of observers estimates the state with equal fidelity, regardless of their position in the measurement sequence and the scenario where all observers use identical measurement apparatuses (up to a mutually unknown orientation) chosen so that a particular observer's estimation fidelity is maximized.
Tampering detection system using quantum-mechanical systems
Humble, Travis S. (Knoxville, TN); Bennink, Ryan S. (Knoxville, TN); Grice, Warren P. (Oak Ridge, TN)
2011-12-13
The use of quantum-mechanically entangled photons for monitoring the integrity of a physical border or a communication link is described. The no-cloning principle of quantum information science is used as protection against an intruder's ability to spoof a sensor receiver using a `classical` intercept-resend attack. Correlated measurement outcomes from polarization-entangled photons are used to protect against quantum intercept-resend attacks, i.e., attacks using quantum teleportation.
Tampering detection system using quantum-mechanical systems
Humble, Travis S. (Knoxville, TN); Bennink, Ryan S. (Knoxville, TN); Grice, Warren P. (Oak Ridge, TN)
2011-12-13
The use of quantum-mechanically entangled photons for monitoring the integrity of a physical border or a communication link is described. The no-cloning principle of quantum information science is used as protection against an intruder's ability to spoof a sensor receiver using a `classical` intercept-resend attack. Correlated measurement outcomes from polarization-entangled photons are used to protect against quantum intercept-resend attacks, i.e., attacks using quantum teleportation.
Galois quantum systems, irreducible polynomials and Riemann surfaces
Finite quantum systems in which the position and momentum take values in the Galois field GF(pl), are studied. Ideas from the subject of field extension are transferred in the context of quantum mechanics. The Frobenius automorphisms in Galois fields lead naturally to the 'Frobenius formalism' in a quantum context. The Hilbert space splits into 'Frobenius subspaces' which are labeled with the irreducible polynomials associated with the ypl-y. The Frobenius maps transform unitarily the states of a Galois quantum system and leave fixed all states in some of its Galois subsystems (where the position and momentum take values in subfields of GF(pl)). An analytic representation of these systems in the l-sheeted complex plane shows deeper links between Galois theory and Riemann surfaces
Galois quantum systems, irreducible polynomials and Riemann surfaces
Vourdas, A.
2006-09-01
Finite quantum systems in which the position and momentum take values in the Galois field GF (pℓ), are studied. Ideas from the subject of field extension are transferred in the context of quantum mechanics. The Frobenius automorphisms in Galois fields lead naturally to the "Frobenius formalism" in a quantum context. The Hilbert space splits into "Frobenius subspaces" which are labeled with the irreducible polynomials associated with the ypℓ-y. The Frobenius maps transform unitarily the states of a Galois quantum system and leave fixed all states in some of its Galois subsystems (where the position and momentum take values in subfields of GF (pℓ)). An analytic representation of these systems in the ℓ-sheeted complex plane shows deeper links between Galois theory and Riemann surfaces.
Smooth controllability of infinite-dimensional quantum-mechanical systems
Manipulation of infinite-dimensional quantum systems is important to controlling complex quantum dynamics with many practical physical and chemical backgrounds. In this paper, a general investigation is casted to the controllability problem of quantum systems evolving on infinite-dimensional manifolds. Recognizing that such problems are related with infinite-dimensional controllability algebras, we introduce an algebraic mathematical framework to describe quantum control systems possessing such controllability algebras. Then we present the concept of smooth controllability on infinite-dimensional manifolds, and draw the main result on approximate strong smooth controllability. This is a nontrivial extension of the existing controllability results based on the analysis over finite-dimensional vector spaces to analysis over infinite-dimensional manifolds. It also opens up many interesting problems for future studies
Manipulating quantum information on the controllable systems or subspaces
Zhang, Ming
2010-01-01
In this paper, we explore how to constructively manipulate quantum information on the controllable systems or subspaces. It is revealed that one can make full use of distinguished properties of Pauli operators to design control Hamiltonian based on the geometric parametrization of quantum states. It is demonstrated in this research that Bang-Bang controls, triangle-function controls and square-function control can be utilized to manipulate controllable qubits or encoded qubits on controllable subspace for both open quantum dynamical systems and uncontrollable closed quantum dynamical systems. Furthermore, we propose a new kind of time-energy performance index to trade-off time and energy resource cost, and comprehensively discuss how to design control magnitude to minimize a kind of time-energy performance. A comparison has been made among these three kind of optimal control. It is underlined in this research that the optimal time performance can be always expressed as J^{*} =\\lamda{\\cdot}t^{*}_{f} +E^{*} for...
Quantum Magnets and Matrix Lorenz Systems
The Landau-Lifshitz-Gilbert equations for the evolution of the magnetization, in presence of an external torque, can be cast in the form of the Lorenz equations and, thus, can describe chaotic fluctuations. To study quantum effects, we describe the magnetization by matrices, that take values in a Lie algebra. The finite dimensionality of the representation encodes the quantum fluctuations, while the non-linear nature of the equations can describe chaotic fluctuations. We identify a criterion, for the appearance of such non-linear terms. This depends on whether an invariant, symmetric tensor of the algebra can vanish or not. This proposal is studied in detail for the fundamental representation of u(2) = u(1) su(2). We find a knotted structure for the attractor, a bimodal distribution for the largest Lyapunov exponent and that the dynamics takes place within the Cartan subalgebra, that does not contain only the identity matrix, thereby can describe the quantum fluctuations
Quantum statistical gravity: time dilation due to local information in many-body quantum systems
Sels, Dries
2016-01-01
We propose a generic mechanism for the emergence of a gravitational potential that acts on all classical objects in a quantum system. Our conjecture is based on the analysis of mutual information in many-body quantum systems. Since measurements in quantum systems affect the surroundings through entanglement, a measurement at one position reduces the entropy in its neighbourhood. This reduction in entropy can be described by a local temperature, that is directly related to the gravitational potential. A crucial ingredient in our argument is that ideal classical mechanical motion occurs at constant probability. This definition is motivated by the analysis of entropic forces in classical systems, which can be formally rewritten in terms of a gravitational potential.
Controllable multiple-quantum transitions in a T-shaped small quantum dot-ring system
Chen, Xiongwen; Chen, Baoju; Song, Kehui; Zhou, Guanghui
2016-05-01
Based on the tight-binding model and the slave boson mean field approximation, we investigate the electron transport properties in a small quantum dot (QD)-ring system. Namely, a strongly correlated QD not only attaches directly to two normal metallic electrodes, but also forms a magnetic control Aharonov-Bohm quantum ring with a few noninteracting QDs. We show that the parity effect, the Kondo effect, and the multiple Fano effects coexist in our system. Moreover, the parities, defined by the odd- and even-numbered energy levels in this system, can be switched by adjusting magnetic flux phase ϕ located at the center of the quantum ring, which induces multiple controllable Fano-interference energy pathways. Therefore, the constructive and destructive multi-Fano interference transition, the Kondo and Fano resonance transition at the Fermi level, the Fano resonance and ani-resonance transition are realized in the even parity system. They can also be observed in the odd parity system when one adjusts the phase ϕ and the gate voltage Vg applied to the noninteracting QDs. The multi-quantum transitions determine some interesting transport properties such as the current switch and its multi-flatsteps, the differential conductance switch at zero bias voltage and its oscillation or quantization at the low bias voltage. These results may be useful for the observation of multiple quantum effect interplays experimentally and the design of controllable QD-based device.
Symmetry in quantum system theory: Rules for quantum architecture design
We investigate universality in the sense of controllability and observability, of multi-qubit systems in architectures of various symmetries of coupling type and topology. By determining the respective dynamic system Lie algebras, explicit reachability sets under symmetry constraints are provided. Thus for a given (possibly symmetric) experimental coupling architecture several decision problems can be solved in a unified way: (i) can a target Hamiltonian be simulated? (ii) can a target gate be synthesised? (iii) to which extent is the system observable by a given set of detection operators? and, as a special case of the latter, (iv) can an underlying system Hamiltonian be identified with a given set of detection operators? Finally, in turn, the absence of symmetry provides a convenient necessary condition for full controllability. Though often easier to assess than the well-established Lie-algebra rank condition, this is not sufficient unless the candidate dynamic simple Lie algebra can be pre-identified uniquely. Thus for architectures with various Ising and Heisenberg coupling types we give design rules sufficient to ensure full controllability. In view of follow-up studies, we relate the unification of necessary and sufficient conditions for universality to filtering simple Lie subalgebras of su(N) comprising classical and exceptional types.
Coherently tracking the covariance matrix of an open quantum system
Miao, Zibo; Hush, Michael R.; James, Matthew R.
2015-07-01
Coherent feedback control of quantum systems has demonstrable advantages over measurement-based control, but so far there has been little work done on coherent estimators and more specifically coherent observers. Coherent observers are input the coherent output of a specified quantum plant and are designed such that some subset of the observer's and plant's expectation values converge in the asymptotic limit. We previously developed a class of mean tracking (MT) observers for open harmonic oscillators that only converged in mean position and momentum; here we develop a class of covariance matrix tracking (CMT) coherent observers that track both the mean and the covariance matrix of a quantum plant. We derive necessary and sufficient conditions for the existence of a CMT observer and find that there are more restrictions on a CMT observer than there are on a MT observer. We give examples where we demonstrate how to design a CMT observer and show that it can be used to track properties like the entanglement of a plant. As the CMT observer provides more quantum information than a MT observer, we expect it will have greater application in future coherent feedback schemes mediated by coherent observers. Investigation of coherent quantum estimators and observers is important in the ongoing discussion of quantum measurement because they provide an estimation of a system's quantum state without explicit use of the measurement postulate in their derivation.
