Quantum Shuttle in Phase Space
DEFF Research Database (Denmark)
Novotny, Tomas; Donarini, Andrea; Jauho, Antti-Pekka
2003-01-01
Abstract: We present a quantum theory of the shuttle instability in electronic transport through a nanostructure with a mechanical degree of freedom. A phase space formulation in terms of the Wigner function allows us to identify a crossover from the tunneling to the shuttling regime, thus...... extending the previously found classical results to the quantum domain. Further, a new dynamical regime is discovered, where the shuttling is driven exclusively by the quantum noise....
Quantum processes on phase space
Anastopoulos, C
2003-01-01
Quantum theory predicts probabilities as well as relative phases between different alternatives of the system. A unified description of both probabilities and phases comes through a generalisation of the notion of a density matrix for histories; this object is the decoherence functional of the consistent histories approach. If we take phases as well as probabilities as primitive elements of our theory, we abandon Kolmogorov probability and can describe quantum theory in terms of fundamental commutative observables, without being obstructed by Bell's and related theorems. Generalising the theory of stochastic processes, we develop the description of relative phases and probabilities for paths on the classical phase space. This description provides a theory of quantum processes. We identify a number of basic postulates and study its corresponding properties. We strongly emphasise the notion of conditioning and are able to write ``quantum differential equations'' as analogous to stochastic differential equations...
Quantum mechanics in phase space
DEFF Research Database (Denmark)
Hansen, Frank
1984-01-01
A reformulation of quantum mechanics for a finite system is given using twisted multiplication of functions on phase space and Tomita's theory of generalized Hilbert algebras. Quantization of a classical observable h is achieved when the twisted exponential Exp0(-h) is defined as a tempered....... Generalized Weyl-Wigner maps related to the notion of Hamiltonian weight are studied and used in the formulation of a twisted spectral theory for functions on phase space. Some inequalities for Wigner functions on phase space are proven. A brief discussion of the classical limit obtained through dilations...
Phase space methods for degenerate quantum gases
Dalton, Bryan J; Barnett, Stephen M
2015-01-01
Recent experimental progress has enabled cold atomic gases to be studied at nano-kelvin temperatures, creating new states of matter where quantum degeneracy occurs - Bose-Einstein condensates and degenerate Fermi gases. Such quantum states are of macroscopic dimensions. This book presents the phase space theory approach for treating the physics of degenerate quantum gases, an approach already widely used in quantum optics. However, degenerate quantum gases involve massive bosonic and fermionic atoms, not massless photons. The book begins with a review of Fock states for systems of identical atoms, where large numbers of atoms occupy the various single particle states or modes. First, separate modes are considered, and here the quantum density operator is represented by a phase space distribution function of phase space variables which replace mode annihilation, creation operators, the dynamical equation for the density operator determines a Fokker-Planck equation for the distribution function, and measurable...
The Quantum Space Phase Transitions for Particles and Force Fields
Chung D.-Y.; Krasnoholovets V.
2006-01-01
We introduce a phenomenological formalism in which the space structure is treated in terms of attachment space and detachment space. Attachment space attaches to an object, while detachment space detaches from the object. The combination of these spaces results in three quantum space phases: binary partition space, miscible space and binary lattice space. Binary lattice space consists of repetitive units of alternative attachment space and detachment spac...
On quantum mechanical phase-space wave functions
DEFF Research Database (Denmark)
Wlodarz, Joachim J.
1994-01-01
An approach to quantum mechanics based on the notion of a phase-space wave function is proposed within the Weyl-Wigner-Moyal representation. It is shown that the Schrodinger equation for the phase-space wave function is equivalent to the quantum Liouville equation for the Wigner distribution...
On Quantum Mechanics on Noncommutative Quantum Phase Space
Institute of Scientific and Technical Information of China (English)
A.E.F. DjemaI; H. Smail
2004-01-01
In this work, we develop a general framework in which Noncommutative Quantum Mechanics (NCQM),characterized by a space noncommutativity matrix parameter θ =∈k ijθk and a momentum noncommutativity matrix parameter βij = ∈k ijβk, is shown to be equivalent to Quantum Mechanics (QM) on a suitable transformed Quantum Phase Space (QPS). Imposing some constraints on this particular transformation, we firstly find that the product of the two parameters θ and β possesses a lower bound in direct relation with Heisenberg incertitude relations, and secondly that the two parameters are equivalent but with opposite sign, up to a dimension factor depending on the physical system under study. This means that noncommutativity is represented by a unique parameter which may play the role of a fundamental constant characterizing the whole NCQPS. Within our framework, we treat some physical systems on NCQPS : free particle, harmonic oscillator, system of two-charged particles, Hydrogen atom. Among the obtained results,we discover a new phenomenon which consists of a free particle on NCQPS viewed as equivalent to a harmonic oscillator with Larmor frequency depending on β, representing the same particle in presence ofa magnetic field B = q-1 β. For the other examples, additional correction terms depending onβ appear in the expression of the energy spectrum. Finally, in the two-particle system case, we emphasize the fact that for two opposite charges noncommutativity is effectively feeled with opposite sign.
Deformed Covariant Quantum Phase Spaces as Hopf Algebroids
Lukierski, Jerzy
2015-01-01
We consider the general D=4 (10+10)-dimensional kappa-deformed quantum phase space as given by Heisenberg double \\mathcal{H} of D=4 kappa-deformed Poincare-Hopf algebra H. The standard (4+4) -dimensional kappa - deformed covariant quantum phase space spanned by kappa - deformed Minkowski coordinates and commuting momenta generators ({x}_{\\mu },{p}_{\\mu }) is obtained as the subalgebra of \\mathcal{H}. We study further the property that Heisenberg double defines particular quantum spaces with Hopf algebroid structure. We calculate by using purely algebraic methods the explicite Hopf algebroid structure of standard kappa - deformed quantum covariant phase space in Majid-Ruegg bicrossproduct basis. The coproducts for Hopf algebroids are not unique, determined modulo the coproduct gauge freedom. Finally we consider the interpretation of the algebraic description of quantum phase spaces as Hopf bialgebroids.
The Quantum Space Phase Transitions for Particles and Force Fields
Directory of Open Access Journals (Sweden)
Chung D.-Y.
2006-07-01
Full Text Available We introduce a phenomenological formalism in which the space structure is treated in terms of attachment space and detachment space. Attachment space attaches to an object, while detachment space detaches from the object. The combination of these spaces results in three quantum space phases: binary partition space, miscible space and binary lattice space. Binary lattice space consists of repetitive units of alternative attachment space and detachment space. In miscible space, attachment space is miscible to detachment space, and there is no separation between attachment space and detachment spaces. In binary partition space, detachment space and attachment space are in two separat continuous regions. The transition from wavefunction to the collapse of wavefuction under interference becomes the quantum space phase transition from binary lattice space to miscible space. At extremely conditions, the gauge boson force field undergoes a quantum space phase transition to a "hedge boson force field", consisting of a "vacuum" core surrounded by a hedge boson shell, like a bubble with boundary.
An extended phase-space SUSY quantum mechanics
Ter-Kazarian, G.
2009-01-01
In the present paper, we will concern ourselves with the extended phase-space quantum mechanics of particles which have both bosonic and fermionic degrees of freedom, i.e., the quantum field theory in (0 + 1) dimensions in q-(position) and p-(momentum) spaces, exhibiting supersymmetry. We present (N
An extended phase-space SUSY quantum mechanics
Ter-Kazarian, G.
2009-01-01
In the present paper, we will concern ourselves with the extended phase-space quantum mechanics of particles which have both bosonic and fermionic degrees of freedom, i.e., the quantum field theory in (0 + 1) dimensions in q-(position) and p-(momentum) spaces, exhibiting supersymmetry. We present (N
Phase space picture of quantum mechanics group theoretical approach
Kim, Y S
1991-01-01
This book covers the theory and applications of the Wigner phase space distribution function and its symmetry properties. The book explains why the phase space picture of quantum mechanics is needed, in addition to the conventional Schrödinger or Heisenberg picture. It is shown that the uncertainty relation can be represented more accurately in this picture. In addition, the phase space picture is shown to be the natural representation of quantum mechanics for modern optics and relativistic quantum mechanics of extended objects.
The Phase Space Formulation of Time-Symmetric Quantum Mechanics
National Research Council Canada - National Science Library
Charlyne de Gosson; Maurice A. de Gosson
2015-01-01
Time-symmetric quantum mechanics can be described in the Weyl–Wigner–Moyal phase space formalism by using the properties of the cross-terms appearing in the Wigner distribution of a sum of states...
Quantum Theory of Reactive Scattering in Phase Space
Goussev, Arseni; Waalkens, Holger; Wiggins, Stephen
2010-01-01
We review recent results on quantum reactive scattering from a phase space perspective. The approach uses classical and quantum versions of normal form theory and the perspective of dynamical systems theory. Over the past ten years the classical normal form theory has provided a method for realizing the phase space structures that are responsible for determining reactions in high dimensional Hamiltonian systems. This has led to the understanding that a new (to reaction dynamics) type of phase space structure, a {\\em normally hyperbolic invariant manifold} (or, NHIM) is the "anchor" on which the phase space structures governing reaction dynamics are built. The quantum normal form theory provides a method for quantizing these phase space structures through the use of the Weyl quantization procedure. We show that this approach provides a solution of the time-independent Schr\\"odinger equation leading to a (local) S-matrix in a neighborhood of the saddle point governing the reaction. It follows easily that the qu...
Phase space formalisms of quantum mechanics with singular kernel
Sala, P R; Muga, J G
1997-01-01
The equivalence of the Rivier-Margenau-Hill and Born-Jordan-Shankara phase space formalisms to the conventional operator approach of quantum mechanics is demonstrated. It is shown that in spite of the presence of singular kernels the mappings relating phase space functions and operators back and forth are possible.
Quantum Theory of Reactive Scattering in Phase Space
Goussev, A.; Schubert, R.; Waalkens, H.; Wiggins, S.; Nicolaides, CA; Brandas, E
2010-01-01
We review recent results on quantum reactive scattering from a phase space perspective. The approach uses classical and quantum versions of Poincare-Birkhoff normal form theory and the perspective of dynamical systems theory. Over the past 10 years the classical normal form theory has provided a met
Quantum and Classical Phase Space Separability and Entanglement
Patwardhan, A
2002-01-01
The formalism of classical and quantum mechanics on phase space leads to symplectic and Heisenberg group representations, respectively. The Wigner functions give a representation of the quantum system using classical variables. The correspondence between the classical and the quantum criterion of separability for the system is obtained in terms of these functions. Entanglement is generic and separability is special. Some applications are discussed in commonly occuring examples and possibly in exotic systems.
Quantum potential and symmetries in extended phase space
Nasiri, S
2005-01-01
Here, we study the concept of the quantum potential using an extended phase space technique. It seems that, for a given potential, there exist an extended canonical transformation that removes the expression for quantum potential in dynamical equation. The situation, mathematically, is similar to the appearance of centrifugal potential in going from Cartesian to spherical coordinates that changes the physical potential to an effective one. As Examples, the cases of harmonic oscillator, particle in a box and hydrogen atom are worked out, where the quantum potential disappears from the Wigner equation as a possible representation of quantum mechanics in the phase space. This representation that keeps the Hamilton-Jacobi equation form invariant could be obtained by a particular extended canonical transformation on Sobouti-Nasiri equation in extended phase space.
Quantum geometry from phase space reduction
Conrady, Florian
2009-01-01
In this work we give an explicit isomorphism between the usual spin network basis and the direct quantization of the reduced phase space of tetrahedra. The main outcome is a formula that describes the space of SU(2) invariant states by an integral over coherent states satisfying the closure constraint exactly, or equivalently, as an integral over the space of classical tetrahedra. This provides an explicit realization of theorems by Guillemin--Sternberg and Hall that describe the commutation of quantization and reduction. In the final part of the paper, we use our result to express the FK spin foam model as an integral over classical tetrahedra and the asymptotics of the vertex amplitude is determined.
Wave mechanics in quantum phase space: hydrogen atom
Institute of Scientific and Technical Information of China (English)
LU Jun
2007-01-01
The rigorous sohutions of the stationary Schr(o)dinger equation for hydrogen atom are solved with the wave-mechanics method within the framework of the quantum phase-space representation established by Torres-Vega and Frederick. The "Fourier-like"projection transformations of wave function from the phase space to position and momentum spaces are extended to three-dimensional systems. The eigenfunctions in general position and momentum spaces could be obtained through the transformations from eigenfunction in the phase space.
Phase space view of quantum mechanical systems and Fisher information
Energy Technology Data Exchange (ETDEWEB)
Nagy, Á., E-mail: anagy@madget.atomki.hu
2016-06-17
Highlights: • Phase-space Fisher information coming from the canonical distribution is derived for the ground state of quantum mechanical systems. • Quantum mechanical phase-space Fisher information contains an extra term due to the position dependence of the temperature. • A complete analogy to the classical case is demonstrated for the linear harmonic oscillator. - Abstract: Pennini and Plastino showed that the form of the Fisher information generated by the canonical distribution function reflects the intrinsic structure of classical mechanics. Now, a quantum mechanical generalization of the Pennini–Plastino theory is presented based on the thermodynamical transcription of the density functional theory. Comparing to the classical case, the phase-space Fisher information contains an extra term due to the position dependence of the temperature. However, for the special case of constant temperature, the expression derived bears resemblance to the classical one. A complete analogy to the classical case is demonstrated for the linear harmonic oscillator.
Quantum phase transition induced by real-space topology
Li, C.; Zhang, G.; Lin, S.; Song, Z.
2016-12-01
A quantum phase transition (QPT), including both topological and symmetry breaking types, is usually induced by the change of global parameters, such as external fields or global coupling constants. In this work, we demonstrate the existence of QPT induced by the real-space topology of the system. We investigate the groundstate properties of the tight-binding model on a honeycomb lattice with the torus geometry based on exact results. It is shown that the ground state experiences a second-order QPT, exhibiting the scaling behavior, when the torus switches to a tube, which reveals the connection between quantum phase and the real-space topology of the system.
Quantum phase transition induced by real-space topology.
Li, C; Zhang, G; Lin, S; Song, Z
2016-12-22
A quantum phase transition (QPT), including both topological and symmetry breaking types, is usually induced by the change of global parameters, such as external fields or global coupling constants. In this work, we demonstrate the existence of QPT induced by the real-space topology of the system. We investigate the groundstate properties of the tight-binding model on a honeycomb lattice with the torus geometry based on exact results. It is shown that the ground state experiences a second-order QPT, exhibiting the scaling behavior, when the torus switches to a tube, which reveals the connection between quantum phase and the real-space topology of the system.
Quantum de Finetti theorem in phase-space representation
Leverrier, Anthony; Cerf, Nicolas J.
2009-07-01
The quantum versions of de Finetti’s theorem derived so far express the convergence of n -partite symmetric states, i.e., states that are invariant under permutations of their n parties, toward probabilistic mixtures of independent and identically distributed (IID) states of the form σ⊗n . Unfortunately, these theorems only hold in finite-dimensional Hilbert spaces, and their direct generalization to infinite-dimensional Hilbert spaces is known to fail. Here, we address this problem by considering invariance under orthogonal transformations in phase space instead of permutations in state space, which leads to a quantum de Finetti theorem particularly relevant to continuous-variable systems. Specifically, an n -mode bosonic state that is invariant with respect to this continuous symmetry in phase space is proven to converge toward a probabilistic mixture of IID Gaussian states (actually, n identical thermal states).
Deformation quantization: Quantum mechanics lives and works in phase space
Directory of Open Access Journals (Sweden)
Zachos Cosmas K.
2014-01-01
A sampling of such intriguing techniques and methods has already been published in C. K. Zachos, Int Jou Mod Phys A17 297-316 (2002, and T. L. Curtright, D. B. Fairlie, and C. K. Zachos, A Concise Treatise on Quantum Mechanics in Phase Space, (Imperial Press & World Scientific, 2014.