De Roeck, W., E-mail: wojciech.deroeck@fys.kuleuven.be, E-mail: christian.maes@fys.kuleuven.be, E-mail: netocny@fzu.cz, E-mail: marius.schutz@fys.kuleuven.be; Maes, C., E-mail: wojciech.deroeck@fys.kuleuven.be, E-mail: christian.maes@fys.kuleuven.be, E-mail: netocny@fzu.cz, E-mail: marius.schutz@fys.kuleuven.be; Schütz, M., E-mail: wojciech.deroeck@fys.kuleuven.be, E-mail: christian.maes@fys.kuleuven.be, E-mail: netocny@fzu.cz, E-mail: marius.schutz@fys.kuleuven.be [Instituut voor Theoretische Fysica, KU Leuven, Leuven (Belgium); Netočný, K., E-mail: wojciech.deroeck@fys.kuleuven.be, E-mail: christian.maes@fys.kuleuven.be, E-mail: netocny@fzu.cz, E-mail: marius.schutz@fys.kuleuven.be [Institute of Physics AS CR, Prague (Czech Republic)
2015-02-15
We study the projection on classical spins starting from quantum equilibria. We show Gibbsianness or quasi-locality of the resulting classical spin system for a class of gapped quantum systems at low temperatures including quantum ground states. A consequence of Gibbsianness is the validity of a large deviation principle in the quantum system which is known and here recovered in regimes of high temperature or for thermal states in one dimension. On the other hand, we give an example of a quantum ground state with strong nonlocality in the classical restriction, giving rise to what we call measurement induced entanglement and still satisfying a large deviation principle.
We study the projection on classical spins starting from quantum equilibria. We show Gibbsianness or quasi-locality of the resulting classical spin system for a class of gapped quantum systems at low temperatures including quantum ground states. A consequence of Gibbsianness is the validity of a large deviation principle in the quantum system which is known and here recovered in regimes of high temperature or for thermal states in one dimension. On the other hand, we give an example of a quantum ground state with strong nonlocality in the classical restriction, giving rise to what we call measurement induced entanglement and still satisfying a large deviation principle
Coherent versus Measurement Feedback: Linear Systems Theory for Quantum Information
Yamamoto, Naoki
2014-10-01
To control a quantum system via feedback, we generally have two options in choosing a control scheme. One is the coherent feedback, which feeds the output field of the system, through a fully quantum device, back to manipulate the system without involving any measurement process. The other one is measurement-based feedback, which measures the output field and performs a real-time manipulation on the system based on the measurement results. Both schemes have advantages and disadvantages, depending on the system and the control goal; hence, their comparison in several situations is important. This paper considers a general open linear quantum system with the following specific control goals: backaction evasion, generation of a quantum nondemolished variable, and generation of a decoherence-free subsystem, all of which have important roles in quantum information science. Some no-go theorems are proven, clarifying that those goals cannot be achieved by any measurement-based feedback control. On the other hand, it is shown that, for each control goal there exists a coherent feedback controller accomplishing the task. The key idea to obtain all the results is system theoretic characterizations of the above three notions in terms of controllability and observability properties or transfer functions of linear systems, which are consistent with their standard definitions.
Tomograms for open quantum systems: In(finite) dimensional optical and spin systems
Thapliyal, Kishore; Banerjee, Subhashish; Pathak, Anirban
2016-03-01
Tomograms are obtained as probability distributions and are used to reconstruct a quantum state from experimentally measured values. We study the evolution of tomograms for different quantum systems, both finite and infinite dimensional. In realistic experimental conditions, quantum states are exposed to the ambient environment and hence subject to effects like decoherence and dissipation, which are dealt with here, consistently, using the formalism of open quantum systems. This is extremely relevant from the perspective of experimental implementation and issues related to state reconstruction in quantum computation and communication. These considerations are also expected to affect the quasiprobability distribution obtained from experimentally generated tomograms and nonclassicality observed from them.
A LONE code for the sparse control of quantum systems
Ciaramella, G.; Borzì, A.
2016-03-01
In many applications with quantum spin systems, control functions with a sparse and pulse-shaped structure are often required. These controls can be obtained by solving quantum optimal control problems with L1-penalized cost functionals. In this paper, the MATLAB package LONE is presented aimed to solving L1-penalized optimal control problems governed by unitary-operator quantum spin models. This package implements a new strategy that includes a globalized semi-smooth Krylov-Newton scheme and a continuation procedure. Results of numerical experiments demonstrate the ability of the LONE code in computing accurate sparse optimal control solutions.
Quantum information transfer between topological and spin qubit systems
Leijnse, Martin; Flensberg, Karsten [Nano-Science Center and Niels Bohr Institute, University of Copenhagen (Denmark)
2012-07-01
In this talk I introduce a method to coherently transfer quantum information, and to create entanglement, between topological qubits and conventional spin qubits. The transfer method uses gated control to transfer an electron (spin qubit) between a quantum dot and edge Majorana modes in adjacent topological superconductors. Because of the spin polarization of the Majorana modes, the electron transfer translates spin superposition states into superposition states of the Majorana system, and vice versa. Furthermore, I discuss how a topological superconductor can be used to facilitate long-distance quantum information transfer and entanglement between spatially separated spin qubits.
Quantum Entanglement and Electron Correlation in Molecular Systems
Wang, H; Kais, Sabre; Wang, Hefeng
2007-01-01
We study the relation between quantum entanglement and electron correlation in quantum chemistry calculations. We prove that the Hartree-Fock (HF) wave function does not violate Bell's inequality, thus is not entangled while the configuration interaction (CI) wave function is entangled since it violates Bell's inequality. Entanglement is related to electron correlation and might be used as an alternative measure of the electron correlation in quantum chemistry calculations. As an example we show the calculations of entanglement for the H$_2$ molecule and how it is related to electron correlation of the system, which is the difference between the exact and the HF energies.
Quantum Effects in the Mechanical Properties of Suspended Nanomechanical Systems
Carr, S M; Wybourne, M N
2001-01-01
We explore the quantum aspects of an elastic bar supported at both ends and subject to compression. If strain rather than stress is held fixed, the system remains stable beyond the buckling instability, supporting two potential minima. The classical equilibrium transverse displacement is analogous to a Ginsburg-Landau order parameter, with strain playing the role of temperature. We calculate the quantum fluctuations about the classical value as a function of strain. Excitation energies and quantum fluctuation amplitudes are compared for silicon beams and carbon nanotubes.
Photoluminescence of hybrid quantum dot systems
Král, Karel; Menšík, Miroslav
2015-01-01
Roč. 7, č. 4 (2015), 347-349. ISSN 2164-6627 R&D Projects: GA MŠk LH12236; GA MŠk LH12186 Institutional support: RVO:68378271 ; RVO:61389013 Keywords : quantum dots * energy transfer * electron-phonon interaction Subject RIV: BM - Solid Matter Physics ; Magnetism
Reversal of Thermal Rectification in Quantum Systems
Zhang, Lifa; Yan, Yonghong; Wu, Chang-Qin; Wang, Jian-Sheng; Li, Baowen
2009-01-01
We study thermal transport in anisotropic Heisenberg spin chains using the quantum master equation. It is found that thermal rectification changes sign when the external homogeneous magnetic field is varied. This reversal also occurs when the magnetic field becomes inhomogeneous. Moreover, we can tune the reversal of rectification by temperatures of the heat baths, the anisotropy and size of the spin chains.
Localization of dynamic chaons in quantum systems
Numerical experiments with a simple quantum model show that the localization length of dynamical chaos is determined by the diffusion rate in the classical limit. The investigation of the localization phenomenon near the critical parameter value is carried out. The conditions of delocalization in the case of inhomogeneous diffusion are determined
Moving Quantum Systems: Particles Versus Vacuum
Kuckert, Bernd
2002-01-01
We give an overview on a couple of recent results concerning the KMS-condition and the characterization of thermodynamic equilibrium states from a moving observer's point of view. These results include a characterization of vacuum states in relativistic quantum field theory and a general derivation of the Unruh effect.
Atomic quantum systems in optical micro-structures
Full text: We combine state-of-the-art technology in micro-optics with the quantum optical techniques of laser cooling, laser trapping, and quantum control to open a new gateway for quantum information processing and matter wave optics with atomic systems. We use micro-fabricated optical systems to create light fields that allow us to trap and guide neutral atoms as a result of the optical dipole force experienced by the atoms. The realization of arrays of laser traps that can serve as registers for atomic quantum bits and as integrated waveguide structures for atom optics and atom interferometry has been achieved. This approach opens the possibility to scale, parallelize, and miniaturize systems for quantum information processing and atom optics. Currently we investigate the production of quantum-degenerate systems in pure optical trapping geometries and the coherent manipulation (1-qubit rotations, Ramsey-oscillations, spin-echo experiments) of internal qubit states for atoms trapped in arrays of dipole traps (author)
Shushin, A. I.
2011-02-01
The manifestation of measurements, randomly distributed in time, on the evolution of quantum systems are analyzed in detail. The set of randomly distributed measurements (RDM) is modeled within the renewal theory, in which the distribution is characterized by the probability density function (PDF) W(t) of times t between successive events (measurements). The evolution of the quantum system affected by the RDM is shown to be described by the density matrix satisfying the stochastic Liouville equation. This equation is applied to the analysis of the RDM effect on the evolution of a two-level system for different types of RDM statistics, corresponding to different PDFs W(t). Obtained general results are illustrated as applied to the cases of the Poissonian (W(t) \\sim \\,e^{-w_r t}) and anomalous (W(t) ~ 1/t1 + α, α RDM statistics. In particular, specific features of the quantum and inverse Zeno effects, resulting from the RDM, are thoroughly discussed.
The manifestation of measurements, randomly distributed in time, on the evolution of quantum systems are analyzed in detail. The set of randomly distributed measurements (RDM) is modeled within the renewal theory, in which the distribution is characterized by the probability density function (PDF) W(t) of times t between successive events (measurements). The evolution of the quantum system affected by the RDM is shown to be described by the density matrix satisfying the stochastic Liouville equation. This equation is applied to the analysis of the RDM effect on the evolution of a two-level system for different types of RDM statistics, corresponding to different PDFs W(t). Obtained general results are illustrated as applied to the cases of the Poissonian (W(t)∼ e-wrt) and anomalous (W(t) ∼ 1/t1+α, α ≤ 1) RDM statistics. In particular, specific features of the quantum and inverse Zeno effects, resulting from the RDM, are thoroughly discussed.
Controlling open quantum systems: tools, achievements, and limitations.
Koch, Christiane P
2016-06-01
The advent of quantum devices, which exploit the two essential elements of quantum physics, coherence and entanglement, has sparked renewed interest in the control of open quantum systems. Successful implementations face the challenge of preserving relevant nonclassical features at the level of device operation. A major obstacle is decoherence, which is caused by interaction with the environment. Optimal control theory is a tool that can be used to identify control strategies in the presence of decoherence. Here we review recent advances in optimal control methodology that allow typical tasks in device operation for open quantum systems to be tackled and discuss examples of relaxation-optimized dynamics. Optimal control theory is also a useful tool to exploit the environment for control. We discuss examples and point out possible future extensions. PMID:27143501
Superconducting quantum spin Hall systems with giant orbital g factors
Reinthaler, R. W.; Tkachov, G.; Hankiewicz, E. M.
2015-10-01
Topological aspects of superconductivity in quantum spin Hall systems (QSHSs) such as thin layers of three-dimensional topological insulators (TIs) or two-dimensional TIs are the focus of current research. Here, we describe a superconducting quantum spin Hall effect (quantum spin Hall system in proximity to an s -wave superconductor and in orbital in-plane magnetic fields), which is protected against elastic backscattering by combined time-reversal and particle-hole symmetry. This effect is characterized by spin-polarized edge states, which can be manipulated in weak magnetic fields due to a giant effective orbital g factor, allowing the generation of spin currents. The phenomenon provides a solution to the outstanding challenge of detecting the spin polarization of the edge states. Here we propose the detection of the edge polarization in a three-terminal junction using unusual transport properties of the superconducting quantum Hall effect: a nonmonotonic excess current and a zero-bias conductance peak splitting.
GRAVITATIONAL WAVES AND STATIONARY STATES OF QUANTUM AND CLASSICAL SYSTEMS
Trunev A. P.
2014-03-01
Full Text Available In this paper, we consider gravitation theory in multidimensional space. The model of the metric satisfying the basic requirements of quantum theory is proposed. It is shown that gravitational waves are described by the Liouville equation and the Schrodinger equation as well. The solutions of the Einstein equations describing the stationary states of arbitrary quantum and classical systems with central symmetry have been obtained. Thus, it is proved that atoms and atomic nuclei can be represented as standing gravitational waves
Scaling law and stability for a noisy quantum system
Sadgrove, Mark; Parkins, Scott; Leonhardt, Rainer
2008-01-01
We show that a scaling law exists for the near resonant dynamics of cold kicked atoms in the presence of a randomly fluctuating pulse amplitude. Analysis of a quasi-classical phase-space representation of the quantum system with noise allows a new scaling law to be deduced. The scaling law and associated stability are confirmed by comparison with quantum simulations and experimental data.
Canonical Typicality of Energy Eigenstates of an Isolated Quantum System
Dymarsky, Anatoly
2015-01-01
Currently there are two main approaches to describe how quantum statistical physics emerges from an isolated quantum many-body system in a pure state: Canonical Typicality (CT) and Eigenstate Thermalization Hypothesis (ETH). These two approaches has different but overlapping areas of validity, phenomenology and set of physical outcomes. In this paper we discuss the relation between CT and ETH and propose a formulation of ETH in terms of the reduced density matrix. We provide strong numerical evidences for the proposal.
A short review on entanglement in quantum spin systems
Latorre, J. I.; Riera, A.
2009-01-01
We review some of the recent progress on the study of entropy of entanglement in many-body quantum systems. Emphasis is placed on the scaling properties of entropy for one-dimensional multi-partite models at quantum phase transitions and, more generally, on the concept of area law. We also briefly describe the relation between entanglement and the presence of impurities, the idea of particle entanglement, the evolution of entanglement along renormalization group trajectories, the dynamical ev...
Quantum hydrodynamic modes in one-dimensional polaron system
Dynamical relaxation process of one-dimensional polaron system weakly coupled with a thermal phonon field is theoretically investigated. In addition to the diffusion relaxation, we have found that there appears a new macroscopic quantum sound mode which stabilizes the wave packet of the quantum particle even under the random collision with the thermal phonon. This coherent sound mode is a new hydrodynamic mode obeying a macroscopic linear wave equation for the density of the particle, instead of wave function
Quantum Evolution Supergenerator of Superparamagnetic System in Discrete Orientation Model
Buslov, V. A.
2001-01-01
The supergenerator of superparamagnetic system quantum evolution is investigated in discrete orientation model (DOM). It is shown that the generator is J-self-adjoint one at the case of potential drift field agreed upon magnetic anisotropy of the sample investigated. Perturbation theory is used for spectral analysis. The qualitative dependence of resonance absorption spectrum on the relation between quantum and stochastic parameters is demonstrated.
A term-rewriting system for computer quantum algebra
J. J. Hudson
2008-01-01
Existing computer algebra packages do not fully support quantum mechanics calculations in Dirac's notation. I present the foundation for building such support: a mathematical system for the symbolic manipulation of expressions used in the invariant formalism of quantum mechanics. I first describe the essential mathematical features of the Hilbert-space invariant formalism. This is followed by a formal characterisation of all possible algebraic expressions in this formalism. This characterisat...
Quantum mechanics of rapidly and periodically driven systems
Malay Bandyopadhyay; Sushanta Dattagupta
2008-03-01
This review deals with the dynamics of quantum systems that are subject to high frequency external perturbations. Though the problem may look hopelessly time-dependent, and poised on the extreme opposite side of adiabaticity, there exists a `Kapitza Window' over which the dynamics can be treated in terms of effective time-independent Hamiltonians. The consequent results are important in the context of atomic traps as well as quantum optic properties of atoms in intense and high-frequency electromagnetic fields.
Far from equilibrium energy flow in quantum critical systems
Bhaseen, M J; Lucas, Andrew; Schalm, Koenraad
2013-01-01
We investigate far from equilibrium energy transport in strongly coupled quantum critical systems. Combining results from gauge-gravity duality, relativistic hydrodynamics, and quantum field theory, we argue that long-time energy transport occurs via a universal steady-state for any spatial dimensionality. This is described by a boosted thermal state. We determine the transport properties of this emergent steady state, including the average energy flow and its long-time fluctuations.
Hierarchy of stochastic pure states for open quantum system dynamics
S, D.; Eisfeld, A.; Strunz, W. T.
2014-01-01
We derive a hierarchy of stochastic evolution equations for pure states (quantum trajectories) to efficiently solve open quantum system dynamics with non-Markovian structured environments. From this hierarchy of pure states (HOPS) the exact reduced density operator is obtained as an ensemble average. We demonstrate the power of HOPS by applying it to the Spin-Boson model, the calculation of absorption spectra of molecular aggregates and energy transfer in a photosynthetic pigment-protein comp...
Quantum Coulomb systems : screening, recombination and van der Waals forces
Alastuey, Angel
2010-01-01
The study of quantum Coulomb systems at equilibrium is important for understanding properties of matter in many physical situations. Screening, recombination and van der Waals forces are basic phenomena which result from the interplay of Coulomb interactions, collective effects and quantum mechanics. Those phenomena are introduced in the first part of this lecture, through various physical examples. Their treatment within mean-field theories and phenomenological approaches is also exposed, wh...
Quantum computing with collective ensembles of multi-level systems
Brion, E.; Moelmer, K.; Saffman, M.
2007-01-01
We propose a new physical approach for encoding and processing of quantum information in ensembles of multi-level quantum systems, where the different bits are not carried by individual particles but associated with the collective population of different internal levels. One- and two-bit gates are implemented by collective internal state transitions taking place in the presence of an excitation blockade mechanism which restricts the population of each internal state to the values zero and uni...