Phase-Space Noncommutative Quantum Cosmology
Bastos, Catarina; Dias, Nuno Costa; Prata, João Nuno
2007-01-01
We present a noncommutative extension of Quantum Cosmology and study the Kantowski-Sachs (KS) cosmological model requiring that the two scale factors of the KS metric, the coordinates of the system, and their conjugate canonical momenta do not commute. Through the ADM formalism, we obtain the Wheeler-DeWitt (WDW) equation for the noncommutative system. The Seiberg-Witten map is used to transform the noncommutative equation into a commutative one, i.e. into an equation with commutative variables, which depend on the noncommutative parameters, $\\theta$ and $\\eta$. Numerical solutions are found both for the classical and the quantum formulations of the system. These solutions are used to characterize the dynamics and the state of the universe. From the classical solutions we obtain the behavior of quantities such as the volume expansion, the shear and the characteristic volume. However the analysis of these quantities does not lead to any restriction on the value of the noncommutative parameters, $\\theta$ and $\\...
A concise treatise on quantum mechanics in phase space
Curtright, Thomas L; Zachos, Cosmas K
2014-01-01
This is a text on quantum mechanics formulated simultaneously in terms of position and momentum, i.e. in phase space. It is written at an introductory level, drawing on the remarkable history of the subject for inspiration and motivation. Wigner functions density -- matrices in a special Weyl representation -- and star products are the cornerstones of the formalism. The resulting framework is a rich source of physical intuition. It has been used to describe transport in quantum optics, structure and dynamics in nuclear physics, chaos, and decoherence in quantum computing. It is also of importance in signal processing and the mathematics of algebraic deformation. A remarkable aspect of its internal logic, pioneered by Groenewold and Moyal, has only emerged in the last quarter-century: it furnishes a third, alternative way to formulate and understand quantum mechanics, independent of the conventional Hilbert space or path integral approaches to the subject. In this logically complete and self-standing formula...
Quantum information processing in phase space: A modular variables approach
Ketterer, A.; Keller, A.; Walborn, S. P.; Coudreau, T.; Milman, P.
2016-08-01
Binary quantum information can be fault-tolerantly encoded in states defined in infinite-dimensional Hilbert spaces. Such states define a computational basis, and permit a perfect equivalence between continuous and discrete universal operations. The drawback of this encoding is that the corresponding logical states are unphysical, meaning infinitely localized in phase space. We use the modular variables formalism to show that, in a number of protocols relevant for quantum information and for the realization of fundamental tests of quantum mechanics, it is possible to loosen the requirements on the logical subspace without jeopardizing their usefulness or their successful implementation. Such protocols involve measurements of appropriately chosen modular variables that permit the readout of the encoded discrete quantum information from the corresponding logical states. Finally, we demonstrate the experimental feasibility of our approach by applying it to the transverse degrees of freedom of single photons.
An extended phase-space SUSY quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Ter-Kazarian, G [Byurakan Astrophysical Observatory, Byurakan 378433, Aragatsotn District (Armenia)], E-mail: gago_50@yahoo.com
2009-02-06
In the present paper, we will concern ourselves with the extended phase-space quantum mechanics of particles which have both bosonic and fermionic degrees of freedom, i.e., the quantum field theory in (0 + 1) dimensions in q-(position) and p-(momentum) spaces, exhibiting supersymmetry. We present (N = 2) realization of extended supersymmetry algebra and discuss the vacuum energy and topology of super-potentials. Shape invariance of exactly solvable extended SUSY potentials allows us to obtain analytic expressions for the entire energy spectrum of an extended Hamiltonian with, for example, Scarf potential without ever referring to an underlying differential equation.
A study on quantum similarity in the phase space
Sellier, J. M.; Ivanova, D. Y.; Dimov, I.
2016-10-01
Quantum similarity represents an important concept in the context of many applied disciplines such as physical and quantum chemistry. Nowadays, two definitions exist based, respectively, on the real and the phase spaces. In this paper, we focus on the second one, which was presented recently, and investigate it. In particular, being its mathematical definition dependent on a given integer s, we study the influence of this parameter on the similarity between two systems. To keep this investigation comprehensible, while still meaningful, we focus on a very simple quantum system represented by a hydrogen atom in the ground and excited states corresponding to the quantum numbers (n , l , m) =(1 , 0 , 0) and (n , l , m) =(2 , 0 , 0) .
Lyapunov exponent in quantum mechanics A phase-space approach
Man'ko, V I
2000-01-01
Using the symplectic tomography map, both for the probability distributionsin classical phase space and for the Wigner functions of its quantumcounterpart, we discuss a notion of Lyapunov exponent for quantum dynamics.Because the marginal distributions, obtained by the tomography map, are alwayswell defined probabilities, the correspondence between classical and quantumnotions is very clear. Then we also obtain the corresponding expressions inHilbert space. Some examples are worked out. Classical and quantum exponentsare seen to coincide for local and non-local time-dependent quadraticpotentials. For non-quadratic potentials classical and quantum exponents aredifferent and some insight is obtained on the taming effect of quantummechanics on classical chaos. A detailed analysis is made for the standard map.Providing an unambiguous extension of the notion of Lyapunov exponent toquantum mechnics, the method that is developed is also computationallyefficient in obtaining analytical results for the Lyapunov expone...
Quantum de Finetti theorems and mean-field theory from quantum phase space representations
Trimborn, F.; Werner, R. F.; Witthaut, D.
2016-04-01
We introduce the number-conserving quantum phase space description as a versatile tool to address fundamental aspects of quantum many-body systems. Using phase space methods we prove two alternative versions of the quantum de Finetti theorem for finite-dimensional bosonic quantum systems, which states that a reduced density matrix of a many-body quantum state can be approximated by a convex combination of product states where the error is proportional to the inverse particle number. This theorem provides a formal justification for the mean-field description of many-body quantum systems, as it shows that quantum correlations can be neglected for the calculation of few-body observables when the particle number is large. Furthermore we discuss methods to derive the exact evolution equations for quantum phase space distribution functions as well as upper and lower bounds for the ground state energy. As an important example, we consider the Bose-Hubbard model and show that the mean-field dynamics is given by a classical phase space flow equivalent to the discrete Gross-Pitaevskii equation.
Quantum simulations in phase-space: from quantum optics to ultra-cold physics
Drummond, Peter D.; Chaturvedi, Subhash
2016-07-01
As a contribution to the international year of light, we give a brief history of quantum optics in phase-space, with new directions including quantum simulations of multipartite Bell violations, opto-mechanics, ultra-cold atomic systems, matter-wave Bell violations, coherent transport and quantum fluctuations in the early Universe. We mostly focus on exact methods using the positive-P representation, and semiclassical truncated Wigner approximations.
Aspects of Phase-Space Noncommutative Quantum Mechanics
Bertolami, O
2015-01-01
In this work some issues in the context of Noncommutative Quantum Mechanics (NCQM) are addressed. The main focus is on finding whether symmetries present in Quantum Mechanics still hold in the phase-space noncommutative version. In particular, the issues related with gauge invariance of the electromagnetic field and the weak equivalence principle (WEP) in the context of the gravitational quantum well (GQW) are considered. The question of the Lorentz symmetry and the associated dispersion relation is also examined. Constraints are set on the relevant noncommutative parameters so that gauge invariance and Lorentz invariance holds. In opposition, the WEP is verified to hold in the noncommutative set up, and it is only possible to observe a violation through an anisotropy of the noncommutative parameters.
Aspects of phase-space noncommutative quantum mechanics
Directory of Open Access Journals (Sweden)
O. Bertolami
2015-11-01
Full Text Available In this work some issues in the context of Noncommutative Quantum Mechanics (NCQM are addressed. The main focus is on finding whether symmetries present in Quantum Mechanics still hold in the phase-space noncommutative version. In particular, the issues related with gauge invariance of the electromagnetic field and the weak equivalence principle (WEP in the context of the gravitational quantum well (GQW are considered. The question of the Lorentz symmetry and the associated dispersion relation is also examined. Constraints are set on the relevant noncommutative parameters so that gauge invariance and Lorentz invariance holds. In opposition, the WEP is verified to hold in the noncommutative setup, and it is only possible to observe a violation through an anisotropy of the noncommutative parameters.
Coherent quantum squeezing due to the phase space noncommutativity
Bernardini, Alex E
2015-01-01
The effect of phase space general noncommutativity on producing deformed coherent squeezed states is examined. A two-dimensional noncommutative quantum system supported by a deformed mathematical structure similar to that of Hadamard billiards is obtained and their components behavior are monitored in time. It is assumed that the independent degrees of freedom are two \\emph{free} 1D harmonic oscillators (HO's), so the system Hamiltonian does not contain interaction terms. Through the noncommutative deformation parameterized by a Seiberg-Witten transform on the original canonical variables, one gets the standard commutation relations for the new ones, such that the obtained Hamiltonian represents then two \\emph{interacting} 1D HO's. By assuming that one HO is inverted relatively to the other, we show that their effective interaction induces a squeezing dynamics for initial coherent states imaged in the phase space. A suitable pattern of logarithmic spirals is obtained and some relevant properties are discussed...
Phase space view of quantum mechanical systems and Fisher information
Nagy, Á.
2016-06-01
Pennini and Plastino showed that the form of the Fisher information generated by the canonical distribution function reflects the intrinsic structure of classical mechanics. Now, a quantum mechanical generalization of the Pennini-Plastino theory is presented based on the thermodynamical transcription of the density functional theory. Comparing to the classical case, the phase-space Fisher information contains an extra term due to the position dependence of the temperature. However, for the special case of constant temperature, the expression derived bears resemblance to the classical one. A complete analogy to the classical case is demonstrated for the linear harmonic oscillator.
Quantum dynamics via a time propagator in Wigner's phase space
DEFF Research Database (Denmark)
Grønager, Michael; Henriksen, Niels Engholm
1995-01-01
that the simple classical deterministic motion breaks down surprisingly fast in an anharmonic potential. Finally, we discuss the possibility of using the scheme as a useful approach to quantum dynamics in many dimensions. To that end we present a Monte Carlo integration scheme using the norm of the propagator......We derive an expression for a short-time phase space propagator. We use it in a new propagation scheme and demonstrate that it works for a Morse potential. The propagation scheme is used to propagate classical distributions which do not obey the Heisenberg uncertainty principle. It is shown...
The Phase Space Formulation of Time-Symmetric Quantum Mechanics
Directory of Open Access Journals (Sweden)
Charlyne de Gosson
2015-11-01
Full Text Available Time-symmetric quantum mechanics can be described in the Weyl–Wigner–Moyal phase space formalism by using the properties of the cross-terms appearing in the Wigner distribution of a sum of states. These properties show the appearance of a strongly oscillating interference between the pre-selected and post-selected states. It is interesting to note that the knowledge of this interference term is sufficient to reconstruct both states.Quanta 2015; 4: 27–34.
Phase-space treatment of the driven quantum harmonic oscillator
Indian Academy of Sciences (India)
DIÓGENES CAMPOS
2017-03-01
A recent phase-space formulation of quantum mechanics in terms of the Glauber coherent states is applied to study the interaction of a one-dimensional harmonic oscillator with an arbitrary time-dependent force. Wave functions of the simultaneous values of position q and momentum p are deduced, which in turn give the standard position and momentum wave functions, together with expressions for the ηth derivatives with respect to q and p, respectively. Afterwards, general formulae for momentum, position and energy expectation values are obtained, and the Ehrenfest theorem is verified. Subsequently, general expressions for the cross-Wigner functions are deduced. Finally, a specific example is considered to numerically and graphically illustrate some results.
Coherent quantum squeezing due to the phase space noncommutativity
Bernardini, Alex E.; Mizrahi, Salomon S.
2015-06-01
The effects of general noncommutativity of operators on producing deformed coherent squeezed states is examined in phase space. A two-dimensional noncommutative (NC) quantum system supported by a deformed mathematical structure, similar to that of Hadamard billiard, is obtained and the components behaviour is monitored in time. It is assumed that the independent degrees of freedom are two free 1D harmonic oscillators (HOs), so the system Hamiltonian does not contain interaction terms. Through the NC deformation parameterized by a Seiberg-Witten transform on the original canonical variables, one gets the standard commutation relations for the new ones, such that the obtained, new, Hamiltonian represents two interacting 1D HOs. By admitting that one HO is inverted relatively to the other, we show that their effective interaction induces a squeezing dynamics for initial coherent states imaged in the phase space. A suitable pattern of logarithmic spirals is obtained and some relevant properties are discussed in terms of Wigner functions, which are essential to put in evidence the effects of the noncommutativity.
Bastos, Catarina; Santos, Jonas F G
2014-01-01
Novel quantization properties related to the state vectors and the energy spectrum of a two-dimensional system of free particles are obtained in the framework of noncommutative (NC) quantum mechanics (QM) supported by the Weyl-Wigner formalism. Besides reproducing the magnetic field aspect of the Zeeman effect, the momentum space NC parameter introduces mutual information properties quantified by the linear entropy related to the relevant Hilbert space coordinates. Supported by the QM in the phase-space, the thermodynamic limit is obtained, and the results are extended to three-dimensional systems. The noncommutativity imprints on the thermodynamic variables related to free particles are identified and, after introducing some suitable constraints to fix an axial symmetry, the analysis is extended to two- and- three dimensional quantum rotor systems, for which the quantization aspects and the deviation from standard QM results are verified.
Quantum Riemannian geometry of phase space and nonassociativity
Directory of Open Access Journals (Sweden)
Beggs Edwin J.
2017-04-01
Full Text Available Noncommutative or ‘quantum’ differential geometry has emerged in recent years as a process for quantizing not only a classical space into a noncommutative algebra (as familiar in quantum mechanics but also differential forms, bundles and Riemannian structures at this level. The data for the algebra quantisation is a classical Poisson bracket while the data for quantum differential forms is a Poisson-compatible connection. We give an introduction to our recent result whereby further classical data such as classical bundles, metrics etc. all become quantised in a canonical ‘functorial’ way at least to 1st order in deformation theory. The theory imposes compatibility conditions between the classical Riemannian and Poisson structures as well as new physics such as typical nonassociativity of the differential structure at 2nd order. We develop in detail the case of ℂℙn where the commutation relations have the canonical form [wi, w̄j] = iλδij similar to the proposal of Penrose for quantum twistor space. Our work provides a canonical but ultimately nonassociative differential calculus on this algebra and quantises the metric and Levi-Civita connection at lowest order in λ.
Semi-classical mechanics in phase space: the quantum target of minimal strings
Energy Technology Data Exchange (ETDEWEB)
Gomez, Cesar [Instituto de Fisica Teorica CSIC/UAM, C-XVI Universidad Autonoma, E-28049 Madrid (Spain); Montanez, Sergio [Instituto de Fisica Teorica CSIC/UAM, C-XVI Universidad Autonoma, E-28049 Madrid (Spain); Resco, Pedro [Instituto de Fisica Teorica CSIC/UAM, C-XVI Universidad Autonoma, E-28049 Madrid (Spain)
2005-11-15
The target space M{sub p,q} of (p,q) minimal strings is embedded into the phase space of an associated integrable classical mechanical model. This map is derived from the matrix model representation of minimal strings. Quantum effects on the target space are obtained from the semiclassical mechanics in phase space as described by the Wigner function. In the classical limit the target space is a fold catastrophe of the Wigner function that is smoothed out by quantum effects. Double scaling limit is obtained by resolving the singularity of the Wigner function. The quantization rules for backgrounds with ZZ branes are also derived.
Semi-Classical Mechanics in Phase Space: The Quantum Target of Minimal Strings
Gómez, C; Resco, P; Gomez, Cesar; Montanez, Sergio; Resco, Pedro
2005-01-01
The target space $M_{p,q}$ of $(p,q)$ minimal strings is embedded into the phase space of an associated integrable classical mechanical model. This map is derived from the matrix model representation of minimal strings. Quantum effects on the target space are obtained from the semiclassical mechanics in phase space as described by the Wigner function. In the classical limit the target space is a fold catastrophe of the Wigner function that is smoothed out by quantum effects. Double scaling limit is obtained by resolving the singularity of the Wigner function. The quantization rules for backgrounds with ZZ branes are also derived.