Coherently tracking the covariance matrix of an open quantum system
Miao, Zibo; Hush, Michael R.; James, Matthew
2015-01-01
Coherent feedback control of quantum systems has demonstrable advantages over measurement-based control, but so far there has been little work done on coherent estimators and more specifically coherent observers. Coherent observers are input the coherent output of a specified quantum plant, and are designed such that some subset of the observer and plant's expectation values converge in the asymptotic limit. We previously developed a class of mean tracking (MT) observers for open harmonic osc...
Computer simulation of mixed classical-quantum systems
We briefly review three important methods that are currently used in the simulation of mixed systems. Two of these techniques, path integral Monte Carlo or molecular dynamics and dynamical simulated annealing, have the limitation that they can only describe the structural properties in the ground state. The third so-called quantum molecular dynamics (QMD) method can provide not only the static properties but also the real-time dynamics of a quantum particle at finite temperatures. 10 refs
Kamleitner, Ingo
2010-01-01
We employ the theoretical framework of positive operator valued measures, to study Markovian open quantum systems. In particular, we discuss how a quantum system influences its environment. Using the theory of indirect measurements, we then draw conclusions about the information we could hypothetically obtain about the system by observing the environment. Although the environment is not actually observed, we can use these results to describe the change of the quantum system due to its interaction with the environment. We apply this technique to two different problems. In the first part, we study the coherently driven dynamics of a particle on a rail of quantum dots. This tunnelling between adjacent quantum dots can be controlled externally. We employ an adiabatic scheme similar to stimulated Raman adiabatic passage, to transfer the particle between different quantum dots. We compare two fundamentally different sources of decoherence. In the second part, we study the dynamics of a free quantum particle, which ...
Quantum state tomography and quantum logical operations in a three qubits NMR quadrupolar system
Araujo-Ferreira, A G; Soares-Pinto, D O; deAzevedo, E R; Bonagamba, T J; Teles, J
2011-01-01
In this work, we present an implementation of quantum logic gates and algorithms in a three effective qubits system, represented by a (I = 7/2) NMR quadrupolar nuclei. To implement these protocols we have used the strong modulating pulses (SMP). The various stages of each implementation were verified by quantum state tomography (QST). It is presented here the results for the computational base states, Toffolli logic gates, and Deutsch-Jozsa and Grover algorithms. Also, we discuss the di?culties and advantages of implementing such protocols using the SMP technique in quadrupolar systems.
Method for adding nodes to a quantum key distribution system
Grice, Warren P
2015-02-24
An improved quantum key distribution (QKD) system and method are provided. The system and method introduce new clients at intermediate points along a quantum channel, where any two clients can establish a secret key without the need for a secret meeting between the clients. The new clients perform operations on photons as they pass through nodes in the quantum channel, and participate in a non-secret protocol that is amended to include the new clients. The system and method significantly increase the number of clients that can be supported by a conventional QKD system, with only a modest increase in cost. The system and method are compatible with a variety of QKD schemes, including polarization, time-bin, continuous variable and entanglement QKD.
Heat-exchange statistics in driven open quantum systems
As the dimensions of physical systems approach the nanoscale, the laws of thermodynamics must be reconsidered due to the increased importance of fluctuations and quantum effects. While the statistical mechanics of small classical systems is relatively well understood, the quantum case still poses challenges. Here, we set up a formalism that allows us to calculate the full probability distribution of energy exchanges between a periodically driven quantum system and a thermalized heat reservoir. The formalism combines Floquet theory with a generalized master equation approach. For a driven two-level system and in the long-time limit, we obtain a universal expression for the distribution, providing clear physical insight into the exchanged energy quanta. We illustrate our approach in two analytically solvable cases and discuss the differences in the corresponding distributions. Our predictions could be directly tested in a variety of systems, including optical cavities and solid-state devices. (paper)
Tucci, Robert R.
2009-01-01
We describe an algorithm for using a quantum computer to calculate mean values of observables and the partition function of a quantum system. Our algorithm includes two sub-algorithms. The first sub-algorithm is for calculating, with polynomial efficiency, certain diagonal matrix elements of an observable. This sub-algorithm is performed on a quantum computer, using quantum phase estimation and tomography. The second sub-algorithm is for sampling a probability distribution. This sub-algorithm...
Petersen, Ian R.
2015-01-01
This paper considers the problem of constructing a direct coupled quantum observer network for a single qubit quantum system. The proposed observer consists of a network of quantum harmonic oscillators and it is shown that the observer network output converges to a consensus in a time averaged sense in which each component of the observer estimates a specified output of the quantum plant. An example and simulations are included.
Quantum metrology in Lipkin-Meshkov-Glick critical systems
Salvatori, Giulio; Mandarino, Antonio; Paris, Matteo G. A.
2014-08-01
The Lipkin-Meshkov-Glick (LMG) model describes critical systems with interaction beyond the first-neighbor approximation. Here we address quantum metrology in LMG systems and show how criticality may be exploited to improve precision. At first we focus on the characterization of LMG systems themselves, i.e., the estimation of anisotropy, and address the problem by considering the quantum Cramr-Rao bound. We evaluate the quantum Fisher information of small-size LMG chains made of N =2, 3, and 4 lattice sites and also analyze the same quantity in the thermodynamical limit. Our results show that criticality is indeed a resource and that the ultimate bounds to precision may be achieved by tuning the external field and measuring the total magnetization of the system. We then address the use of LMG systems as quantum thermometers and show that (i) precision is governed by the gap between the lowest energy levels of the systems and (ii) field-dependent level crossing is a metrological resource to extend the operating range of the quantum thermometer.
Quantum dynamics of deformed open systems
A master equation for the deformed quantum harmonic oscillator interacting with a dissipative environment, in particular with a thermal bath, is derived in the microscopic model using perturbation theory . The coefficient of the master equation depend on the deformation function. The steady state solution of the equation for the density matrix in the number representation is obtained and the equilibrium energy of the deformed harmonic oscillator is calculated in the approximation of small deformation. (author)
Quantum Gravity as a Dissipative Deterministic System
Hooft, G. 't
1999-01-01
It is argued that the so-called holographic principle will obstruct attempts to produce physically realistic models for the unification of general relativity with quantum mechanics, unless determinism in the latter is restored. The notion of time in GR is so different from the usual one in elementary particle physics that we believe that certain versions of hidden variable theories can -- and must -- be revived. A completely natural procedure is proposed, in which the dissipation of informati...
Conditions for Nondistortion Interrogation of Quantum System
Zhou, Zheng-Wei; Zhou, Xingxiang; Feldman, Marc J.; Guo, Guang-Can
2001-01-01
Under some physical considerations, we present a universal formulation to study the possibility of localizing a quantum object in a given region without disturbing its unknown internal state. When the interaction between the object and probe wave function takes place only once, we prove the necessary and sufficient condition that the object's presence can be detected in an initial state preserving way. Meanwhile, a conditioned optimal interrogation probability is obtained.
Numerical approaches to complex quantum, semiclassical and classical systems
Schubert, Gerald
2008-11-03
In this work we analyse the capabilities of several numerical techniques for the description of different physical systems. Thereby, the considered systems range from quantum over semiclassical to classical and from few- to many-particle systems. In chapter 1 we investigate the behaviour of a single quantum particle in the presence of an external disordered background (static potentials). Starting from the quantum percolation problem, we address the fundamental question of a disorder induced (Anderson-) transition from extended to localised single-particle eigenstates. Distinguishing isolating from conducting states by applying a local distribution approach for the local density of states (LDOS), we detect the quantum percolation threshold in two- and three-dimensions. Extending the quantum percolation model to a quantum random resistor model, we comment on the possible relevance of our results to the influence of disorder on the conductivity in graphene sheets. For the calculation of the LDOS as well as for the Chebyshev expansion of the time evolution operator, the kernel polynomial method (KPM) is the key numerical technique. In chapter 2 we examine how a single quantum particle is influenced by retarded bosonic fields that are inherent to the system. Within the Holstein model, these bosonic degrees of freedom (phonons) give rise to an infinite dimensional Hilbert space, posing a true many-particle problem. Constituting a minimal model for polaron formation, the Holstein model allows us to study the optical absorption and activated transport in polaronic systems. Using a two-dimensional variant of the KPM, we calculate for the first time quasi-exactly the optical absorption and dc-conductivity as a function of temperature. In chapter 3 we come back to the time evolution of a quantum particle in an external, static potential and investigate the capability of semiclassical approximations to it. We address basic quantum effects as tunneling, interference and anharmonicity. To this end we consider the linearised semiclassical propagator method, the Wigner-Moyal approach and the recently proposed quantum tomography. Finally, in chapter 4 we calculate the dynamics of a classical many-particle system under the influence of external fields. Considering a low-temperature rf-plasma, we investigate the interplay of the plasma dynamics and the motion of dust particles, immersed into the plasma for diagnostic reasons. (orig.)
Numerical approaches to complex quantum, semiclassical and classical systems
In this work we analyse the capabilities of several numerical techniques for the description of different physical systems. Thereby, the considered systems range from quantum over semiclassical to classical and from few- to many-particle systems. In chapter 1 we investigate the behaviour of a single quantum particle in the presence of an external disordered background (static potentials). Starting from the quantum percolation problem, we address the fundamental question of a disorder induced (Anderson-) transition from extended to localised single-particle eigenstates. Distinguishing isolating from conducting states by applying a local distribution approach for the local density of states (LDOS), we detect the quantum percolation threshold in two- and three-dimensions. Extending the quantum percolation model to a quantum random resistor model, we comment on the possible relevance of our results to the influence of disorder on the conductivity in graphene sheets. For the calculation of the LDOS as well as for the Chebyshev expansion of the time evolution operator, the kernel polynomial method (KPM) is the key numerical technique. In chapter 2 we examine how a single quantum particle is influenced by retarded bosonic fields that are inherent to the system. Within the Holstein model, these bosonic degrees of freedom (phonons) give rise to an infinite dimensional Hilbert space, posing a true many-particle problem. Constituting a minimal model for polaron formation, the Holstein model allows us to study the optical absorption and activated transport in polaronic systems. Using a two-dimensional variant of the KPM, we calculate for the first time quasi-exactly the optical absorption and dc-conductivity as a function of temperature. In chapter 3 we come back to the time evolution of a quantum particle in an external, static potential and investigate the capability of semiclassical approximations to it. We address basic quantum effects as tunneling, interference and anharmonicity. To this end we consider the linearised semiclassical propagator method, the Wigner-Moyal approach and the recently proposed quantum tomography. Finally, in chapter 4 we calculate the dynamics of a classical many-particle system under the influence of external fields. Considering a low-temperature rf-plasma, we investigate the interplay of the plasma dynamics and the motion of dust particles, immersed into the plasma for diagnostic reasons. (orig.)
A quantum information perspective of fermionic quantum many-body systems
Kraus, Christina V.
2009-11-02
In this Thesis fermionic quantum many-body system are theoretically investigated from a quantum information perspective. Quantum correlations in fermionic many-body systems, though central to many of the most fascinating effects of condensed matter physics, are poorly understood from a theoretical perspective. Even the notion of ''paired'' fermions which is widely used in the theory of superconductivity and has a clear physical meaning there, is not a concept of a systematic and mathematical theory so far. Applying concepts and tools from entanglement theory, we close this gap, developing a pairing theory allowing to unambiguously characterize paired states. We develop methods for the detection and quantification of pairing according to our definition which are applicable to current experimental setups. Pairing is shown to be a quantum correlation distinct from any notion of entanglement proposed for fermionic systems, giving further understanding of the structure of highly correlated quantum states. In addition, we show the resource character of paired states for precision metrology, proving that BCS-states allow phase measurements at the Heisenberg limit. Next, the power of fermionic systems is considered in the context of quantum simulations, where we study the possibility to simulate Hamiltonian time evolutions on a cubic lattice under the constraint of translational invariance. Given a set of translationally invariant local Hamiltonians and short range interactions we determine time evolutions which can and those which can not be simulated. Bosonic and finite-dimensional quantum systems (''spins'') are included in our investigations. Furthermore, we develop new techniques for the classical simulation of fermionic many-body systems. First, we introduce a new family of states, the fermionic Projected Entangled Pair States (fPEPS) on lattices in arbitrary spatial dimension. These are the natural generalization of the PEPS known for spin systems, and they approximate efficiently ground and thermal states of systems with short-range interaction. We give an explicit mapping between fPEPS and PEPS, allowing to extend previous simulation methods to fermions. In addition, we show that fPEPS naturally arise as exact ground states of certain fermionic Hamiltonians, and give an example that exhibits criticality while fulfilling the area law. Finally, we derive methods for the determination of ground and thermal states, as well as the time evolution, of interacting fermionic systems using generalized Hartree-Fock theory (gHFT). With the computational complexity scaling polynomially with the number of particles, this method can deal with large systems. As a benchmark we apply our methods to the translationally invariant Hubbard model with attractive interaction and find excellent agreement with known results. (orig.)
A quantum information perspective of fermionic quantum many-body systems
In this Thesis fermionic quantum many-body system are theoretically investigated from a quantum information perspective. Quantum correlations in fermionic many-body systems, though central to many of the most fascinating effects of condensed matter physics, are poorly understood from a theoretical perspective. Even the notion of ''paired'' fermions which is widely used in the theory of superconductivity and has a clear physical meaning there, is not a concept of a systematic and mathematical theory so far. Applying concepts and tools from entanglement theory, we close this gap, developing a pairing theory allowing to unambiguously characterize paired states. We develop methods for the detection and quantification of pairing according to our definition which are applicable to current experimental setups. Pairing is shown to be a quantum correlation distinct from any notion of entanglement proposed for fermionic systems, giving further understanding of the structure of highly correlated quantum states. In addition, we show the resource character of paired states for precision metrology, proving that BCS-states allow phase measurements at the Heisenberg limit. Next, the power of fermionic systems is considered in the context of quantum simulations, where we study the possibility to simulate Hamiltonian time evolutions on a cubic lattice under the constraint of translational invariance. Given a set of translationally invariant local Hamiltonians and short range interactions we determine time evolutions which can and those which can not be simulated. Bosonic and finite-dimensional quantum systems (''spins'') are included in our investigations. Furthermore, we develop new techniques for the classical simulation of fermionic many-body systems. First, we introduce a new family of states, the fermionic Projected Entangled Pair States (fPEPS) on lattices in arbitrary spatial dimension. These are the natural generalization of the PEPS known for spin systems, and they approximate efficiently ground and thermal states of systems with short-range interaction. We give an explicit mapping between fPEPS and PEPS, allowing to extend previous simulation methods to fermions. In addition, we show that fPEPS naturally arise as exact ground states of certain fermionic Hamiltonians, and give an example that exhibits criticality while fulfilling the area law. Finally, we derive methods for the determination of ground and thermal states, as well as the time evolution, of interacting fermionic systems using generalized Hartree-Fock theory (gHFT). With the computational complexity scaling polynomially with the number of particles, this method can deal with large systems. As a benchmark we apply our methods to the translationally invariant Hubbard model with attractive interaction and find excellent agreement with known results. (orig.)
Autonomous quantum thermal machines in atom-cavity systems
Mitchison, Mark T; Prior, Javier; Woods, Mischa P; Plenio, Martin B
2016-01-01
An autonomous quantum thermal machine comprising a trapped atom or ion placed inside an optical cavity is proposed and analysed. Such a machine can operate as a heat engine whose working medium is the quantised atomic motion, or as an absorption refrigerator which cools without any work input. Focusing on the refrigerator mode, we predict that it is possible with state-of-the-art technology to cool a trapped ion almost to its motional ground state using a thermal light source such as sunlight. We nonetheless find that a laser or similar reference system is necessary to stabilise the cavity frequencies. Furthermore, we establish a direct and heretofore unacknowledged connection between the abstract theory of quantum absorption refrigerators and practical sideband cooling techniques. We also highlight and clarify some assumptions underlying several recent theoretical studies on self-contained quantum engines and refrigerators. Our work indicates that cavity quantum electrodynamics is a promising and versatile e...
Thermodynamics of quantum dissipative many-body systems
Cuccoli, A; Tognetti, V; Vaia, R
1999-01-01
We consider quantum nonlinear many-body systems with dissipation described within the Caldeira-Leggett model, i.e., by a nonlocal action in the path integral for the density matrix. Approximate classical-like formulas for thermodynamic quantities are derived for the case of many degrees of freedom, with general kinetic and dissipative quadratic forms. The underlying scheme is the pure-quantum self-consistent harmonic approximation (PQSCHA), equivalent to the variational approach by the Feynman-Jensen inequality with a suitable quadratic nonlocal trial action. A low-coupling approximation permits to get manageable PQSCHA expressions for quantum thermal averages with a classical Boltzmann factor involving an effective potential and an inner Gaussian average that describes the fluctuations originating from the interplay of quanticity and dissipation. The application of the PQSCHA to a quantum phi4-chain with Drude-like dissipation shows nontrivial effects of dissipation, depending upon its strength and bandwidth...
Effect of Noise on Practical Quantum Communication Systems
Vishal Sharma
2016-03-01
Full Text Available Entanglement is an important resource for various applications of quantum computation. Another important endeavor is to establish the role of entanglement in practical implementation where system of interest is affected by various kinds of noisy channels. Here, a single classical bit is used to send information under the influence of a noisy quantum channel. The entanglement content of quantum states is computed under noisy channels such as amplitude damping, phase damping, squeesed generalised amplitude damping, Pauli channels and various collective noise models on the protocols of quantum key distribution.Defence Science Journal, Vol. 66, No. 2, March 2016, pp. 186-192, DOI: http://dx.doi.org/10.14429/dsj.66.9771
Nexus: A modular workflow management system for quantum simulation codes
Krogel, Jaron T.
2016-01-01
The management of simulation workflows represents a significant task for the individual computational researcher. Automation of the required tasks involved in simulation work can decrease the overall time to solution and reduce sources of human error. A new simulation workflow management system, Nexus, is presented to address these issues. Nexus is capable of automated job management on workstations and resources at several major supercomputing centers. Its modular design allows many quantum simulation codes to be supported within the same framework. Current support includes quantum Monte Carlo calculations with QMCPACK, density functional theory calculations with Quantum Espresso or VASP, and quantum chemical calculations with GAMESS. Users can compose workflows through a transparent, text-based interface, resembling the input file of a typical simulation code. A usage example is provided to illustrate the process.