Deformation Quantization Quantum Mechanics Lives and Works in Phase-Space
Zachos, C K
2002-01-01
Wigner's quasi-probability distribution function in phase-space is a special (Weyl) representation of the density matrix. It has been useful in describing quantum transport in quantum optics; nuclear physics; decoherence (eg, quantum computing); quantum chaos; "Welcher Weg" discussions; semiclassical limits. It is also of importance in signal processing. Nevertheless, a remarkable aspect of its internal logic, pioneered by Moyal, has only emerged in the last quarter-century: It furnishes a third, alternative, formulation of Quantum Mechanics, independent of the conventional Hilbert Space, or Path Integral formulations. In this logically complete and self-standing formulation, one need not choose sides--coordinate or momentum space. It works in full phase-space, accommodating the uncertainty principle. This is an introductory overview of the formulation with simple illustrations.
Linear phase-space representations of quantum mechanics with minimal uncertainty in position
Energy Technology Data Exchange (ETDEWEB)
Menge, Edmund [Univ. Mainz (Germany); Leschke, Hajo [Univ. Erlangen (Germany)
2010-07-01
Quantum mechanics with a non-zero uncertainty in position can be generated by a one-parameter generalisation of the canonical commutation relation of ordinary quantum mechanics. This generalisation may be, for example, used in ''Quantum Loop Gravity''. For such a quantum mechanics with non-zero uncertainty in position a class of linear phase-space representations is defined, covering the well known phase space representation of Weyl, Wigner and Moyal as a limiting case. Applying the Lie-Trotter formula, these representations lead to a transcription of the new Schroedinger-Semigroup as a sequence of finite-dimensional integrals. These integrals can be informally be interpreted as a phase-space path integral.
Discrete Phase Space: Quantum mechanics and non-singular potential functions
Das, Anadijiban
2015-01-01
The three-dimensional potential equation, motivated by representations of quantum mechanics, is investigated in four different scenarios: (i) In the usual Euclidean space $\\mathbb{E}_{3}$ where the potential is singular but invariant under the continuous inhomogeneous orthogonal group $\\mathcal{I}O(3)$. The invariance under the translation subgroup is compared to the corresponding unitary transformation in the Schr\\"{o}dinger representation of quantum mechanics. This scenario is well known but serves as a reference point for the other scenarios. (ii) Next, the discrete potential equation as a partial difference equation in a three-dimensional lattice space is studied. In this arena the potential is non-singular but invariance under $\\mathcal{I}O(3)$ is broken. This is the usual picture of lattice theories and numerical approximations. (iii) Next we study the six-dimensional continuous phase space. Here a phase space representation of quantum mechanics is utilized. The resulting potential is singular but posse...
An Alternative Formulation of Hall Effect and Quantum Phases in Noncommutative Space
Dayi, O F
2010-01-01
A recent method of constructing quantum mechanics in noncommutative coordinates alternative to imply noncommutativity by means of star product or the equivalent coordinate shift is discussed. The formulation is based on introducing some generalized theta-deformed commutation relations among quantum phase space variables and providing their realizations. Each realization furnishes us with a diverse theta-deformation. This procedure is suitable to consider theta-deformation of matrix observables which may be even coordinate independent. Within this alternative approach we give a formulation of Hall effect in noncommutative coordinates and calculate the deformed Hall conductivities for the realizations adopted. Before presenting our formulation of the theta-deformed quantum phases we discussed in a unified manner the existing formulations of quantum phases in noncommutative coordinates. The theta-deformed Aharonov-Bohm, Aharonov-Casher, He-McKellar-Wilkens and Anandan phases which we obtain are not velocity depe...
The Harari Shupe preon model and nonrelativistic quantum phase space
Żenczykowski, P.
2008-03-01
We propose that the whole algebraic structure of the Harari-Shupe rishon model originates via a Dirac-like linearization of quadratic form x2 +p2, with position and momentum satisfying standard commutation relations. The scheme does not invoke the concept of preons as spin-1/2 subparticles, thus evading the problem of preon confinement, while fully explaining all symmetries emboded in the Harari-Shupe model. Furthermore, the concept of quark colour is naturally linked to the ordering of rishons. Our scheme leads to group U (1) ⊗ SU (3) combined with SU (2), with two of the SU (2) generators not commuting with reflections. An interpretation of intra-generation quark-lepton transformations in terms of genuine rotations and reflections in phase space is proposed.
Nonlinear Landau-Zener tunneling in quantum phase space
Energy Technology Data Exchange (ETDEWEB)
Trimborn, F [Institut fuer theoretische Physik, Leibniz Universitaet Hannover, D-30167 Hannover (Germany); Witthaut, D [QUANTOP, Niels Bohr Institute, University of Copenhagen, DK-2100 Copenhagen (Denmark); Kegel, V; Korsch, H J, E-mail: friederike.trimborn@itp.uni-hannover.d [Fachbereich Physik, TU Kaiserslautern, D-67663 Kaiserslautern (Germany)
2010-05-15
We present a detailed analysis of the Landau-Zener problem for an interacting Bose-Einstein condensate in a time-varying double-well trap, especially focusing on the relation between the full many-particle problem and the mean-field approximation. Due to the nonlinear self-interaction a dynamical instability occurs, which leads to a breakdown of adiabaticity and thus fundamentally alters the dynamics. It is shown that essentially all the features of the Landau-Zener problem including the depletion of the condensate mode can be already understood within a semiclassical phase-space picture. In particular, this treatment resolves the formerly imputed incommutability of the adiabatic and semiclassical limits. The possibility of exploiting Landau-Zener sweeps to generate squeezed states for spectroscopic tasks is analyzed in detail. Moreover, we study the influence of phase noise and propose a Landau-Zener sweep as a sensitive yet readily implementable probe for decoherence, since the noise has significant effect on the transition rate for slow parameter variations.
Nonlinear Landau-Zener tunneling in quantum phase space
Trimborn, F; Kegel, V; Korsch, H J; 10.1088/1367-2630/12/5/053010
2010-01-01
We present a detailed analysis of the Landau-Zener problem for an interacting Bose-Einstein condensate in a time-varying double-well trap, especially focussing on the relation between the full many-particle problem and the mean-field approximation. Due to the nonlinear self-interaction a dynamical instability occurs, which leads to a breakdown of adiabaticity condition and thus fundamentally alters the dynamics. It is shown that essentially all features of the Landau-Zener problem including the depletion of the condensate mode can be already understood within a semiclassical phase space picture. In particular, this treatment resolves the formerly imputed incommutability of the adiabatic and semiclassical limits. The possibility to exploit Landau-Zener sweeps to generate squeezed states for spectroscopic tasks is analysed in detail. Moreover, we study the influence of phase noise and propose a Landau-Zener sweep as a sensitive, yet readily implementable probe for decoherence, since this has a significant effec...
On phase-space representations of quantum mechanics using Glauber coherent states
Indian Academy of Sciences (India)
DIÓGENES CAMPOS
2016-08-01
A phase-space formulation of quantum mechanics is proposed by constructing two representations (identified as $pq$ and $qp$) in terms of the Glauber coherent states, in which phase-space wave functions (probability amplitudes) play the central role, and position $q$ and momentum $p$ are treated on equal footing. After finding some basic properties of the $pq$ and $qp$ wave functions, the quantum operators in phase-space are represented by differential operators, and the Schrödinger equation is formulated in both pictures. Afterwards, the method is generalized to work with the density operator by converting the quantum Liouville equation into $pq$ and $qp$ equations of motion for two-point functions in phase-space. A coordinate transformation between those points allows one to construct a cell in phase-space, whose central point can be treated as a parameter. In this way, one gets equations of motion describing the evolution of one-point functions in phase-space. Finally, it is shown that some quantities obtained in this paper are related in a natural way with cross-Wigner functions, which are constructed with either the position or the momentum wave functions.
Wigner's dynamical transition state theory in phase space : classical and quantum
Waalkens, Holger; Schubert, Roman; Wiggins, Stephen
2008-01-01
We develop Wigner's approach to a dynamical transition state theory in phase space in both the classical and quantum mechanical settings. The key to our development is the construction of a normal form for describing the dynamics in the neighbourhood of a specific type of saddle point that governs t
"Einstein Moon", "Schrodinger Cat", and "Quantity in Phase Space" - About Quantum Measurement (Ⅰ)
Institute of Scientific and Technical Information of China (English)
REN De-Ming
2004-01-01
Generalizing the idea involved in a previous paper [Commun. Theor. Phys. (Beijing, China) 41 (2004)685], "quantity in phase space" is introduced. Thus starting from quantum mechanics, with standard criteria, the disappearing of interference in a macroscopic system is explicitly shown. Then the confusions involved in "the Einstein Moon" and "the Schrodinger Cat" are clarified, at least principally.
Efficient molecular quantum dynamics in coordinate and phase space using pruned bases
Larsson, Henrik R; Tannor, David J
2016-01-01
We present an efficient implementation of dynamically pruned quantum dynamics, both in coordinate space and in phase space. We combine the ideas behind the biorthogonal von Neumann basis (PvB) with the orthogonalized momentum-symmetrized Gaussians (Weylets) to create a new basis, projected Weylets, that takes the best from both methods. We benchmark pruned dynamics using phase-space-localized PvB, projected Weylets, and coordinate-space-localized DVR bases, with real-world examples in up to six dimensions. We show that coordinate-space localization is most important for efficient pruning and that pruned dynamics is much faster compared to unpruned, exact dynamics. Phase-space localization is useful for more demanding dynamics where many basis functions are required. There, projected Weylets offer a more compact representation than pruned DVR bases.
Efficient molecular quantum dynamics in coordinate and phase space using pruned bases
Larsson, H. R.; Hartke, B.; Tannor, D. J.
2016-11-01
We present an efficient implementation of dynamically pruned quantum dynamics, both in coordinate space and in phase space. We combine the ideas behind the biorthogonal von Neumann basis (PvB) with the orthogonalized momentum-symmetrized Gaussians (Weylets) to create a new basis, projected Weylets, that takes the best from both methods. We benchmark pruned time-dependent dynamics using phase-space-localized PvB, projected Weylets, and coordinate-space-localized DVR bases, with real-world examples in up to six dimensions. For the examples studied, coordinate-space localization is the most important factor for efficient pruning and the pruned dynamics is much faster than the unpruned, exact dynamics. Phase-space localization is useful for more demanding dynamics where many basis functions are required. There, projected Weylets offer a more compact representation than pruned DVR bases.
Berry's Phase in Noncommutative Spaces
Institute of Scientific and Technical Information of China (English)
S. A. Alavi
2003-01-01
We discuss the perturbative aspects of noncommutative quantum mechanics. Then we study Berry's phase within the framework of noncommutative quantum mechanics. The results show deviations from the usual quantum mechanics, which depend on the parameter of space/space noncommutativity.
Ray space `Riccati' evolution and geometric phases for -level quantum systems
Indian Academy of Sciences (India)
S Chaturvedi; E Ercolessi; G Marmo; G Morandi; N Mukunda; R Simon
2007-09-01
We present a simple derivation of the matrix Riccati equations governing the reduced dynamics as one descends from the group $\\mathbb{U}(N)$ describing the Schrõdinger evolution of an -level quantum system to the various coset spaces and Grassmanian manifolds associated with it. The special case pertaining to the geometric phase in -level systems is described in detail. Further, we show how the matrix Riccati equation thus obtained can be reformulated as an equation describing Hamiltonian evolution in a classical phase space and establish correspondences between the two descriptions.
Phase space localization for anti-de Sitter quantum mechanics and its zero curvature limit
Elgradechi, Amine M.
1993-01-01
Using techniques of geometric quantization and SO(sub 0)(3,2)-coherent states, a notion of optimal localization on phase space is defined for the quantum theory of a massive and spinning particle in anti-de Sitter space time. It is shown that this notion disappears in the zero curvature limit, providing one with a concrete example of the regularizing character of the constant (nonzero) curvature of the anti-de Sitter space time. As a byproduct a geometric characterization of masslessness is obtained.
Universal space-time scaling symmetry in the dynamics of bosons across a quantum phase transition
Clark, Logan W; Chin, Cheng
2016-01-01
The dynamics of many-body systems spanning condensed matter, cosmology, and beyond is hypothesized to be universal when the systems cross continuous phase transitions. The universal dynamics is expected to satisfy a scaling symmetry of space and time with the crossing rate, inspired by the Kibble-Zurek mechanism. We test this symmetry based on Bose condensates in a shaken optical lattice. Shaking the lattice drives condensates across an effectively ferromagnetic quantum phase transition. After crossing the critical point, the condensates manifest delayed growth of spin fluctuations and develop anti-ferromagnetic spatial correlations resulting from sub-Poisson generation of topological defects. The characteristic times and lengths scale as power-laws of the crossing rate, yielding the temporal exponent 0.50(2) and the spatial exponent 0.26(2), consistent with theory. Furthermore, the fluctuations and correlations are invariant in scaled space-time coordinates, in support of the scaling symmetry of quantum crit...
Influence of phase space localization on the energy diffusion in a quantum chaotic billiard
Wisniacki, D A
1999-01-01
The quantum dynamics of a chaotic billiard with moving boundary is considered in this work. We found a shape parameter Hamiltonian expansion which enables us to obtain the spectrum of the deformed billiard for deformations so large as the characteristic wave length. Then, for a specified time dependent shape variation, the quantum dynamics of a particle inside the billiard is integrated directly. In particular, the dispersion of the energy is studied in the Bunimovich stadium billiard with oscillating boundary. The results showed that the distribution of energy spreads diffusively for the first oscillations of the boundary (${ =2 D t$). We studied the diffusion contant $D$ as a function of the boundary velocity and found differences with theoretical predictions based on random matrix theory. By extracting highly phase space localized structures from the spectrum, previous differences were reduced significantly. This fact provides the first numerical evidence of the influence of phase space localization on the...
A Quantum Space behind Simple Quantum Mechanics
Directory of Open Access Journals (Sweden)
Chuan Sheng Chew
2017-01-01
Full Text Available In physics, experiments ultimately inform us about what constitutes a good theoretical model of any physical concept: physical space should be no exception. The best picture of physical space in Newtonian physics is given by the configuration space of a free particle (or the center of mass of a closed system of particles. This configuration space (as well as phase space can be constructed as a representation space for the relativity symmetry. From the corresponding quantum symmetry, we illustrate the construction of a quantum configuration space, similar to that of quantum phase space, and recover the classical picture as an approximation through a contraction of the (relativity symmetry and its representations. The quantum Hilbert space reduces into a sum of one-dimensional representations for the observable algebra, with the only admissible states given by coherent states and position eigenstates for the phase and configuration space pictures, respectively. This analysis, founded firmly on known physics, provides a quantum picture of physical space beyond that of a finite-dimensional manifold and provides a crucial first link for any theoretical model of quantum space-time at levels beyond simple quantum mechanics. It also suggests looking at quantum physics from a different perspective.
Gangopadhyay, Sunandan; Saha, Swarup
2016-01-01
Owing to the extreme smallness of any noncommutative scale that may exist in nature, both in the spatial and momentum sector of the quantum phase-space, a credible possibility of their detection lies in the present day gravitational wave detector set-ups, which effectively detects the relative length-scale variations ${\\cal{O}}\\left[10^{-23} \\right]$. With this motivation, we have considered how a free particle and harmonic oscillator in a quantum domain will respond to linearly and circularly polarized gravitational waves if the given phase-space has a noncommutative structure. The results show resonance behaviour in the responses of both free particle and HO systems to GW with both kind of polarizations. We critically analyze all the responses, and their implications in possible detection of noncommutativity. We use the currently available upper-bound estimates on various noncommutative parameters to anticipate the relative size of various response terms. We also argue how the quantum harmonic oscillator sy...
Quantum harmonic Brownian motion in a general environment: A modified phase-space approach
Energy Technology Data Exchange (ETDEWEB)
Yeh, L. [Univ. of California, Berkeley, CA (United States). Dept. of Physics]|[Lawrence Berkeley Lab., CA (United States)
1993-06-23
After extensive investigations over three decades, the linear-coupling model and its equivalents have become the standard microscopic models for quantum harmonic Brownian motion, in which a harmonically bound Brownian particle is coupled to a quantum dissipative heat bath of general type modeled by infinitely many harmonic oscillators. The dynamics of these models have been studied by many authors using the quantum Langevin equation, the path-integral approach, quasi-probability distribution functions (e.g., the Wigner function), etc. However, the quantum Langevin equation is only applicable to some special problems, while other approaches all involve complicated calculations due to the inevitable reduction (i.e., contraction) operation for ignoring/eliminating the degrees of freedom of the heat bath. In this dissertation, the author proposes an improved methodology via a modified phase-space approach which employs the characteristic function (the symplectic Fourier transform of the Wigner function) as the representative of the density operator. This representative is claimed to be the most natural one for performing the reduction, not only because of its simplicity but also because of its manifestation of geometric meaning. Accordingly, it is particularly convenient for studying the time evolution of the Brownian particle with an arbitrary initial state. The power of this characteristic function is illuminated through a detailed study of several physically interesting problems, including the environment-induced damping of quantum interference, the exact quantum Fokker-Planck equations, and the relaxation of non-factorizable initial states. All derivations and calculations axe shown to be much simplified in comparison with other approaches. In addition to dynamical problems, a novel derivation of the fluctuation-dissipation theorem which is valid for all quantum linear systems is presented.
Phase-space quantum control; Quantenkontrolle im Zeit-Frequenz-Phasenraum
Energy Technology Data Exchange (ETDEWEB)
Fechner, Susanne
2008-08-06
The von Neumann-representation introduced in this thesis describes each laser pulse in a one-to-one manner as a sum of bandwidth-limited, Gaussian laser pulses centered around different points in phase space. These pulses can be regarded as elementary building blocks from which every single laser pulse can be constructed. The von Neumann-representation combines different useful properties for applications in quantum control. First, it is a one-to-one map between the degrees of freedom of the pulse shaper and the phase-space representation of the corresponding shaped laser pulse. In other words: Every possible choice of pulse shaper parameters corresponds to exactly one von Neumann-representation and vice versa. Moreover, since temporal and spectral structures become immediately sizable, the von Neumann-representation, as well as the Husimi- or the Wigner-representations, allows for an intuitive interpretation of the represented laser pulse. (orig.)
Quantum effects in nanosystems: Good reasons to use phase-space Weyl symbols
Vaia, Ruggero
2016-12-01
Bogoliubov transformations have been successfully applied in several condensed-matter contexts, e.g., in the theory of superconductors, superfluids, and antiferromagnets. These applications are based on bulk models where translation symmetry can be assumed, so that few degrees of freedom in Fourier space can be "diagonalized" separately, and in this way it is easy to find the approximate ground state and its excitations. As translation symmetry cannot be invoked when it comes to nanoscopic systems, the corresponding multidimensional Bogoliubov transformations are more complicated. For bosonic systems it is much simpler to proceed using phase-space variables, i.e., coordinates and momenta. Interactions can be accounted for by the self-consistent harmonic approximation, which is naturally developed using phase-space Weyl symbols. The spin-flop transition in a short antiferromagnetic chain is illustrated as an example. This approach, rarely used in the past, is expected to be generally useful to estimate quantum effects, e.g., on phase diagrams of ordered vs disordered phases.
A Quantum Space Behind Simple Quantum Mechanics
Chew, Chuan Sheng; Payne, Jason
2016-01-01
In physics, we are supposed to learn from experiments what constitutes a good/correct theoretical/mathematical model of any physical concept, the physical space should not be an exception. The best picture of the physical space, in Newtonian physics, is given by the configuration space of a free particle. The space, as well as the phase space, can be constructed as a representation space of the relativity symmetry. Starting with the corresponding quantum symmetry, we illustrate the construction of a quantum space along the lines of the quantum phase space and demonstrate the retrieval of the classical picture as an approximation through the contraction of the (relativity) symmetry and the representations of it. The result suggests a picture of the physical space beyond that of a finite dimensional manifold.
Quantum Enhanced Phase Retrieval
Liberman, Liat; Poem, Eilon; Silberberg, Yaron
2015-01-01
The retrieval of phases from intensity measurements is a key process in many fields in science, from optical microscopy to x-ray crystallography. Here we study phase retrieval of a one-dimensional multi-phase object that is illuminated by quantum states of light. We generalize the iterative Gerchberg-Saxton algorithm to photon correlation measurements on the output plane, rather than the standard intensity measurements. We report a numerical comparison of classical and quantum phase retrieval of a small one-dimensional object of discrete phases from its far-field diffraction. While the classical algorithm was ambiguous and often converged to wrong solutions, quantum light produced a unique reconstruction with smaller errors and faster convergence. We attribute these improvements to a larger Hilbert space that constrains the algorithm.
Phase Space for the Breakdown of the Quantum Hall Effect in Epitaxial Graphene
Alexander-Webber, J. A.; Baker, A. M. R.; Janssen, T. J. B. M.; Tzalenchuk, A.; Lara-Avila, S.; Kubatkin, S.; Yakimova, R.; Piot, B. A.; Maude, D. K.; Nicholas, R. J.
2013-08-01
We report the phase space defined by the quantum Hall effect breakdown in polymer gated epitaxial graphene on SiC (SiC/G) as a function of temperature, current, carrier density, and magnetic fields up to 30 T. At 2 K, breakdown currents (Ic) almost 2 orders of magnitude greater than in GaAs devices are observed. The phase boundary of the dissipationless state (ρxx=0) shows a [1-(T/Tc)2] dependence and persists up to Tc>45K at 29 T. With magnetic field Ic was found to increase ∝B3/2 and Tc∝B2. As the Fermi energy approaches the Dirac point, the ν=2 quantized Hall plateau appears continuously from fields as low as 1 T up to at least 19 T due to a strong magnetic field dependence of the carrier density.
Quantum engines and the range of the second law of thermodynamics in the noncommutative phase-space
Santos, Jonas F G
2016-01-01
Two experimentally testable schemes for quantum heat engines are investigated under the quantization framework of noncommutative (NC) quantum mechanics (QM). By identifying the phenomenological connection between the phase-space NC driving parameters and an effective external magnetic field, the NC effects on the efficiency coefficient, \\mathcal{N} , of quantum engines can be quantified for two different cycles: an isomagnetic one and an isoenergetic one. In addition, paying a special attention to the quantum Carnot cycle, one notices that the inclusion of NC effects does not affect the maximal (Carnot) efficiency, \\mathcal{N}^C, ratifying the robustness of the second law of thermodynamics.
Indian Academy of Sciences (India)
R S Kaushal
2009-08-01
Certain aspects of classical and quantum mechanics of complex Hamiltonian systems in one dimension investigated within the framework of an extended complex phase space approach, characterized by the transformation = 1 + 2, = 1 + 2, are revisited. It is argued that Carl Bender inducted $\\mathcal{PT}$ symmetry in the studies of complex power potentials as a particular case of the present general framework in which two additional degrees of freedom are produced by extending each coordinate and momentum into complex planes. With a view to account for the subjective component of physical reality inherent in the collected data, e.g., using a Chevreul (hand-held) pendulum, a generalization of the Hamilton’s principle of least action is suggested.
On coherent-state representations of quantum mechanics: Wave mechanics in phase space
DEFF Research Database (Denmark)
Møller, Klaus Braagaard; Jørgensen, Thomas Godsk; Torres-Vega, Gabino
1997-01-01
one wants to solve the stationary Schrodinger equation in phase space and we devise two schemes for the removal of these ambiguities. The physical interpretation of the phase-space wave functions is discussed and a procedure for computing expectation values as integrals over phase space is presented...
Energy Technology Data Exchange (ETDEWEB)
Leverrier, A [Institut Telecom/Telecom ParisTech, CNRS LTCI, 46, rue Barrault, 75634 Paris Cedex 13 (France); Karpov, E; Cerf, N J [Quantum Information and Communication, Ecole Polytechnique, CP 165/59, Universite Libre de Bruxelles, 50 avenue F D Roosevelt, B-1050 Brussels (Belgium); Grangier, P [Laboratoire Charles Fabry, Institut d' Optique, CNRS, Universite Paris-Sud, Campus Polytechnique, RD 128, 91127 Palaiseau Cedex (France)], E-mail: anthony.leverrier@enst.fr
2009-11-15
Proving the unconditional security of quantum key distribution (QKD) is a highly challenging task as one needs to determine the most efficient attack compatible with experimental data. This task is even more demanding for continuous-variable QKD as the Hilbert space where the protocol is described is infinite dimensional. A possible strategy to address this problem is to make an extensive use of the symmetries of the protocol. In this paper, we investigate a rotation symmetry in phase space that is particularly relevant to continuous-variable QKD, and explore the way towards a new quantum de Finetti theorem that would exploit this symmetry and provide a powerful tool to assess the security of continuous-variable protocols. As a first step, a single-party asymptotic version of this quantum de Finetti theorem in phase space is derived.
Leverrier, A.; Karpov, E.; Grangier, P.; Cerf, N. J.
2009-11-01
Proving the unconditional security of quantum key distribution (QKD) is a highly challenging task as one needs to determine the most efficient attack compatible with experimental data. This task is even more demanding for continuous-variable QKD as the Hilbert space where the protocol is described is infinite dimensional. A possible strategy to address this problem is to make an extensive use of the symmetries of the protocol. In this paper, we investigate a rotation symmetry in phase space that is particularly relevant to continuous-variable QKD, and explore the way towards a new quantum de Finetti theorem that would exploit this symmetry and provide a powerful tool to assess the security of continuous-variable protocols. As a first step, a single-party asymptotic version of this quantum de Finetti theorem in phase space is derived.
Phase conjugate of quantum states in finite-dimensional Hilbert space
Zhou, X F; Guo, G C; Zhou, Xiang-Fa; Zhang, Yong-Sheng; Guo, Guang-Can
2006-01-01
We show that, for $N$ parallel input states, an anti-linear map with respect to a specific basis is essentially a classical operator. We also consider the information contained in phase-conjugate pairs $|\\phi > |\\phi^*>$, and prove that there is more information about a quantum state encoded in phase-conjugate pairs than in parallel pairs.
Beniaminov, E M
2001-01-01
There are considered some corollaries of certain hypotheses on the observation process of microphenomena. We show that an enlargement of the phase space and of its motion group and an account for the diffusion motions of microsystems in the enlarged space, the motions which act by small random translations along the enlarged group, lead to observable quantum effects. This approach enables one to recover probability distributions in the phase space for wave functions. The parameters of the model considered here are estimated on the base of Lamb's shift in the spectrum of the hydrogen's atom.
Indian Academy of Sciences (India)
ARCHANA SHUKLA; SRIHARI KESHAVAMURTHY
2017-07-01
The present work aims to control the rotational excitations of an ac-driven planar rotor, a model for rigid diatomic molecules, by rebuilding barriers in the classical phase space. The barriers are invariant tori with irrational winding ratios which are perturbatively constructed at desired locations in the phase space. Weestablish that constructing such barriers, equivalent to additional weak fields, can efficiently suppress the chaos leading to the control of various processes. The phase space barriers are shown to be effective in controlling the quantum dynamics as well. In particular, the efficiency of the phase space barriers towards controlling dynamical tunneling in the system is explored. Our studies are relevant to understanding the role of the chaotic regions in dynamical tunneling and for molecular alignment using bichromatic fields.
Jennewein, Thomas; Higgins, Brendon
2013-03-01
Sending satellites equipped with quantum technologies into space will be the first step towards a global quantum-communication network. As Thomas Jennewein and Brendon Higgins explain, these systems will also enable physicists to test fundamental physics in new regimes.
Freidel, Laurent; Minic, Djordje
2016-01-01
At present, our notion of space is a classical concept. Taking the point of view that quantum theory is more fundamental than classical physics, and that space should be given a purely quantum definition, we revisit the notion of Euclidean space from the point of view of quantum mechanics. Since space appears in physics in the form of labels on relativistic fields or Schrodinger wave functionals, we propose to define Euclidean quantum space as a choice of polarization for the Heisenberg algebra of quantum theory. We show, following Mackey, that generically, such polarizations contain a fundamental length scale and that contrary to what is implied by the Schrodinger polarization, they possess topologically distinct spectra. These are the modular spaces. We show that they naturally come equipped with additional geometrical structures usually encountered in the context of string theory or generalized geometry. Moreover, we show how modular space reconciles the presence of a fundamental scale with translation and...
Superanalysis on quantum spaces
Energy Technology Data Exchange (ETDEWEB)
Schmidt, Alexander [Max-Planck-Institute for Mathematics in the Sciences, Inselstr. 22, D-04103 Leipzig (Germany); Arnold-Sommerfeld-Center, Ludwig-Maximilians-Universitaet, Theresienstr. 37, D-80333 Munich (Germany); Wachter, Hartmut [Max-Planck-Institute for Mathematics in the Sciences, Inselstr. 22, D-04103 Leipzig (Germany); Arnold-Sommerfeld-Center, Ludwig-Maximilians-Universitaet, Theresienstr. 37, D-80333 Munich (Germany)
2006-01-15
Attention is focused on antisymmetrised versions of quantum spaces that are of particular importance in physics, i.e. Manin plane, q-deformed euclidean space in three or four dimensions as well as q-deformed Minkowski space. For each of these quantum spaces we provide q-analogs for elements of superanalysis, i.e. Grassmann integrals, Grassmann exponentials, Grassmann translations and braided products with supernumbers.
Comment on "Quantum phase for an arbitrary system with finite-dimensional Hilbert space"
Hall, Michael J. W.; Pegg, David T.
2012-01-01
A construction of covariant quantum phase observables, for Hamiltonians with a finite number of energy eigenvalues, has been recently given by D. Arsenovic et al. [Phys. Rev. A 85, 044103 (2012)]. For Hamiltonians generating periodic evolution, we show that this construction is just a simple rescaling of the known canonical 'time' or 'age' observable, with the period T rescaled to 2\\pi. Further, for Hamiltonians generating quasiperiodic evolution, we note that the construction leads to a phas...
Freidel, Laurent; Leigh, Robert G.; Minic, Djordje
2016-11-01
At present, our notion of space is a classical concept. Taking the point of view that quantum theory is more fundamental than classical physics, and that space should be given a purely quantum definition, we revisit the notion of Euclidean space from the point of view of quantum mechanics. Since space appears in physics in the form of labels on relativistic fields or Schrödinger wave functionals, we propose to define Euclidean quantum space as a choice of polarization for the Heisenberg algebra of quantum theory. We show, following Mackey, that generically, such polarizations contain a fundamental length scale and that contrary to what is implied by the Schrödinger polarization, they possess topologically distinct spectra. These are the modular spaces. We show that they naturally come equipped with additional geometrical structures usually encountered in the context of string theory or generalized geometry. Moreover, we show how modular space reconciles the presence of a fundamental scale with translation and rotation invariance. We also discuss how the usual classical notion of space comes out as a form of thermodynamical limit of modular space while the Schrödinger space is a singular limit.
Monthus, Cécile
2017-07-01
When random quantum spin chains are submitted to some periodic Floquet driving, the eigenstates of the time-evolution operator over one period can be localized in real space. For the case of periodic quenches between two Hamiltonians (or periodic kicks), where the time-evolution operator over one period reduces to the product of two simple transfer matrices, we propose a block-self-dual renormalization procedure to construct the localized eigenstates of the Floquet dynamics. We also discuss the corresponding strong disorder renormalization procedure, that generalizes the RSRG-X procedure to construct the localized eigenstates of time-independent Hamiltonians.
Zagoya, C; Ronto, M; Shalashilin, D V; Faria, C Figueira de Morisson
2014-01-01
We assess the suitability of quantum and semiclassical initial value representations, exemplified by the coupled coherent states (CCS) method and the Herman Kluk (HK) propagator, respectively, for modeling the dynamics of an electronic wave packet in a strong laser field, if this wave packet is initially bound. Using Wigner quasiprobability distributions and ensembles of classical trajectories, we identify signatures of over-the-barrier and tunnel ionization in phase space for static and time-dependent fields and the relevant sets of phase-space trajectories in order to model such features. Overall, we find good agreement with the full solution of the time-dependent Schr\\"odinger equation (TDSE) for Wigner distributions constructed with both initial-value representations. Our results indicate that the HK propagator does not fully account for tunneling and over-the-barrier reflections. However, it is able to partly reproduce features associated with the wave packet crossing classically forbidden regions, altho...