Quantifying Quantum Correlations in Fermionic Systems using Witness Operators
Iemini, Fernando; Debarba, Tiago; Vianna, Reinaldo O
2012-01-01
We present a method to quantify quantum correlations in arbitrary systems of indistinguishable fermions using witness operators. The method associates the problem of finding the optimal entan- glement witness of a state with a class of problems known as semidefinite programs (SDPs), which can be solved efficiently with arbitrary accuracy. Based on these optimal witnesses, we introduce a measure of quantum correlations which has an interpretation analogous to the Generalized Robust- ness of entanglement. We also extend the notion of quantum discord to the case of indistinguishable fermions, and propose a geometric quantifier, which is compared to our entanglement measure. Our numerical results show a remarkable equivalence between the proposed Generalized Robustness and the Schliemann concurrence, which are equal for pure states. For mixed states, the Schliemann con- currence presents itself as an upper bound for the Generalized Robustness. The quantum discord is also found to be an upper bound for the entangl...
Time evolution of open quantum many-body systems
Overbeck, Vincent R.; Weimer, Hendrik
2016-01-01
We establish a generic method to analyze the time evolution of open quantum many-body systems. Our approach is based on a variational integration of the quantum master equation describing the dynamics and naturally connects to a variational principle for its nonequilibrium steady state. We successfully apply our variational method to study dissipative Rydberg gases, finding very good quantitative agreement with small-scale simulations of the full quantum master equation. We observe that correlations related to non-Markovian behavior play a significant role during the relaxation dynamics towards the steady state. We further quantify this non-Markovianity and find it to be closely connected to an information-theoretical measure of quantum and classical correlations.
Communication theory of quantum systems. Ph.D. Thesis, 1970
Yuen, H. P. H.
1971-01-01
Communication theory problems incorporating quantum effects for optical-frequency applications are discussed. Under suitable conditions, a unique quantum channel model corresponding to a given classical space-time varying linear random channel is established. A procedure is described by which a proper density-operator representation applicable to any receiver configuration can be constructed directly from the channel output field. Some examples illustrating the application of our methods to the development of optical quantum channel representations are given. Optimizations of communication system performance under different criteria are considered. In particular, certain necessary and sufficient conditions on the optimal detector in M-ary quantum signal detection are derived. Some examples are presented. Parameter estimation and channel capacity are discussed briefly.
RKKY interaction in a chirally coupled double quantum dot system
Heine, A. W.; Tutuc, D.; Haug, R. J. [Institut fr Festkrperphysik, Leibniz Universitt Hannover, Appelstr. 2, 30167 Hannover (Germany); Zwicknagl, G. [Institut fr Mathematische Physik, TU Braunschweig, Mendelssohnstr. 3, 38106 Braunschweig (Germany); Schuh, D. [Institut fr Experimentelle und Angewandte Physik, Universitt Regensburg, Universittstr. 31, 93053 Regensburg (Germany); Wegscheider, W. [Laboratorium fr Festkrperphysik, ETH Zrich, Schafmattstr. 16, 8093 Zrich, Switzerland and Institut fr Experimentelle und Angewandte Physik, Universitt Regensburg, Universittstr. 31, 93053 Regens (Germany)
2013-12-04
The competition between the Kondo effect and the Ruderman-Kittel-Kasuya-Yoshida (RKKY) interaction is investigated in a double quantum dots system, coupled via a central open conducting region. A perpendicular magnetic field induces the formation of Landau Levels which in turn give rise to the so-called Kondo chessboard pattern in the transport through the quantum dots. The two quantum dots become therefore chirally coupled via the edge channels formed in the open conducting area. In regions where both quantum dots exhibit Kondo transport the presence of the RKKY exchange interaction is probed by an analysis of the temperature dependence. The thus obtained Kondo temperature of one dot shows an abrupt increase at the onset of Kondo transport in the other, independent of the magnetic field polarity, i.e. edge state chirality in the central region.
Hidden symmetries enhance quantum transport in Light Harvesting systems
Zech, Tobias; Wellens, Thomas; Buchleitner, Andreas
2012-01-01
For more than 50 years we have known that photosynthetic systems harvest solar energy with almost unit {\\it quantum efficiency}. However, recent experimental evidence of {\\it quantum coherence} during the excitonic energy transport in photosynthetic organisms challenges our understanding of this fundamental biological function. Currently, and despite numerous efforts, the causal connection between coherence and efficiency is still a matter of debate. We show, through the study of extensive simulations of quantum coherent transport on networks, that three dimensional structures characterized by centro-symmetric Hamiltonians are statistically more efficient than random arrangements. Moreover, we demonstrate that the experimental data available for the electronic Hamiltonians of the Fenna-Mathew-Olson (FMO) complex of sulfur bacteria and of the crypophyte PC645 complex of marine algae are consistent with this strong correlation of centro-symmetry with quantum efficiency. These results show that what appears to b...
Tunable supercurrent in a triangular triple quantum dot system
The supercurrent in a triangular triple quantum dot system is investigated by using the nonequilibrium Green's function method. It is found that the sign of the supercurrent can be changed from positive to negative with increasing the strength of spin-flip scattering, resulting in the π-junction transition. The supercurrent and the π-junction transition are also modulated by tuning the system parameters such as the gate voltage and the interdot coupling. The tunable π-junction transition is explained in terms of the current carrying density of states. These results provide the ways of manipulating the supercurrent in a triple quantum dot system.
Quantum parameter identification for a chaotic atom ensemble system
Li, Wenlin; Li, Chong; Song, Heshan
2016-02-01
We propose an indirect method based on an adaptive technique for analyzing the chaos behavior of a general quantum system with complex nonlinear evolution. Using this method, we design an identification function that effectively recognizes the uncertain parameters in a chaotic quantum system only by measuring the system outputs. As an example, we study an atom ensemble in an optical cavity and we obtain a specific parameter identification scheme after analyzing the chaos behaviors. We also verify the accuracy of the identification scheme using numerical simulations and we discuss the influence of different types of errors on the accuracy.
Entangled quantum state discrimination using a pseudo-Hermitian system
We demonstrate how to discriminate two non-orthogonal, entangled quantum states which are slightly different from each other by using a pseudo-Hermitian system. The positive definite metric operator which makes the pseudo-Hermitian system fully consistent with quantum theory is used for such a state discrimination. We further show that non-orthogonal states can evolve through a suitably constructed pseudo-Hermitian Hamiltonian to orthogonal states. Such an evolution ceases at exceptional points of the pseudo-Hermitian system. (paper)
Real-time simulation of dissipation-driven quantum systems
Banerjee, Debasish; Jiang, Fu-Jiun; Kon, Mark; Wiese, Uwe-Jens
2015-01-01
We set up a real-time path integral to study the evolution of quantum systems driven in real-time completely by the coupling of the system to the environment. For specifically chosen interactions, this can be interpreted as measurements being performed on the system. For a spin-1/2 system, in particular, when the measurement results are averaged over, the resulting sign problem completely disappears, and the system can be simulated with an efficient cluster algorithm.
Kepler-16 Circumbinary System Validates Quantum Celestial Mechanics
Potter F.
2012-01-01
Full Text Available We report the application of quantum celestial mechanics (QCM to the Kepler-16 circumbinary system which has a single planet orbiting binary stars with the important system parameters known to within one percent. Other gravitationally bound systems such as the Solar System of planets and the Jovian satellite systems have large uncertainties in their total angular momentum. Therefore, Kepler-16 allows us for the ?rst time to determine whether the QCM predicted angular momentum per mass quantization isvalid.
Scattering Theory for Open Quantum Systems with Finite Rank Coupling
Behrndt, Jussi [Technische Universitaet Berlin, Institut fuer Mathematik (Germany)], E-mail: behrndt@math.tu-berlin.de; Malamud, Mark M. [Donetsk National University, Department of Mathematics (Ukraine)], E-mail: mmm@telenet.dn.ua; Neidhardt, Hagen [WIAS Berlin (Germany)], E-mail: neidhard@wias-berlin.de
2007-11-15
Quantum systems which interact with their environment are often modeled by maximal dissipative operators or so-called Pseudo-Hamiltonians. In this paper the scattering theory for such open systems is considered. First it is assumed that a single maximal dissipative operator A{sub D} in a Hilbert space is used to describe an open quantum system. In this case the minimal self-adjoint dilation of A{sub D} can be regarded as the Hamiltonian of a closed system which contains the open system, but since K-tilde is necessarily not semibounded from below, this model is difficult to interpret from a physical point of view. In the second part of the paper an open quantum system is modeled with a family {l_brace}A({mu}){r_brace} of maximal dissipative operators depending on energy {mu}, and it is shown that the open system can be embedded into a closed system where the Hamiltonian is semibounded. Surprisingly it turns out that the corresponding scattering matrix can be completely recovered from scattering matrices of single pseudo-Hamiltonians as in the first part of the paper. The general results are applied to a class of Sturm-Liouville operators arising in dissipative and quantum transmitting Schroedinger-Poisson systems.
Quantum Algorithm for Obtaining the Energy Spectrum of Molecular Systems
Wang, Hefeng; Aspuru-Guzik, Alán; Hoffmann, Mark R; 10.1039/b804804e
2009-01-01
Simulating a quantum system is more efficient on a quantum computer than on a classical computer. The time required for solving the Schr\\"odinger equation to obtain molecular energies has been demonstrated to scale polynomially with system size on a quantum computer, in contrast to the well-known result of exponential scaling on a classical computer. In this paper, we present a quantum algorithm to obtain the energy spectrum of molecular systems based on the multi-configurational self-consistent field (MCSCF) wave function. By using a MCSCF wave function as the initial guess, the excited states are accessible; Entire potential energy surfaces of molecules can be studied more efficiently than if the simpler Hartree-Fock guess was employed. We show that a small increase of the MCSCF space can dramatically increase the success probability of the quantum algorithm, even in regions of the potential energy surface that are far from the equilibrium geometry. For the treatment of larger systems, a multi-reference con...
Electronic transport and noise in quantum dot systems
In this thesis we describe the current and shot noise properties of quantum dot systems. Their transport characteristics reveal information about interesting quantum mechanical effects such as the energy quantization and electronic correlations due to Coulomb interactions of electrons. Based on a diagrammatic real time approach we developed a numerical method to describe the current and shot noise. The method includes all relevant quantities such as the electron spin, the Coulomb interaction as well as thedelocalized nature of the electronic wavefunctions in coupled quantum dots. Our approach is based on a perturbative expansion in terms of the coupling constant to the leads and thus allows to describe sequential tunneling as well as co-tunneling transport in local as well as non-local multilevel systems. For a system of a double quantum dot we analyzed in detail the influence of asymmetries on the electronic transport properties and found strong correlations. In contrast, larger systems such as three and more coupled quantum dots display a strong noise enhancement even in fully symmetric situations due to their complex delocalized wavefunctions. Within the Coulomb blockade transport is governed by co-tunneling processes. In particular we investigated the regime of co-tunneling assisted sequential tunneling and described characteristic features in the differential conductance as well as the noise properties. (orig.)
Quantum transport through the system of parallel quantum dots with Majorana bound states
We study the tunneling transport properties through a system of parallel quantum dots which are coupled to Majorana bound states (MBSs). The conductance and spectral function are computed using the retarded Green's function method based on the equation of motion. The conductance of the system is 2e2/h at zero Fermi energy and is robust against the coupling between the MBSs and the quantum dots. The dependence of the Fermi energy on the spectral function is different for the first dot (dot1) than for the second dot (dot2) with fixed dot2-MBSs coupling. The influence of the Majorana bound states on the spectral function was studied for the series and parallel configurations of the system. It was found that when the configuration is in series, the Majorana bound states play an important role, resulting in a spectral function with three peaks. However, the spectral function shows two peaks when the system is in a parallel configuration. The zero Fermi energy spectral function is always 1/2 not only in series but also in the parallel configuration and robust against the coupling between the MBSs and the quantum dots. The phase diagram of the Fermi energy versus the quantum dot energy levels was also investigated
Phase representation of quantum-optical systems via nonnegative quantum distribution function
We propose a new method for describing phase distributions of nonclassical states in optical systems based on the nonnegative quantum distribution function. A comparison of the proposed method with other known methods such as the Pegg-Barnett and operational ones is given
GRAVITATIONAL WAVES AND EMERGENCE PARAMETER OF CLASSICAL AND QUANTUM SYSTEMS
Trunev A. P.
2014-03-01
Full Text Available It was established that the Fermi-Dirac statistics, Bose-Einstein and Maxwell-Boltzmann distribution can be described by a single equation, which follows from Einstein's equations for systems with central symmetry. Emergence parameter of classical and quantum systems composed by the rays of gravitational waves interacting with gravitational field of the universe has been computed
Hidden symmetry of the quantum Calogero-Moser system
Kuzentsov, Vadim b
The hidden symmetry of the quantum Calogero-Moser system with an inverse-square potential is algebraically demonstrated making use of Dunkl's operators. We find the underlying algebra explaining the super-integrability phenomenon for this system. Applications to related multi-variable Bessel...
Quantum railroads and directed localization at the juncture of quantum Hall systems
Nonoyama, S; Nonoyama, Shinji; Kirczenow, George
2002-01-01
The integer quantum Hall effect (QHE) and one-dimensional Anderson localization (AL) are limiting special cases of a more general phenomenon, directed localization (DL), predicted to occur in disordered one-dimensional wave guides called "quantum railroads" (QRR). Here we explain the surprising results of recent measurements by Kang et al. [Nature 403, 59 (2000)] of electron transfer between edges of two-dimensional electron systems and identify experimental evidence of QRR's in the general, but until now entirely theoretical, DL regime that unifies the QHE and AL. We propose direct experimental tests of our theory.
On the Physical Realizability of a Class of Nonlinear Quantum Systems
Maalouf, Aline I.; Petersen, Ian R
2012-01-01
In this paper, the physical realizability property is investigated for a class of nonlinear quantum systems. This property determines whether a given set of nonlinear quantum stochastic differential equations corresponds to a physical nonlinear quantum system satisfying the laws of quantum mechanics.
Quantum ergodicity for a class of non-generic systems
Asadi, P.; Bakhshinezhad, F.; Rezakhani, A. T.
2016-02-01
We examine quantum normal typicality and ergodicity properties for quantum systems whose dynamics are generated by Hamiltonians which have residual degeneracy in their spectrum and resonance in their energy gaps. Such systems can be considered atypical in the sense that degeneracy, which is usually a sign of symmetry, is naturally broken in typical systems due to stochastic perturbations. In particular, we prove a version of von Neumanns quantum ergodic theorem, where a modified condition needs to hold in order to have normal typicality and ergodicity. As a result, we show that degeneracy of spectrum does not considerably modify the condition of the theorem, whereas the existence of resonance is more dominant for obstructing ergodicity.
Coulomb drag in graphene quantum Hall bilayer systems
Liu, Xiaomeng; Wang, Lei; Fong, Kin Chung; Gao, Yuanda; Maher, Patrick; Watanabe, Kenji; Taniguchi, Takashi; Hone, James; Dean, Cory; Kim, Philip
2015-03-01
Coulomb drag between electrons in closely spaced two-dimensional electron systems has provided an exciting avenue for research on quantum Hall bilayer systems. Employing dual-gated, encapsulated graphene double layers separated by a thin hBN dielectric, we investigate density tunable magneto and Hall drag in quantum Hall bilayer systems. Large variations of magneto-drag and Hall-drag are observed, which can be related to the Landau level (LL) filling status of both driving and drag layers. The measured drag resistivity tensor can be associated with the tensor product of the differential magneto-resistivity tensors of the drive and drag layers. The temperature and field dependence of magneto-drag can be described in terms of the phase space for Coulomb scattering between LLs in the drag and drive layers. In the strong interaction regime and ultra-low temperature, we observe the effect of symmetry broken integer quantum Hall States in magneto and Hall drag signals.
Continuity of the entropy of macroscopic quantum systems
Swendsen, Robert H.
2015-11-01
The proper definition of entropy is fundamental to the relationship between statistical mechanics and thermodynamics. It also plays a major role in the recent debate about the validity of the concept of negative temperature. In this paper, I analyze and calculate the thermodynamic entropy for large but finite quantum mechanical systems. A special feature of this analysis is that the thermodynamic energy of a quantum system is shown to be a continuous variable, rather than being associated with discrete energy eigenvalues. Calculations of the entropy as a function of energy can be carried out with a Legendre transform of thermodynamic potentials obtained from a canonical ensemble. The resultant expressions for the entropy are able to describe equilibrium between quantum systems having incommensurate energy-level spacings. This definition of entropy preserves all required thermodynamic properties, including satisfaction of all postulates and laws of thermodynamics. It demonstrates the consistency of the concept of negative temperature with the principles of thermodynamics.
Planetary systems based on a quantum-like model
T., N Poveda; C, N Y Buitrago
2015-01-01
Planetary systems have their origin in the gravitational collapse of a cloud of gas and dust. Through a process of accretion, is formed a massive star and a disk of planetesimals orbiting the star. Using a formalism analogous to quantum mechanics (quantum-like model), the star-planetesimal system is described and the flow quantizing the gravitational field theoretical model parameters are obtained. Goodness of fit (chi-square) of the observed data with model quantum-like, to the solar system, satellites, exoplanets and protoplanetary disk around HL Tauri is determined. Shows that the radius, eccentricity, energy, angular momentum and orbital inclination of planetary objects formed take discrete values depending only on the mass star.
Controllable quantum information network with a superconducting system
Zhang, Feng-yang, E-mail: zhangfy@mail.dlut.edu.cn [School of Physics and Materials Engineering, Dalian Nationalities University, Dalian 116600 (China); Liu, Bao [Beijing Computational Science Research Center (CSRC), Beijing 100084 (China); Chen, Zi-hong [School of Physics and Optoelectronic Technology, Dalian University of Technology, Dalian 116024 (China); Wu, Song-lin [School of Physics and Materials Engineering, Dalian Nationalities University, Dalian 116600 (China); Song, He-shan [School of Physics and Optoelectronic Technology, Dalian University of Technology, Dalian 116024 (China)
2014-07-15
We propose a controllable and scalable architecture for quantum information processing using a superconducting system network, which is composed of current-biased Josephson junctions (CBJJs) as tunable couplers between the two superconducting transmission line resonators (TLRs), each coupling to multiple superconducting qubits (SQs). We explicitly demonstrate that the entangled state, the phase gate, and the information transfer between any two selected SQs can be implemented, respectively. Lastly, numerical simulation shows that our scheme is robust against the decoherence of the system. -- Highlights: •An architecture for quantum information processing is proposed. •The quantum information transfer between any two selected SQs is implemented. •This proposal is robust against the decoherence of the system. •This architecture can be fabricated on a chip down to the micrometer scale.