Nonclassical phase-space trajectories for the damped harmonic quantum oscillator
Energy Technology Data Exchange (ETDEWEB)
Pachon, L.A. [Departamento de Fisica, Universidad Nacional de Colombia, Bogota D.C. (Colombia); Institut fuer Physik, Universitaet Augsburg, Universitaetsstrasse 1, D-86135 Augsburg (Germany); CeiBA - Complejidad, Bogota D.C. (Colombia); Ingold, G.-L., E-mail: gert.ingold@physik.uni-augsburg.de [Institut fuer Physik, Universitaet Augsburg, Universitaetsstrasse 1, D-86135 Augsburg (Germany); Dittrich, T. [Departamento de Fisica, Universidad Nacional de Colombia, Bogota D.C. (Colombia); CeiBA - Complejidad, Bogota D.C. (Colombia)
2010-10-05
Graphical abstract: The phase-space path-integral approach to the damped harmonic oscillator is analyzed beyond the Markovian approximation and the appearance of nonclassical trajectories is discussed. - Abstract: The phase-space path-integral approach to the damped harmonic oscillator is analyzed beyond the Markovian approximation. It is found that pairs of nonclassical trajectories contribute to the path-integral representation of the Wigner propagating function. Due to the linearity of the problem, the sum coordinate of a pair still satisfies the classical equation of motion. Furthermore, it is shown that the broadening of the Wigner propagating function of the damped oscillator arises due to the time-nonlocal interaction mediated by the heat bath.
Hosten, O.; Krishnakumar, R.; Engelsen, N. J.; Kasevich, M. A.
2016-06-01
Quantum metrology exploits entangled states of particles to improve sensing precision beyond the limit achievable with uncorrelated particles. All previous methods required detection noise levels below this standard quantum limit to realize the benefits of the intrinsic sensitivity provided by these states. We experimentally demonstrate a widely applicable method for entanglement-enhanced measurements without low-noise detection. The method involves an intermediate quantum phase magnification step that eases implementation complexity. We used it to perform squeezed-state metrology 8 decibels below the standard quantum limit with a detection system that has a noise floor 10 decibels above the standard quantum limit.
Understanding quantum phase transitions
Carr, Lincoln
2010-01-01
Quantum phase transitions (QPTs) offer wonderful examples of the radical macroscopic effects inherent in quantum physics: phase changes between different forms of matter driven by quantum rather than thermal fluctuations, typically at very low temperatures. QPTs provide new insight into outstanding problems such as high-temperature superconductivity and display fundamental aspects of quantum theory, such as strong correlations and entanglement. Over the last two decades, our understanding of QPTs has increased tremendously due to a plethora of experimental examples, powerful new numerical meth
Energy Technology Data Exchange (ETDEWEB)
Wachter, H.; Wohlgenannt, M. [Sektion Physik der Ludwig-Maximilians-Universitaet Muenchen (Germany)
2002-04-01
In this paper we present explicit formulas for the *-product on quantum spaces which are of particular importance in physics, i.e., the q-deformed Minkowski space and the q-deformed Euclidean space in 3 and 4 dimensions, respectively. Our formulas are complete and formulated using the deformation parameter q. In addition, we worked out an expansion in powers of h=ln q up to second order, for all considered cases. (orig.)
Directory of Open Access Journals (Sweden)
Ronald E. Meyers
2015-03-01
Full Text Available We report on an experimental and theoretical investigation of quantum imaging where the images are stored in both space and time. Ghost images of remote objects are produced with either one or two beams of chaotic laser light generated by a rotating ground glass and two sensors measuring the reference field and bucket field at different space-time points. We further observe that the ghost images translate depending on the time delay between the sensor measurements. The ghost imaging experiments are performed both with and without turbulence. A discussion of the physics of the space-time imaging is presented in terms of quantum nonlocal two-photon analysis to support the experimental results. The theoretical model includes certain phase factors of the rotating ground glass. These experiments demonstrated a means to investigate the time and space aspects of ghost imaging and showed that ghost imaging contains more information per measured photon than was previously recognized where multiple ghost images are stored within the same ghost imaging data sets. This suggests new pathways to explore quantum information stored not only in multi-photon coincidence information but also in time delayed multi-photon interference. The research is applicable to making enhanced space-time quantum images and videos of moving objects where the images are stored in both space and time.
Geometrical Phases in Quantum Mechanics
Christian, Joy Julius
In quantum mechanics, the path-dependent geometrical phase associated with a physical system, over and above the familiar dynamical phase, was initially discovered in the context of adiabatically changing environments. Subsequently, Aharonov and Anandan liberated this phase from the original formulation of Berry, which used Hamiltonians, dependent on curves in a classical parameter space, to represent the cyclic variations of the environments. Their purely quantum mechanical treatment, independent of Hamiltonians, instead used the non-trivial topological structure of the projective space of one-dimensional subspaces of an appropriate Hilbert space. The geometrical phase, in their treatment, results from a parallel transport of the time-dependent pure quantum states along a curve in this space, which is endowed with an abelian connection. Unlike Berry, they were able to achieve this without resort to an adiabatic approximation or to a time-independent eigenvalue equation. Prima facie, these two approaches are conceptually quite different. After a review of both approaches, an exposition bridging this apparent conceptual gap is given; by rigorously analyzing a model composite system, it is shown that, in an appropriate correspondence limit, the Berry phase can be recovered as a special case from the Aharonov-Anandan phase. Moreover, the model composite system is used to show that Berry's correction to the traditional Born-Oppenheimer energy spectra indeed brings the spectra closer to the exact results. Then, an experimental arrangement to measure geometrical phases associated with cyclic and non-cyclic variations of quantum states of an entangled composite system is proposed, utilizing the fundamental ideas of the recently opened field of two-particle interferometry. This arrangement not only resolves the controversy regarding the true nature of the phases associated with photon states, but also unequivocally predicts experimentally accessible geometrical phases in a
Husimi's $Q(\\alpha)$ function and quantum interference in phase space
Mundarain, D F
2003-01-01
We discuss a phase space description of the photon number distribution of non classical states which is based on Husimi's $Q(\\alpha)$ function and does not rely in the WKB approximation. We illustrate this approach using the examples of displaced number states and two photon coherent states and show it to provide an efficient method for computing and interpreting the photon number distribution . This result is interesting in particular for the two photon coherent states which, for high squeezing, have the probabilities of even and odd photon numbers oscillating independently.
Ashtekar, Abhay
In general relativity space-time ends at singularities. The big bang is considered as the Beginning and the big crunch, the End. However these conclusions are arrived at by using general relativity in regimes which lie well beyond its physical domain of validity. Examples where detailed analysis is possible show that these singularities are naturally resolved by quantum geometry effects. Quantum space-times can be vastly larger than what Einstein had us believe. These non-trivial space-time extensions enable us to answer of some long standing questions and resolve of some puzzles in fundamental physics. Thus, a century after Minkowski's revolutionary ideas on the nature of space and time, yet another paradigm shift appears to await us in the wings.
The Harari-Shupe preon model and nonrelativistic quantum phase space
Zenczykowski, Piotr
2008-01-01
We propose that the whole algebraic structure of the Harari-Shupe rishon model originates via a Dirac-like linearization of quadratic form x^2+p^2, with position and momentum satisfying standard commutation relations. The scheme does not invoke the concept of preons as spin-1/2 subparticles, thus evading the problem of preon confinement, while fully explaining all symmetries emboded in the Harari-Shupe model. Furthermore, the concept of quark colour is naturally linked to the ordering of rishons. Our scheme leads to group U(1)xSU(3) combined with SU(2), with two of the SU(2) generators not commuting with reflections. An interpretation of intra-generation quark-lepton transformations in terms of genuine rotations and reflections in phase space is proposed.
The Harari-Shupe preon model and nonrelativistic quantum phase space
Energy Technology Data Exchange (ETDEWEB)
Zenczykowski, P. [Division of Theoretical Physics, Institute of Nuclear Physics, Polish Academy of Sciences, Radzikowskiego 152, 31-342 Cracow (Poland)], E-mail: piotr.zenczykowski@ifj.edu.pl
2008-03-06
We propose that the whole algebraic structure of the Harari-Shupe rishon model originates via a Dirac-like linearization of quadratic form x{sup 2}+p{sup 2}, with position and momentum satisfying standard commutation relations. The scheme does not invoke the concept of preons as spin-1/2 subparticles, thus evading the problem of preon confinement, while fully explaining all symmetries emboded in the Harari-Shupe model. Furthermore, the concept of quark colour is naturally linked to the ordering of rishons. Our scheme leads to group U(1)xSU(3) combined with SU(2), with two of the SU(2) generators not commuting with reflections. An interpretation of intra-generation quark-lepton transformations in terms of genuine rotations and reflections in phase space is proposed.
Geometrical aspects of quantum spaces
Energy Technology Data Exchange (ETDEWEB)
Ho, P.M. [Lawrence Berkeley Lab., CA (United States). Theoretical Physics Group
1996-05-11
Various geometrical aspects of quantum spaces are presented showing the possibility of building physics on quantum spaces. In the first chapter the authors give the motivations for studying noncommutative geometry and also review the definition of a Hopf algebra and some general features of the differential geometry on quantum groups and quantum planes. In Chapter 2 and Chapter 3 the noncommutative version of differential calculus, integration and complex structure are established for the quantum sphere S{sub 1}{sup 2} and the quantum complex projective space CP{sub q}(N), on which there are quantum group symmetries that are represented nonlinearly, and are respected by all the aforementioned structures. The braiding of S{sub q}{sup 2} and CP{sub q}(N) is also described. In Chapter 4 the quantum projective geometry over the quantum projective space CP{sub q}(N) is developed. Collinearity conditions, coplanarity conditions, intersections and anharmonic ratios is described. In Chapter 5 an algebraic formulation of Reimannian geometry on quantum spaces is presented where Riemannian metric, distance, Laplacian, connection, and curvature have their quantum counterparts. This attempt is also extended to complex manifolds. Examples include the quantum sphere, the complex quantum projective space and the two-sheeted space. The quantum group of general coordinate transformations on some quantum spaces is also given.
Evolution of Quantum Phase Space Distribution: a Trajectory-Density Approach
Institute of Scientific and Technical Information of China (English)
ZHANG Xue-Feng; ZHENG Yu-Jun
2009-01-01
The trajectory-density method of a quantum system is developed by using local Koopman and Frobenius-Perron operators. We propose a new scheme of approximation from two sets of trajectory-density mixed equations. By examining the local generation and termination of trajectories, we show how they can be adopted to the propagation of negative values of the Wigner function even if it starts off positive everywhere.
The eigenvalue problem in phase space.
Cohen, Leon
2017-07-27
We formulate the standard quantum mechanical eigenvalue problem in quantum phase space. The equation obtained involves the c-function that corresponds to the quantum operator. We use the Wigner distribution for the phase space function. We argue that the phase space eigenvalue equation obtained has, in addition to the proper solutions, improper solutions. That is, solutions for which no wave function exists which could generate the distribution. We discuss the conditions for ascertaining whether a position momentum function is a proper phase space distribution. We call these conditions psi-representability conditions, and show that if these conditions are imposed, one extracts the correct phase space eigenfunctions. We also derive the phase space eigenvalue equation for arbitrary phase space distributions functions. © 2017 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc.
Quantum cryptography in free space.
Jacobs, B C; Franson, J D
1996-11-15
The range of quantum cryptography systems using optical fibers is limited to roughly 30 km because amplifiers cannot be used. A fully operational system for quantum cryptography based on the transmission of single photons in free space under daylight conditions has been demonstrated. The feasibility of a global system for quantum cryptography based on a network of ground stations and satellites is discussed.
Grassmann variables on quantum spaces
Energy Technology Data Exchange (ETDEWEB)
Mikulovic, D.; Schmidt, A.; Wachter, H. [Ludwig-Maximilians-Universitaet, Sektion Physik, Muenchen (Germany)
2006-02-01
Attention is focused on antisymmetrized versions of quantum spaces that are of particular importance in physics, i.e. two-dimensional quantum plane, q-deformed Euclidean space in three or four dimensions as well as q-deformed Minkowski space. For each case standard techniques for dealing with q-deformed Grassmann variables are developed. Formulae for multiplying supernumbers are given. The actions of symmetry generators and fermionic derivatives upon antisymmetrized quantum spaces are calculated. The complete Hopf structure for all types of quantum space generators is written down. From the formulae for the coproduct a realization of the L-matrices in terms of symmetry generators can be read off. The L-matrices together with the action of symmetry generators determine how quantum spaces of different type have to be fused together. (orig.)
Space searches with a quantum robot
Energy Technology Data Exchange (ETDEWEB)
Benioff, P.
2000-02-15
Quantum robots are described as mobile quantum computers and ancillary systems that move in and interact with arbitrary environments. Their dynamics is given as tasks which consist of sequences of alternating computation and action phases. A task example is considered in which a quantum robot searches a space region to find the location of a system. The possibility that the search can be more efficient than a classical search is examined by considering use of Grover's Algorithm to process the search results. This is problematic for two reasons. One is the removal of entanglements generated by the (reversible) search process. The other is that (ignoring the entanglement problem), the search process in 2 dimensional space regions is no more efficient than a classical search. However quantum searches of higher dimensional space regions are more efficient than classical searches. Reasons why quantum robots are interesting independent of these results are briefly summarized.
Operator representations on quantum spaces
Energy Technology Data Exchange (ETDEWEB)
Bauer, C.; Wachter, H. [Sektion Physik, Ludwig-Maximilians-Universitaet, Theresienstr. 37, 80333, Muenchen (Germany)
2003-11-01
In this article we present explicit formulae for q-differentiation on quantum spaces which could be of particular importance in physics, i.e., q-deformed Minkowski space and q-deformed Euclidean space in three or four dimensions. The calculations are based on the covariant differential calculus of these quantum spaces. Furthermore, our formulae can be regarded as a generalization of Jackson's q-derivative to three and four dimensions. (orig.)
Chemla, D. S.; Bar-Joseph, I.; Klingshirn, C.; Miller, D. A. B.; Kuo, J. M.
1987-03-01
Absorption switching in a semiconductor quantum well by electrically varying the charge density in the quantum well conducting channel of a selectively doped heterostructure transistor is reported for the first time. The phase-space absorption quenching (PAQ) is observed at room temperature in an InGaAs/InAlAs grown on InP FET, and it shows large absorption coefficient changes with relatively broad spectral bandwidth. This PAQ is large enough to be used for direct optical determination of the logic state of the FET.
Energy Technology Data Exchange (ETDEWEB)
Chao, Alexander Wu; /SLAC
2012-03-01
As accelerator technology advances, the requirements on accelerator beam quality become increasingly demanding. Facing these new demands, the topic of phase space gymnastics is becoming a new focus of accelerator physics R&D. In a phase space gymnastics, the beam's phase space distribution is manipulated and precision tailored to meet the required beam qualities. On the other hand, all realization of such gymnastics will have to obey accelerator physics principles as well as technological limitations. Recent examples of phase space gymnastics include Emittance exchanges, Phase space exchanges, Emittance partitioning, Seeded FELs and Microbunched beams. The emittance related topics of this list are reviewed in this report. The accelerator physics basis, the optics design principles that provide these phase space manipulations, and the possible applications of these gymnastics, are discussed. This fascinating new field promises to be a powerful tool of the future.
Entanglement, quantum phase transitions and quantum algorithms
Orus, R
2006-01-01
The work that we present in this thesis tries to be at the crossover of quantum information science, quantum many-body physics, and quantum field theory. We use tools from these three fields to analyze problems that arise in the interdisciplinary intersection. More concretely, in Chapter 1 we consider the irreversibility of renormalization group flows from a quantum information perspective by using majorization theory and conformal field theory. In Chapter 2 we compute the entanglement of a single copy of a bipartite quantum system for a variety of models by using techniques from conformal field theory and Toeplitz matrices. The entanglement entropy of the so-called Lipkin-Meshkov-Glick model is computed in Chapter 3, showing analogies with that of (1+1)-dimensional quantum systems. In Chapter 4 we apply the ideas of scaling of quantum correlations in quantum phase transitions to the study of quantum algorithms, focusing on Shor's factorization algorithm and quantum algorithms by adiabatic evolution solving a...
National Research Council Canada - National Science Library
Ronald E Meyers; Keith S Deacon
2015-01-01
.... The ghost imaging experiments are performed both with and without turbulence. A discussion of the physics of the space-time imaging is presented in terms of quantum nonlocal two-photon analysis to support the experimental results...
Formulation and picture of quantum phase
Institute of Scientific and Technical Information of China (English)
YAO ZhiXin; ZHONG JianWei; PAN BaiLiang
2009-01-01
Based on the concept of classical phase, we formulate a new explanation for the quantum phase from the quantum mechanical point of view. The quantum phase is the canonically conjugate variable of an angular momentum operator, which corresponds to the angular position φ in an actual physical space with a classical reference frame, but it takes a complex exponential form e~(iφ)-cosφ+i sinφin the abstract Hilbert space of a quantum reference frame. This formulation is simply the famous Euler formula in a complex number field. In particular, when φ= π/2, the correlative quantum phase is a unitary pure imaginary number e~(iπ/2)=cos(π/2)+i sin(π/2) = i. By using a photon state-vector function that is the general solution of photon Schrodinger equation and can completely describe a photon's behavior, we discuss the relationship between the angular momentum of a photon and the phase of the photon; we also analyze the intrinsic relationship between the macroscopic light wave phase and the microscopic photon phase.
Formulation and picture of quantum phase
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
Based on the concept of classical phase,we formulate a new explanation for the quantum phase from the quantum mechanical point of view. The quantum phase is the canonically conjugate variable of an angular momentum operator,which corresponds to the angular position θ in an actual physical space with a classical reference frame,but it takes a complex exponential form eiθ≡cosθ +i sinθ in the abstract Hilbert space of a quantum reference frame. This formulation is simply the famous Euler formula in a complex number field. In particular,when θ = π/2,the correlative quantum phase is a unitary pure imaginary number eiπ/2 ≡cos(π/2)+i sin(π/2) ≡ i. By using a photon state-vector function that is the general solution of photon Schrdinger equation and can completely describe a photon’s behavior,we discuss the relationship between the angular momentum of a photon and the phase of the photon; we also analyze the intrinsic relationship between the macroscopic light wave phase and the microscopic photon phase.
Space Searches with a Quantum Robot
Benioff, P
2000-01-01
Quantum robots are described as mobile quantum computers and ancillarysystems that move in and interact with arbitrary environments. Their dynamicsis given as tasks which consist of sequences of alternating computation andaction phases. A task example is considered in which a quantum robot searches aspace region to find the location of a system. The possibility that the searchcan be more efficient than a classical search is examined by considering use ofGrover's Algorithm to process the search results. For reversible searches thisis problematic for two reasons. One is the removal of entanglements generatedby the search process. The other is that even if the entanglement can beavoided, the search process in 2-D space regions is no more efficient than aclassical search. However, quantum searches of space regions with 3 or moredimensions are more efficient than classical searches. Reasons why quantumrobots are interesting independent of these results are briefly summarized.
Joint estimation of phase and phase diffusion for quantum metrology
Vidrighin, Mihai D; Genoni, Marco G; Jin, Xian-Min; Kolthammer, W Steven; Kim, M S; Datta, Animesh; Barbieri, Marco; Walmsley, Ian A
2014-01-01
Phase estimation, at the heart of many quantum metrology and communication schemes, can be strongly affected by noise, whose amplitude may not be known, or might be subject to drift. Here, we investigate the joint estimation of a phase shift and the amplitude of phase diffusion, at the quantum limit. For several relevant instances, this multiparameter estimation problem can be effectively reshaped as a two-dimensional Hilbert space model, encompassing the description of an interferometer phase probed with relevant quantum states -- split single-photons, coherent states or N00N states. For these cases, we obtain a trade-off bound on the statistical variances for the joint estimation of phase and phase diffusion, as well as optimum measurement schemes. We use this bound to quantify the effectiveness of an actual experimental setup for joint parameter estimation for polarimetry. We conclude by discussing the form of the trade-off relations for more general states and measurements.
Quantum Phases of Matter in Optical Lattices
2015-06-30
findings contained in this report are those of the author(s) and should not contrued as an official Department of the Army position , policy or...phases in beyond-standard optical lattices”, Oct 25, 2013 Nikhil Monga, John Shumway, Kaden Hazzard, Erich Mueller, Steven Desch, " Renormalization of...Ho, “Cold Atoms in Curved Space ”, Quantum Materials-Perspectives and Opportunities, The Rice Center for Quantum Materials, December 15, 2014
Robust Adaptive Quantum Phase Estimation
Roy, Shibdas; Huntington, Elanor H
2014-01-01
Quantum parameter estimation is central to many fields such as quantum computation, communications and metrology. Optimal estimation theory has been instrumental in achieving the best accuracy in quantum parameter estimation, which is possible when we have very precise knowledge of and control over the model. However, uncertainties in key parameters underlying the system are unavoidable and may impact the quality of the estimate. We show here how quantum optical phase estimation of a squeezed state of light exhibits improvement when using a robust fixed-interval smoother designed with uncertainties explicitly introduced in parameters underlying the phase noise.
Energy Technology Data Exchange (ETDEWEB)
Fu, Houqiang; Lu, Zhijian; Zhao, Yuji [School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, AZ 85287 (United States)
2016-06-15
We study the low efficiency droop characteristics of semipolar InGaN light-emitting diodes (LEDs) using modified rate equation incoporating the phase-space filling (PSF) effect where the results on c-plane LEDs are also obtained and compared. Internal quantum efficiency (IQE) of LEDs was simulated using a modified ABC model with different PSF filling (n{sub 0}), Shockley-Read-Hall (A), radiative (B), Auger (C) coefficients and different active layer thickness (d), where the PSF effect showed a strong impact on the simulated LED efficiency results. A weaker PSF effect was found for low-droop semipolar LEDs possibly due to small quantum confined Stark effect, short carrier lifetime, and small average carrier density. A very good agreement between experimental data and the theoretical modeling was obtained for low-droop semipolar LEDs with weak PSF effect. These results suggest the low droop performance may be explained by different mechanisms for semipolar LEDs.
Entropic Phase Maps in Discrete Quantum Gravity
Directory of Open Access Journals (Sweden)
Benjamin F. Dribus
2017-06-01
Full Text Available Path summation offers a flexible general approach to quantum theory, including quantum gravity. In the latter setting, summation is performed over a space of evolutionary pathways in a history configuration space. Discrete causal histories called acyclic directed sets offer certain advantages over similar models appearing in the literature, such as causal sets. Path summation defined in terms of these histories enables derivation of discrete Schrödinger-type equations describing quantum spacetime dynamics for any suitable choice of algebraic quantities associated with each evolutionary pathway. These quantities, called phases, collectively define a phase map from the space of evolutionary pathways to a target object, such as the unit circle S 1 ⊂ C , or an analogue such as S 3 or S 7 . This paper explores the problem of identifying suitable phase maps for discrete quantum gravity, focusing on a class of S 1 -valued maps defined in terms of “structural increments” of histories, called terminal states. Invariants such as state automorphism groups determine multiplicities of states, and induce families of natural entropy functions. A phase map defined in terms of such a function is called an entropic phase map. The associated dynamical law may be viewed as an abstract combination of Schrödinger’s equation and the second law of thermodynamics.
Revealing novel quantum phases in quantum antiferromagnets on random lattices
Directory of Open Access Journals (Sweden)
R. Yu
2009-01-01
Full Text Available Quantum magnets represent an ideal playground for the controlled realization of novel quantum phases and of quantum phase transitions. The Hamiltonian of the system can be indeed manipulated by applying a magnetic field or pressure on the sample. When doping the system with non-magnetic impurities, novel inhomogeneous phases emerge from the interplay between geometric randomness and quantum fluctuations. In this paper we review our recent work on quantum phase transitions and novel quantum phases realized in disordered quantum magnets. The system inhomogeneity is found to strongly affect phase transitions by changing their universality class, giving the transition a novel, quantum percolative nature. Such transitions connect conventionally ordered phases to unconventional, quantum disordered ones - quantum Griffiths phases, magnetic Bose glass phases - exhibiting gapless spectra associated with low-energy localized excitations.
Quantum Phase Liquids-Fermionic Superfluid without Phase Coherence
Wu, Ya-Jie; Zhou, Jiang; Kou, Su-Peng
2014-01-01
We investigate the two dimensional generalized attractive Hubbard model in a bipartite lattice, and and a "quantum phase liquid" phase, in which the fermions are paired but don't have phase coherence at zero temperature, in analogy to quantum spin liquid phase. Then, two types of topological quantum phase liquids with a small external magnetic field-Z2 quantum phase liquids and chiral quantum phase liquids-are discussed.
Adiabatic quantum computation and quantum phase transitions
Latorre, J I; Latorre, Jose Ignacio; Orus, Roman
2003-01-01
We analyze the ground state entanglement in a quantum adiabatic evolution algorithm designed to solve the NP-complete Exact Cover problem. The entropy of entanglement seems to obey linear and universal scaling at the point where the mass gap becomes small, suggesting that the system passes near a quantum phase transition. Such a large scaling of entanglement suggests that the effective connectivity of the system diverges as the number of qubits goes to infinity and that this algorithm cannot be efficiently simulated by classical means. On the other hand, entanglement in Grover's algorithm is bounded by a constant.
The topological AC effect on noncommutative phase space
Li, K; Li, Kang; Wang, Jianhua
2006-01-01
The Aharonov-Casher (AC) effect in non-commutative(NC) quantum mechanics is studied. Instead of using the star product method, we use a generalization of Bopp's shift method. After solving the Dirac equations both on noncommutative space and noncommutative phase space by the new method, we obtain the corrections to AC phase on NC space and NC phase space respectively.
Compactification on phase space
Lovelady, Benjamin; Wheeler, James
2016-03-01
A major challenge for string theory is to understand the dimensional reduction required for comparison with the standard model. We propose reducing the dimension of the compactification by interpreting some of the extra dimensions as the energy-momentum portion of a phase-space. Such models naturally arise as generalized quotients of the conformal group called biconformal spaces. By combining the standard Kaluza-Klein approach with such a conformal gauge theory, we may start from the conformal group of an n-dimensional Euclidean space to form a 2n-dimensional quotient manifold with symplectic structure. A pair of involutions leads naturally to two n-dimensional Lorentzian manifolds. For n = 5, this leaves only two extra dimensions, with a countable family of possible compactifications and an SO(5) Yang-Mills field on the fibers. Starting with n=6 leads to 4-dimensional compactification of the phase space. In the latter case, if the two dimensions each from spacetime and momentum space are compactified onto spheres, then there is an SU(2)xSU(2) (left-right symmetric electroweak) field between phase and configuration space and an SO(6) field on the fibers. Such a theory, with minor additional symmetry breaking, could contain all parts of the standard model.
Quantum dynamics in dual spaces
Energy Technology Data Exchange (ETDEWEB)
Sudarshan, E.C.G.
1993-12-31
Quantum mechanics gives us information about spectra of dynamical variables and transition rates including scattering cross sections. They can be exhibited as spectral information in analytically continued spaces and their duals. Quantum mechanics formulated in these generalized spaces is used to study scattering and time evolution. It is shown that the usual asymptotic condition is inadequate to deal with scattering of composite or unstable particles. Scattering theory needs amendment when the interacting system is not isospectral with the free Hamiltonian, and the amendment is formulated. Perturbation theory in generalized spaces is developed and used to study the deletion and augmentation of the spectrum of the Hamiltonian. A complete set of algebraically independent constants for an interacting system is obtained. The question of the breaking of time symmetry is discussed.
Simplicity in simplicial phase space
Dittrich, Bianca
2010-01-01
A key point in the spin foam approach to quantum gravity is the implementation of simplicity constraints in the partition functions of the models. Here, we discuss the imposition of these constraints in a phase space setting corresponding to simplicial geometries. On the one hand, this could serve as a starting point for a derivation of spin foam models by canonical quantisation. On the other, it elucidates the interpretation of the boundary Hilbert space that arises in spin foam models. More precisely, we discuss different versions of the simplicity constraints, namely gauge-variant and gauge-invariant versions. In the gauge-variant version, the primary and secondary simplicity constraints take a similar form to the reality conditions known already in the context of (complex) Ashtekar variables. Subsequently, we describe the effect of these primary and secondary simplicity constraints on gauge-invariant variables. This allows us to illustrate their equivalence to the so-called diagonal, cross and edge simpli...
Energy Technology Data Exchange (ETDEWEB)
Fewster, Christopher J [Department of Mathematics, University of York, Heslington, York YO10 5DD (United Kingdom); Sahlmann, Hanno [Spinoza Institute, Universiteit Utrecht (Netherlands)
2008-11-21
We give a definition for the Wigner function for quantum mechanics on the Bohr compactification of the real line and prove a number of simple consequences of this definition. We then discuss how this formalism can be applied to loop quantum cosmology. As an example, we use the Wigner function to give a new quantization of an important building block of the Hamiltonian constraint.
Fewster, C.J.; Sahlmann, H.
2008-01-01
We give a definition for the Wigner function for quantum mechanics on the Bohr compactification of the real line and prove a number of simple consequences of this definition. We then discuss how this formalism can be applied to loop quantum cosmology. As an example, we use the Wigner function to giv
Semiclassical TEM image formation in phase space
Energy Technology Data Exchange (ETDEWEB)
Lubk, Axel; Röder, Falk
2015-04-15
Current developments in TEM such as high-resolution imaging at low acceleration voltages and large fields of view, the ever larger capabilities of hardware aberration correction and the systematic shaping of electron beams require accurate descriptions of TEM imaging in terms of wave optics. Since full quantum mechanic solutions have not yet been established for, e.g., the theory of aberrations, we are exploring semiclassical image formation in the TEM from the perspective of quantum mechanical phase space, here. Firstly, we use two well-known semiclassical approximations, Miller's semiclassical algebra and the frozen Gaussian method, for describing the wave optical generalization of arbitrary geometric aberrations, including nonisoplanatic and slope aberrations. Secondly, we demonstrate that the Wigner function representation of phase space is well suited to also describe incoherent aberrations as well as the ramifications of partial coherence due to the emission process at the electron source. We identify a close relationship between classical phase space and Wigner function distortions due to aberrations as well as classical brightness and quantum mechanical purity. - Highlights: • We discuss several semiclassical approximations to describe image formation in the TEM. • We provide laws how aberrations modify quantum mechanical phase space. • We exhibit the close relation between quantum mechanical purity and axial brightness.
Poirier, Bill; Salam, A
2004-07-22
In a previous paper [J. Theo. Comput. Chem. 2, 65 (2003)], one of the authors (B.P.) presented a method for solving the multidimensional Schrodinger equation, using modified Wilson-Daubechies wavelets, and a simple phase space truncation scheme. Unprecedented numerical efficiency was achieved, enabling a ten-dimensional calculation of nearly 600 eigenvalues to be performed using direct matrix diagonalization techniques. In a second paper [J. Chem. Phys. 121, 1690 (2004)], and in this paper, we extend and elaborate upon the previous work in several important ways. The second paper focuses on construction and optimization of the wavelength functions, from theoretical and numerical viewpoints, and also examines their localization. This paper deals with their use in representations and eigenproblem calculations, which are extended to 15-dimensional systems. Even higher dimensionalities are possible using more sophisticated linear algebra techniques. This approach is ideally suited to rovibrational spectroscopy applications, but can be used in any context where differential equations are involved.
Chaotic eigenfunctions in phase space
Nonnenmacher, S
1997-01-01
We study individual eigenstates of quantized area-preserving maps on the 2-torus which are classically chaotic. In order to analyze their semiclassical behavior, we use the Bargmann-Husimi representations for quantum states, as well as their stellar parametrization, which encodes states through a minimal set of points in phase space (the constellation of zeros of the Husimi density). We rigorously prove that a semiclassical uniform distribution of Husimi densities on the torus entails a similar equidistribution for the corresponding constellations. We deduce from this property a universal behavior for the phase patterns of chaotic Bargmann eigenfunctions, which reminds of the WKB approximation for eigenstates of integrable systems (though in a weaker sense). In order to obtain more precise information on ``chaotic eigenconstellations", we then model their properties by ensembles of random states, generalizing former results on the 2-sphere to the torus geometry. This approach yields statistical predictions fo...