Relativistic quantum econophysics - new paradigms in complex systems modelling
Saptsin, Vladimir
2009-01-01
This work deals with the new, relativistic direction in quantum econophysics, within the bounds of which a change of the classical paradigms in mathematical modelling of socio-economic system is offered. Classical physics proceeds from the hypothesis that immediate values of all the physical quantities, characterizing system's state, exist and can be accurately measured in principle. Non-relativistic quantum mechanics does not reject the existence of the immediate values of the classical physical quantities, nevertheless not each of them can be simultaneously measured (the uncertainty principle). Relativistic quantum mechanics rejects the existence of the immediate values of any physical quantity in principle, and consequently the notion of the system state, including the notion of the wave function, which becomes rigorously nondefinable. The task of this work consists in econophysical analysis of the conceptual fundamentals and mathematical apparatus of the classical physics, relativity theory, non-relativis...
The Kitaev–Feynman clock for open quantum systems
We show that Kitaev's construction of Feynman's clock, in which the time-evolution of a closed quantum system is encoded as a ground state problem, can be extended to open quantum systems. In our formalism, the ground states of an ensemble of non-Hermitian Kitaev–Feynman clock Hamiltonians yield stochastic trajectories, which unravel the evolution of a Lindblad master equation. In this way, one can use the Kitaev–Feynman clock not only to simulate the evolution of a quantum system, but also its interaction with an environment such as a heat bath or measuring apparatus. A simple numerical example of a two-level atom undergoing spontaneous emission is presented and analyzed. (paper)
Adiabatic passage and ensemble control of quantum systems
Leghtas, Z [INRIA Paris-Rocquencourt Domaine de Voluceau, BP105 78153 Le Chesnay Cedex (France); Sarlette, A [Department of Electrical Engineering and Computer Science, University of Liege, 4000 Liege (Belgium); Rouchon, P, E-mail: zaki.leghtas@inria.fr, E-mail: alain.sarlette@ulg.ac.be, E-mail: pierre.rouchon@mines-paristech.fr [Mines-ParisTech, Centre Automatique et Systemes, 60, boulevard Saint-Michel 75272 Paris Cedex (France)
2011-08-14
This paper considers population transfer between eigenstates of a finite quantum ladder controlled by a classical electric field. Using an appropriate change of variables, we show that this setting can be set in the framework of adiabatic passage, which is known to facilitate ensemble control of quantum systems. Building on this insight, we present a mathematical proof of robustness for a control protocol-chirped pulse-practised by experimentalists to drive an ensemble of quantum systems from the ground state to the most excited state. We then propose new adiabatic control protocols using a single chirped and amplitude-shaped pulse, to robustly perform any permutation of eigenstate populations, on an ensemble of systems with unknown coupling strengths. These adiabatic control protocols are illustrated by simulations on a four-level ladder.
Controllable quantum information network with a superconducting system
We propose a controllable and scalable architecture for quantum information processing using a superconducting system network, which is composed of current-biased Josephson junctions (CBJJs) as tunable couplers between the two superconducting transmission line resonators (TLRs), each coupling to multiple superconducting qubits (SQs). We explicitly demonstrate that the entangled state, the phase gate, and the information transfer between any two selected SQs can be implemented, respectively. Lastly, numerical simulation shows that our scheme is robust against the decoherence of the system. -- Highlights: •An architecture for quantum information processing is proposed. •The quantum information transfer between any two selected SQs is implemented. •This proposal is robust against the decoherence of the system. •This architecture can be fabricated on a chip down to the micrometer scale
Emergent hydrodynamics in integrable quantum systems out of equilibrium
Castro-Alvaredo, Olalla A; Yoshimura, Takato
2016-01-01
Understanding the general principles underlying strongly interacting quantum states out of equilibrium is one of the most important tasks of current theoretical physics. With experiments now able to access the intricate dynamics of many-body quantum systems, it is paramount to develop powerful and widely applicable methods that encode the emergent physics. Up to now, the strong dichotomy observed between integrable and non-integrable evolutions made an overarching theory difficult to build, especially for transport phenomena where space-time profiles show drastically different behaviours. We present a novel framework for studying transport in integrable systems: that of emergent hydrodynamics with infinitely-many conservation laws. This method bridges the conceptual gap between integrable and non-integrable quantum dynamics. We apply it to the description of energy transport between heat baths in interacting integrable systems. We provide for the first time a full description of the current-carrying non-equil...
Novel optical probe for quantum Hall system
Biswajit Karmakar; Brij Mohan Arora
2006-07-01
Surface photovoltage (SPV) spectroscopy has been used for the first time to explore Landau levels of a two-dimensional electron gas (2DEG) in modulation doped InP/InGaAs/InP QW in the quantum Hall regime. The technique gives spectroscopically distinct signals from the bulk Landau levels and the edge states. Evolution of the bulk Landau levels and the edge electronic states is investigated at 2.0 K for magnetic field up to 8 T using SPV spectroscopy.
Integrable quantum systems and classical Lie algebras
Six new infinite series of trigonometric solutions to triangule equations (quantum R-matrices) associated with the nonexceptional simple Lie algebras: sl(N), sp(N), o(N) have been obtained. R-matrices are given in two equivalent representations: in an additive one (as a sum of poles with matrix coefficients) and in a multiplicative one (as a ratio of entire matrix functions). These R-matrices provide an exact integrability of anisotropic generalizations of sl(N), sp(N), o(N) invariant one-dimensional lattice magnetics and two-dimensional periodic Toda lattices associated with the above algebras
Entanglement Routers via Wireless Quantum Network Based on Arbitrary Two Qubit Systems
Metwally, N.
2014-01-01
A wireless quantum network is generated between multi-hop, where each hop consists of two entangled nodes. These nodes share a finite number of entangled two qubit systems randomly. Different types of wireless quantum bridges are generated between the non-connected nodes. The efficiency of these wireless quantum bridges to be used as quantum channels between its terminals to perform quantum teleportation is investigated. We suggest a theoretical wireless quantum communication protocol to tele...
Quantum sweeps, synchronization, and Kibble-Zurek physics in dissipative quantum spin systems
Henriet, Loïc; Le Hur, Karyn
2016-02-01
We address dissipation effects on the nonequilibrium quantum dynamics of an ensemble of spins-1/2 coupled via an Ising interaction. Dissipation is modeled by a (Ohmic) bath of harmonic oscillators at zero temperature and correspond either to the sound modes of a one-dimensional Bose-Einstein (quasi-)condensate or to the zero-point fluctuations of a long transmission line. We consider the dimer comprising two spins and the quantum Ising chain with long-range interactions and develop an (mathematically and numerically) exact stochastic approach to address nonequilibrium protocols in the presence of an environment. For the two-spin case, we first investigate the dissipative quantum phase transition induced by the environment through quantum quenches and study the effect of the environment on the synchronization properties. Then we address Landau-Zener-Stueckelberg-Majorana protocols for two spins and for the spin array. In this latter case, we adopt a stochastic mean-field point of view and present a Kibble-Zurek-type argument to account for interaction effects in the lattice. Such dissipative quantum spin arrays can be realized in ultracold atoms, trapped ions, and mesoscopic systems and are related to Kondo lattice models.
Quantum Simulation of Quantum Field Theory with a Trapped Ion System
Zhang, Xiang; Zhang, Kuan; Shen, Yangchao; Zhang, Jingning; Yung, Man-Hong; Kim, Kihwan; Simon, Julen; Lamata, Lucas; Solano, Enrique; Casanova, Jorge
2015-05-01
We report on the experimental quantum simulation of interacting bosonic and fermionic quantum field modes with a trapped ion system. We consider a basic model of only one fermion and one anti-fermion interacting through a bosonic field mode, which reveals interesting features such as self-interactions, particle creation and annihilation and non-perturbative regimes. We experimentally study these phenomena by manipulating the internal degrees of freedom of a multi-level single 171Yb+ ion and its motional state, based on the proposal of Ref.. Our experimental scheme is a scalable approach and can be extended beyond the limit of classical computation of quantum field theory when more fermions and bosons are included. This work was supported by the National Basic Research Program of China under Grants No. 2011CBA00300 (No. 2011CBA00301), the National Natural Science Foundation of China 11374178.
Quantum Monte Carlo studies of novel phases in strongly correlated systems
Meng, Zi Yang
2011-01-01
Three models of strongly correlated electron systems have been studied in this thesis: the Shastry-Sutherland quantum antiferromagnet, the quantum spin liquid emerging out of correlated Dirac fermions on the honeycomb lattice, and the edge-state magnetism in the graphene nanoribbons. The methods applied are quantum Monte Carlo simulations, namely, stochastic series expansion quantum Monte Carlo for bosonic (spin) systems and projector auxiliary field quantum Monte Carlo for fermionic systems....
Controlling Atomic, Solid-State and Hybrid Systems for Quantum Information Processing
Gullans, Michael John
2013-01-01
Quantum information science involves the use of precise control over quantum systems to explore new technologies. However, as quantum systems are scaled up they require an ever deeper understanding of many-body physics to achieve the required degree of control. Current experiments are entering a regime which requires active control of a mesoscopic number of coupled quantum systems or quantum bits (qubits). This thesis describes several approaches to this goal and shows how mesoscopic quan...