Quantum correlation and quantum phase transition in the one-dimensional extended Ising model
Zhang, Xi-Zheng; Guo, Jin-Liang
2017-09-01
Quantum phase transitions can be understood in terms of Landau's symmetry-breaking theory. Following the discovery of the quantum Hall effect, a new kind of quantum phase can be classified according to topological rather than local order parameters. Both phases coexist for a class of exactly solvable quantum Ising models, for which the ground state energy density corresponds to a loop in a two-dimensional auxiliary space. Motivated by this we study quantum correlations, measured by entanglement and quantum discord, and critical behavior seen in the one-dimensional extended Ising model with short-range interaction. We show that the quantum discord exhibits distinctive behaviors when the system experiences different topological quantum phases denoted by different topological numbers. Quantum discords capability to detect a topological quantum phase transition is more reliable than that of entanglement at both zero and finite temperatures. In addition, by analyzing the divergent behaviors of quantum discord at the critical points, we find that the quantum phase transitions driven by different parameters of the model can also display distinctive critical behaviors, which provides a scheme to detect the topological quantum phase transition in practice.
Geometric phase in the G3+ quantum state evolution
Soiguine, Alexander
2015-01-01
When quantum mechanical qubits as elements of two dimensional complex Hilbert space are generalized to elements of even subalgebra of geometric algebra over three dimensional Euclidian space, geometrically formal complex plane becomes explicitly defined as an arbitrary, variable plane in 3D. The result is that the quantum state definition and evolution receive more detailed description, including clear calculations of geometric phase, with important consequences for topological quantum computing.
A geometric approach to quantum control in projective hilbert spaces
Pastorello, Davide
2017-02-01
A quantum theory in a finite-dimensional Hilbert space can be formulated as a proper geometric Hamiltonian theory as explained in [2, 3, 7, 9]. From this point of view a quantum system can be described within a classical-like framework where quantum dynamics is represented by a Hamiltonian flow in the phase space given by a projective Hilbert space. This paper is devoted to investigating how the notion of an accessibility algebra from classical control theory can be applied within the geometric Hamiltonian formulation of quantum mechanics to study controllability of a quantum system. A new characterization of quantum controllability in terms of Killing vector fields w.r.t. the Fubini-Study metric on projective space is also discussed.
Wigner Functions for harmonic oscillator in noncommutative phase space
Wang, Jianhua; Li, Kang; Dulat, Sayipjamal
2009-01-01
We study the Wigner Function in non-commutative quantum mechanics. By solving the time independent Schr\\"{o}dinger equation both on a non-commutative (NC) space and a non-commutative phase space, we obtain the Wigner Function for the harmonic oscillator on NC space and NC phase space respectively.
Phase-selective quantum eraser
Heuer, A.; Pieplow, G.; Menzel, R.
2015-07-01
A quantum-eraser experiment is reported with photon pairs generated by two synchronously pumped parametric down-converters coupled via induced coherence. The complementarity between which-source information and two-photon interference fringe visibility is demonstrated explicitly. Changing the phase in a Mach-Zehnder interferometer allows a continuous transition from wavelike to particlelike behavior of photons.
Quantum scaling in many-body systems an approach to quantum phase transitions
Continentino, Mucio
2017-01-01
Quantum phase transitions are strongly relevant in a number of fields, ranging from condensed matter to cold atom physics and quantum field theory. This book, now in its second edition, approaches the problem of quantum phase transitions from a new and unifying perspective. Topics addressed include the concepts of scale and time invariance and their significance for quantum criticality, as well as brand new chapters on superfluid and superconductor quantum critical points, and quantum first order transitions. The renormalisation group in real and momentum space is also established as the proper language to describe the behaviour of systems close to a quantum phase transition. These phenomena introduce a number of theoretical challenges which are of major importance for driving new experiments. Being strongly motivated and oriented towards understanding experimental results, this is an excellent text for graduates, as well as theorists, experimentalists and those with an interest in quantum criticality.
Free-space quantum cryptography
Energy Technology Data Exchange (ETDEWEB)
Hughes, R.J.; Buttler, W.T.; Kwiat, P.G.; Lamoreaux, S.K.; Morgan, G.L.; Nordholt, J.E.; Peterson, C.G.
1998-12-31
An experimental free-space quantum key distribution (QKD) system has been tested over an outdoor optical path of {approximately}1 km under nighttime conditions at Los Alamos National Laboratory. This system employs the Bennett 92 protocol; here the authors give a brief overview of this protocol, and describe the experimental implementation of it. An analysis of the system efficiency is presented, as well as a description of the error detection protocol, which employs a two-dimensional parity check scheme. Finally, the susceptibility of this system to eavesdropping by various techniques is determined. Possible applications include the rekeying of satellites in low earth orbit.
Quantum classifying spaces and universal quantum characteristic classes
Durdevic, M
1996-01-01
A construction of the noncommutative-geometric counterparts of classical classifying spaces is presented, for general compact matrix quantum structure groups. A quantum analogue of the classical concept of the classifying map is introduced and analyzed. Interrelations with the abstract algebraic theory of quantum characteristic classes are discussed. Various non-equivalent approaches to defining universal characteristic classes are outlined.
Cyclotomy and Ramanujan sums in quantum phase locking
Planat, M
2003-01-01
Phase locking governs the phase noise in classical clocks through effects described in precise mathematical terms. We seek here a quantum counterpart of these effects by working in a finite Hilbert space. We use a coprimality condition to define phase-locked quantum states and the corresponding Pegg-Barnett type phase operator. Cyclotomic symmetries in matrix elements are revealed and related to Ramanujan sums in the theory of prime numbers. The phase-number commutator vanishes as in the classical case, but a new type of quantum phase noise emerges in expectation values of phase and phase variance. The employed mathematical procedures also emphasize the isomorphism between algebraic number theory and the theory of quantum entanglement
Transition probability spaces in loop quantum gravity
Guo, Xiao-Kan
2016-01-01
We study the (generalized) transition probability spaces, in the sense of Mielnik and Cantoni, for spacetime quantum states in loop quantum gravity. First, we show that loop quantum gravity admits the structures of transition probability spaces. This is achieved by first checking such structures in covariant quantum mechanics, and then passing to spin foam models via the general boundary formulation. The transition probability space thus defined gives a simple way to reconstruct the Hilbert space of the canonical theory and the relevant quantum logical structure. Second, we show that the transition probability space and in particular the spin foam model are 2-categories. Then we discuss how to realize property transitions and causality in this categorical context in connection with presheaves on quantaloids and respectively causal categories. We conclude that transition probability spaces provide us with an alternative framework to understand various foundational questions of loop quantum gravity.
Quantum Teichm\\"uller space from quantum plane
Frenkel, Igor B
2010-01-01
We derive the quantum Teichm\\"uller space, previously constructed by Kashaev and by Fock and Chekhov, from tensor products of a single canonical representation of the modular double of the quantum plane. We show that the quantum dilogarithm function appears naturally in the decomposition of the tensor square, the quantum mutation operator arises from the tensor cube, the pentagon identity from the tensor fourth power of the canonical representation, and an operator of order three from isomorphisms between canonical representation and its left and right duals. We also show that the quantum universal Teichm\\"uller space is realized in the infinite tensor power of the canonical representation naturally indexed by rational numbers including the infinity. This suggests a relation to the same index set in the classification of projective modules over the quantum torus, the unitary counterpart of the quantum plane, and points to a new quantization of the universal Teichm\\"uller space.
Quantum Information in Space and Time
Volovich, I V
2001-01-01
Many important results in modern quantum information theory have been obtained for an idealized situation when the spacetime dependence of quantum phenomena is neglected. However the transmission and processing of (quantum) information is a physical process in spacetime. Therefore such basic notions in quantum information theory as the notions of composite systems, entangled states and the channel should be formulated in space and time. We emphasize the importance of the investigation of quantum information in space and time. Entangled states in space and time are considered. A modification of Bell`s equation which includes the spacetime variables is suggested. A general relation between quantum theory and theory of classical stochastic processes is proposed. It expresses the condition of local realism in the form of a {\\it noncommutative spectral theorem}. Applications of this relation to the security of quantum key distribution in quantum cryptography are considered.
Quantum gates with topological phases
Ionicioiu, R
2003-01-01
We investigate two models for performing topological quantum gates with the Aharonov-Bohm (AB) and Aharonov-Casher (AC) effects. Topological one- and two-qubit Abelian phases can be enacted with the AB effect using charge qubits, whereas the AC effect can be used to perform all single-qubit gates (Abelian and non-Abelian) for spin qubits. Possible experimental setups suitable for a solid state implementation are briefly discussed.
Phase-space quantization of field theory.
Energy Technology Data Exchange (ETDEWEB)
Curtright, T.; Zachos, C.
1999-04-20
In this lecture, a limited introduction of gauge invariance in phase-space is provided, predicated on canonical transformations in quantum phase-space. Exact characteristic trajectories are also specified for the time-propagating Wigner phase-space distribution function: they are especially simple--indeed, classical--for the quantized simple harmonic oscillator. This serves as the underpinning of the field theoretic Wigner functional formulation introduced. Scalar field theory is thus reformulated in terms of distributions in field phase-space. This is a pedagogical selection from work published and reported at the Yukawa Institute Workshop ''Gauge Theory and Integrable Models'', 26-29 January, 1999.
Quantum Phase Extraction in Isospectral Electronic Nanostructures
Energy Technology Data Exchange (ETDEWEB)
Moon, Christopher
2010-04-28
Quantum phase is not a direct observable and is usually determined by interferometric methods. We present a method to map complete electron wave functions, including internal quantum phase information, from measured single-state probability densities. We harness the mathematical discovery of drum-like manifolds bearing different shapes but identical resonances, and construct quantum isospectral nanostructures possessing matching electronic structure but divergent physical structure. Quantum measurement (scanning tunneling microscopy) of these 'quantum drums' [degenerate two-dimensional electron states on the Cu(111) surface confined by individually positioned CO molecules] reveals that isospectrality provides an extra topological degree of freedom enabling robust quantum state transplantation and phase extraction.
Characterizing maximally singular phase-space distributions
Sperling, J.
2016-07-01
Phase-space distributions are widely applied in quantum optics to access the nonclassical features of radiations fields. In particular, the inability to interpret the Glauber-Sudarshan distribution in terms of a classical probability density is the fundamental benchmark for quantum light. However, this phase-space distribution cannot be directly reconstructed for arbitrary states, because of its singular behavior. In this work, we perform a characterization of the Glauber-Sudarshan representation in terms of distribution theory. We address important features of such distributions: (i) the maximal degree of their singularities is studied, (ii) the ambiguity of representation is shown, and (iii) their dual space for nonclassicality tests is specified. In this view, we reconsider the methods for regularizing the Glauber-Sudarshan distribution for verifying its nonclassicality. This treatment is supported with comprehensive examples and counterexamples.
Quantum mechanics in an evolving Hilbert space
Artacho, Emilio; O'Regan, David D.
2017-03-01
Many basis sets for electronic structure calculations evolve with varying external parameters, such as moving atoms in dynamic simulations, giving rise to extra derivative terms in the dynamical equations. Here we revisit these derivatives in the context of differential geometry, thereby obtaining a more transparent formalization, and a geometrical perspective for better understanding the resulting equations. The effect of the evolution of the basis set within the spanned Hilbert space separates explicitly from the effect of the turning of the space itself when moving in parameter space, as the tangent space turns when moving in a curved space. New insights are obtained using familiar concepts in that context such as the Riemann curvature. The differential geometry is not strictly that for curved spaces as in general relativity, a more adequate mathematical framework being provided by fiber bundles. The language used here, however, will be restricted to tensors and basic quantum mechanics. The local gauge implied by a smoothly varying basis set readily connects with Berry's formalism for geometric phases. Generalized expressions for the Berry connection and curvature are obtained for a parameter-dependent occupied Hilbert space spanned by nonorthogonal Wannier functions. The formalism is applicable to basis sets made of atomic-like orbitals and also more adaptative moving basis functions (such as in methods using Wannier functions as intermediate or support bases), but should also apply to other situations in which nonorthogonal functions or related projectors should arise. The formalism is applied to the time-dependent quantum evolution of electrons for moving atoms. The geometric insights provided here allow us to propose new finite-difference time integrators, and also better understand those already proposed.
Gaussian quantum metrology and space-time probes
Šafránek, Dominik
2016-01-01
In this thesis we focus on Gaussian quantum metrology in the phase-space formalism and its applications in quantum sensing and the estimation of space-time parameters. We derive new formulae for the optimal estimation of multiple parameters encoded into Gaussian states. We discuss the discontinuous behavior of the figure of merit - the quantum Fisher information. Using derived expressions we devise a practical method of finding optimal probe states for the estimation of Gaussian channels and we illustrate this method on several examples. We show that the temperature of a probe state affects the estimation generically and always appears in the form of four multiplicative factors. We also discuss how well squeezed thermal states perform in the estimation of space-time parameters. Finally we study how the estimation precision changes when two parties exchanging a quantum state with the encoded parameter do not share a reference frame. We show that using a quantum reference frame could counter this effect.
Quantum asymmetry between time and space
Vaccaro, Joan A
2015-01-01
In special relativity, time and space are necessarily interconvertible in order that the speed of light is an invariant. This places time and space on an equal footing which, perplexingly, does not carry over to other areas of physics. For example in quantum mechanics, time is treated classically whereas space is associated with a quantum description. Differences between time and space are also found in the violation of the discrete symmetries of charge conjugation, parity inversion and time reversal---the violations are inferred from the decay of particles over time irrespective of their position in space, and so they are associated with translations in time but not in space. Although these violations are clearly important, their wider implications are unknown. We show here that when the violations are included explicitly in a quantum formalism, remarkable differences arise between the character of quantum states in time and space. In particular, despite time and space having an equal footing at a fundamenta...
The topological AC effect on non-commutative phase space
Energy Technology Data Exchange (ETDEWEB)
Li, Kang [Hangzhou Teachers College, Department of Physics, Hangzhou (China); The Abdus Salam International Center for Theoretical Physics, Trieste (Italy); Wang, Jianhua [Shaanxi University of Technology, Department of Physics, Hanzhong (China); The Abdus Salam International Center for Theoretical Physics, Trieste (Italy)
2007-05-15
The Aharonov-Casher (AC) effect in non-commutative (NC) quantum mechanics is studied. Instead of using the star product method, we use a generalization of Bopp's shift method. After solving the Dirac equations both on non-commutative space and non-commutative phase space by the new method, we obtain corrections to the AC phase on NC space and NC phase space, respectively. (orig.)
Topological phases: Wormholes in quantum matter
Schoutens, K.
2009-01-01
Proliferation of so-called anyonic defects in a topological phase of quantum matter leads to a critical state that can be visualized as a 'quantum foam', with topology-changing fluctuations on all length scales.
Quantum phase transitions in constrained Bose systems
Bonnes, Lars
2011-01-01
This doctoral thesis studies low dimensional quantum systems that can be realized in recent cold atom experiments. From the viewpoint of quantum statistical mechanics, the main emphasis is on the detailed study of the different quantum and thermal phases and their transitions using numerical methods, such as quantum Monte Carlo and the Tensor Network Renormalization Group. The first part of this work deals with a lattice Boson model subject to strong three-body losses. In a quantum-Zeno li...
Entropy of phase measurement quantum phase via quadrature measurement
My, R; My, Robert; Uni, Palacky
1995-01-01
The content of phase information of an arbitrary phase--sensitive measurement is evaluated using the maximum likelihood estimation. The phase distribution is characterized by the relative entropy--a nonlinear functional of input quantum state. As an explicit example the multiple measurement of quadrature operator is interpreted as quantum phase detection achieving the ultimate resolution predicted by the Fisher information.
Dynamical quantum phase transitions (Review Article)
Zvyagin, A. A.
2016-11-01
During recent years the interest to dynamics of quantum systems has grown considerably. Quantum many body systems out of equilibrium often manifest behavior, different from the one predicted by standard statistical mechanics and thermodynamics in equilibrium. Since the dynamics of a many-body quantum system typically involve many excited eigenstates, with a non-thermal distribution, the time evolution of such a system provides an unique way for investigation of non-equilibrium quantum statistical mechanics. Last decade such new subjects like quantum quenches, thermalization, pre-thermalization, equilibration, generalized Gibbs ensemble, etc. are among the most attractive topics of investigation in modern quantum physics. One of the most interesting themes in the study of dynamics of quantum many-body systems out of equilibrium is connected with the recently proposed important concept of dynamical quantum phase transitions. During the last few years a great progress has been achieved in studying of those singularities in the time dependence of characteristics of quantum mechanical systems, in particular, in understanding how the quantum critical points of equilibrium thermodynamics affect their dynamical properties. Dynamical quantum phase transitions reveal universality, scaling, connection to the topology, and many other interesting features. Here we review the recent achievements of this quickly developing part of low-temperature quantum physics. The study of dynamical quantum phase transitions is especially important in context of their connection to the problem of the modern theory of quantum information, where namely non-equilibrium dynamics of many-body quantum system plays the major role.
Rescuing a Quantum Phase Transition with Quantum Noise
Zhang, Gu; Novais, E.; Baranger, Harold U.
2017-02-01
We show that placing a quantum system in contact with an environment can enhance non-Fermi-liquid correlations, rather than destroy quantum effects, as is typical. The system consists of two quantum dots in series with two leads; the highly resistive leads couple charge flow through the dots to the electromagnetic environment, the source of quantum noise. While the charge transport inhibits a quantum phase transition, the quantum noise reduces charge transport and restores the transition. We find a non-Fermi-liquid intermediate fixed point for all strengths of the noise. For strong noise, it is similar to the intermediate fixed point of the two-impurity Kondo model.
Quantum Structure of Space and Time
Duff, M. J.; Isham, C. J.
2012-07-01
Foreword Abdus Salam; Preface; List of participants; Part I. Quantum Gravity, Fields and Topology: 1. Some remarks on gravity and quantum mechanics Roger Penrose; 2. An experimental test of quantum gravity Don N. Page and C. D. Geilker; 3. Quantum mechanical origin of the sandwich theorem in classical gravitation theory Claudio Teitelboim; 4. θ-States induced by the diffeomorphism group in canonically quantized gravity C. J. Isham; 5. Strong coupling quantum gravity: an introduction Martin Pilati; 6. Quantizing fourth order gravity theories S. M. Christensen; 7. Green's functions, states and renormalisation M. R. Brown and A. C. Ottewill; 8. Introduction to quantum regge calculus Martin Roček and Ruth Williams; 9. Spontaneous symmetry breaking in curved space-time D. J. Toms; 10. Spontaneous symmetry breaking near a black hole M. S. Fawcett and B. F. Whiting; 11. Yang-Mills vacua in a general three-space G. Kunstatter; 12. Fermion fractionization in physics R. Jackiw; Part II. Supergravity: 13. The new minimal formulation of N=1 supergravity and its tensor calculus M. F. Sohnius and P. C. West; 14. A new deteriorated energy-momentum tensor M. J. Duff and P. K. Townsend; 15. Off-shell N=2 and N=4 supergravity in five dimensions P. Howe; 16. Supergravity in high dimensions P. van Niewenhuizen; 17. Building linearised extended supergravities J. G. Taylor; 18. (Super)gravity in the complex angular momentum plane M. T. Grisaru; 19. The multiplet structure of solitons in the O(2) supergravity theory G. W. Gibbons; 20. Ultra-violet properties of supersymmetric gauge theory S. Ferrara; 21. Extended supercurrents and the ultra-violet finiteness of N=4 supersymmetric Yang-Mills theories K. S. Stelle; 22. Duality rotations B. Zumino; Part III. Cosmology and the Early Universe: 23. Energy, stability and cosmological constant S. Deser; 24. Phase transitions in the early universe T. W. B. Kibble; 25. Complete cosmological theories L. P. Grishchuk and Ya. B. Zeldovich; 26. The
Classifying the Quantum Phases of Matter
2015-01-01
2013), arXiv:1305.2176. [10] J. Haah, Lattice quantum codes and exotic topological phases of matter , arXiv:1305.6973. [11[ M. Hastings and S...CLASSIFYING THE QUANTUM PHASES OF MATTER CALIFORNIA INSTITUTE OF TECHNOLOGY JANUARY 2015 FINAL TECHNICAL REPORT...REPORT 3. DATES COVERED (From - To) JAN 2012 – AUG 2014 4. TITLE AND SUBTITLE CLASSIFYING THE QUANTUM PHASES OF MATTER 5a. CONTRACT NUMBER FA8750-12-2
Quantum charge pumps with topological phases in a Creutz ladder
Sun, Ning; Lim, Lih-King
2017-07-01
The quantum charge pumping phenomenon connects band topology through the dynamics of a one-dimensional quantum system. In terms of a microscopic model, the Su-Schrieffer-Heeger/Rice-Mele quantum pump continues to serve as a fruitful starting point for many considerations of topological physics. Here we present a generalized Creutz scheme as a distinct two-band quantum pump model. By noting that it undergoes two kinds of topological band transitions accompanying with a Zak-phase difference of π and 2 π , respectively, various charge pumping schemes are studied by applying an elaborate Peierls phase substitution. Translating into real space, the transportation of quantized charges is a result of cooperative quantum interference effect. In particular, an all-flux quantum pump emerges which operates with time-varying fluxes only and transports two charge units. This makes cold atoms with artificial gauge fields a unique system where this kind of phenomena can be realized.
Free-Space Quantum Key Distribution
Carrasco-Casado, Alberto; Denisenko, Natalia
2016-01-01
Based on the firm laws of physics rather than unproven foundations of mathematical complexity, quantum cryptography provides a radically different solution for encryption and promises unconditional security. Quantum cryptography systems are typically built between two nodes connected to each other through fiber optic. This chapter focuses on quantum cryptography systems operating over free-space optical channels as a cost-effective and license-free alternative to fiber optic counterparts. It provides an overview of the different parts of an experimental free-space quantum communication link developed in the Spanish National Research Council (Madrid, Spain).
Slow phase relaxation as a route to quantum computing beyond the quantum chaos border
Flores, J.; Kun, S. Yu.; Seligman, T. H.
2005-07-01
We reveal that phase memory can be much longer than energy relaxation in systems with exponentially large dimensions of Hilbert space; this finding is documented by 50 years of nuclear experiments, though the information is somewhat hidden. For quantum computers Hilbert spaces of dimension 2100 or larger will be typical and therefore this effect may contribute significantly to reduce the problems of scaling of quantum computers to a useful number of qubits.
Semiclassical TEM image formation in phase space.
Lubk, Axel; Röder, Falk
2015-04-01
Current developments in TEM such as high-resolution imaging at low acceleration voltages and large fields of view, the ever larger capabilities of hardware aberration correction and the systematic shaping of electron beams require accurate descriptions of TEM imaging in terms of wave optics. Since full quantum mechanic solutions have not yet been established for, e.g., the theory of aberrations, we are exploring semiclassical image formation in the TEM from the perspective of quantum mechanical phase space, here. Firstly, we use two well-known semiclassical approximations, Miller's semiclassical algebra and the frozen Gaussian method, for describing the wave optical generalization of arbitrary geometric aberrations, including nonisoplanatic and slope aberrations. Secondly, we demonstrate that the Wigner function representation of phase space is well suited to also describe incoherent aberrations as well as the ramifications of partial coherence due to the emission process at the electron source. We identify a close relationship between classical phase space and Wigner function distortions due to aberrations as well as classical brightness and quantum mechanical purity. Copyright © 2014 Elsevier B.V. All rights reserved.
Quantum Hall effect in momentum space
Ozawa, Tomoki; Price, Hannah M.; Carusotto, Iacopo
2016-05-01
We theoretically discuss a momentum-space analog of the quantum Hall effect, which could be observed in topologically nontrivial lattice models subject to an external harmonic trapping potential. In our proposal, the Niu-Thouless-Wu formulation of the quantum Hall effect on a torus is realized in the toroidally shaped Brillouin zone. In this analogy, the position of the trap center in real space controls the magnetic fluxes that are inserted through the holes of the torus in momentum space. We illustrate the momentum-space quantum Hall effect with the noninteracting trapped Harper-Hofstadter model, for which we numerically demonstrate how this effect manifests itself in experimental observables. Extension to the interacting trapped Harper-Hofstadter model is also briefly considered. We finally discuss possible experimental platforms where our proposal for the momentum-space quantum Hall effect could be realized.
Murphy, Andrew; Haestad, Jace; Morgan, Thomas
2015-09-01
We report characteristics of closed classical orbits in an electric field in phase space produced in photoabsorption. Rydberg states of atomic and molecular hydrogen and helium are considered. The core potential used for the hydrogen molecule is an effective one electron one center core potential evaluated at the internuclear equilibrium distance. Poincare surfaces of section in phase space are generated by integrating the equations of motion in semiparabolic coordinates u = (r + z) 1 / 2 and v = (r - z) 1 / 2, and plotting the location in phase space (pv versus v) whenever u = 0, with the electric field in the z direction. Combination orbits produced by Rydberg electron core scattering are studied and the evolution in phase space of these combination orbits due to scattering from one closed orbit into another is investigated. Connections are made to measured laser photoabsorption experiments that excite Rydberg states (20 recurrence spectra. The phase space structures responsible for the spectra are identified.
Phase Information in Quantum Oracle Computing
Machta, J.
1998-01-01
Computational devices may be supplied with external sources of information (oracles). Quantum oracles may transmit phase information which is available to a quantum computer but not a classical computer. One consequence of this observation is that there is an oracle which is of no assistance to a classical computer but which allows a quantum computer to solve undecidable problems. Thus useful relativized separations between quantum and classical complexity classes must exclude the transmissio...
q-exponentials on quantum spaces
Energy Technology Data Exchange (ETDEWEB)
Wachter, H. [Ludwig-Maximilians-Universitaet, Sektion Physik, Muenchen (Germany)
2004-10-01
We present explicit formulae for q-exponentials on quantum spaces which could be of particular importance in physics, i.e. the q-deformed Minkowski space and the q-deformed Euclidean space with two, three or four dimensions. Furthermore, these formulae can be viewed as 2-, 3- or 4-dimensional analogues of the well-known q-exponential function. (orig.)
Gosson, Maurice A. de
2012-01-01
Quantum blobs are the smallest phase space units of phase space compatible with the uncertainty principle of quantum mechanics and having the symplectic group as group of symmetries. Quantum blobs are in a bijective correspondence with the squeezed coherent states from standard quantum mechanics, of which they are a phase space picture. This allows us to propose a substitute for phase space in quantum mechanics. We study the relationship between quantum blobs with a certain class of level set...
Quantum Correlations in de Sitter Space
Directory of Open Access Journals (Sweden)
Jiro Soda
2017-01-01
Full Text Available We study quantum correlation of a massive scalar field in a maximally entangled state in de Sitter space. We prepare two observers, one in a global chart and the other in an open chart of de Sitter space. We find that the state becomes less entangled as the curvature of the open chart gets larger. In particular, for the cases of a massless and a conformally coupled scalar field, the quantum entanglement vanishes in the limit of infinite curvature. However, we find that the quantum discord never disappears, even in the limit that entanglement disappears.
Quantum mechanics in Hilbert space
Prugovecki, Eduard
2006-01-01
A critical presentation of the basic mathematics of nonrelativistic quantum mechanics, this text is suitable for courses in functional analysis at the advanced undergraduate and graduate levels. Its readable and self-contained form is accessible even to students without an extensive mathematical background. Applications of basic theorems to quantum mechanics make it of particular interest to mathematicians working in functional analysis and related areas.This text features the rigorous proofs of all the main functional-analytic statements encountered in books on quantum mechanics. It fills the
The quantum phase operator a review
Barnett, Stephen M
2013-01-01
Describing the phase of an electromagnetic field mode or harmonic oscillator has been an obstacle since the early days of modern quantum theory. The quantum phase operator was even more problematic with the invention of the maser and laser in the 1950s and 1960s. This problem was not solved until the Pegg-Barnett formalism was developed in the 1980s. Edited by one of the scientists who created this key solution, The Quantum Phase Operator: A Review charts the development of phase and angle operators from their first appearance to modern theory. Bringing together vital works that have been publ
The Fourier Transform on Quantum Euclidean Space
Directory of Open Access Journals (Sweden)
Kevin Coulembier
2011-05-01
Full Text Available We study Fourier theory on quantum Euclidean space. A modified version of the general definition of the Fourier transform on a quantum space is used and its inverse is constructed. The Fourier transforms can be defined by their Bochner's relations and a new type of q-Hankel transforms using the first and second q-Bessel functions. The behavior of the Fourier transforms with respect to partial derivatives and multiplication with variables is studied. The Fourier transform acts between the two representation spaces for the harmonic oscillator on quantum Euclidean space. By using this property it is possible to define a Fourier transform on the entire Hilbert space of the harmonic oscillator, which is its own inverse and satisfies the Parseval theorem.
q-Integration on Quantum Spaces
Wachter, Hartmut
2002-01-01
In this article we present formulae for q-integration on quantum spaces which could be of particular importance in physics, i.e. q-deformed Minkowski space and q-deformed Euclidean space in 3 or 4 dimensions. Furthermore, our formulae can be regarded as a generalization of Jackson's q-integral to 3 and 4 dimensions and provide a new possibility for an integration over the whole space being invariant under translations and rotations.
q-Integration on quantum spaces
Energy Technology Data Exchange (ETDEWEB)
Wachter, H. [Sektion Physik, Ludwig-Maximilians-Universitaet, Theresienstr. 37, 80333, Muenchen (Germany)
2004-01-01
In this article we present explicit formulae for q-integration on quantum spaces which could be of particular importance in physics, i.e., q-deformed Minkowski space and q-deformed Euclidean space in three or four dimensions. Furthermore, our formulae can be regarded as a generalization of Jackson's q-integral to three or four dimensions and provide a new possibility for an integration over the whole space being invariant under translations and rotations. (orig.)
Hilbert space and quantum mechanics
Gallone, Franco
2015-01-01
The topics of this book are the mathematical foundations of non-relativistic quantum mechanics and the mathematical theory they require. The main characteristic of the book is that the mathematics is developed assuming familiarity with elementary analysis only. Moreover, all the proofs are carried out in detail. These features make the book easily accessible to readers with only the mathematical training offered by undergraduate education in mathematics or in physics, and also ideal for individual study. The principles of quantum mechanics are discussed with complete mathematical accuracy and an effort is made to always trace them back to the experimental reality that lies at their root. The treatment of quantum mechanics is axiomatic, with definitions followed by propositions proved in a mathematical fashion. No previous knowledge of quantum mechanics is required. This book is designed so that parts of it can be easily used for various courses in mathematics and mathematical physics, as suggested in the Pref...
Projective loop quantum gravity. I. State space
Lanéry, Suzanne; Thiemann, Thomas
2016-12-01
Instead of formulating the state space of a quantum field theory over one big Hilbert space, it has been proposed by Kijowski to describe quantum states as projective families of density matrices over a collection of smaller, simpler Hilbert spaces. Beside the physical motivations for this approach, it could help designing a quantum state space holding the states we need. In a latter work by Okolów, the description of a theory of Abelian connections within this framework was developed, an important insight being to use building blocks labeled by combinations of edges and surfaces. The present work generalizes this construction to an arbitrary gauge group G (in particular, G is neither assumed to be Abelian nor compact). This involves refining the definition of the label set, as well as deriving explicit formulas to relate the Hilbert spaces attached to different labels. If the gauge group happens to be compact, we also have at our disposal the well-established Ashtekar-Lewandowski Hilbert space, which is defined as an inductive limit using building blocks labeled by edges only. We then show that the quantum state space presented here can be thought as a natural extension of the space of density matrices over this Hilbert space. In addition, it is manifest from the classical counterparts of both formalisms that the projective approach allows for a more balanced treatment of the holonomy and flux variables, so it might pave the way for the development of more satisfactory coherent states.
The flat phase of quantum polymerized membranes
Coquand, O
2016-01-01
We investigate the flat phase of quantum polymerized phantom membranes by means of a nonperturbative renormalization group approach. We first implement this formalism for general quantum polymerized membranes and derive the flow equations that encompass both quantum and thermal fluctuations. We then deduce and analyze the flow equations relevant to study the flat phase and discuss their salient features : quantum to classical crossover and, in each of these regimes, strong to weak coupling crossover. We finally illustrate these features in the context of free standing graphene physics.
Periodic orbits and TDHF phase space structure
Energy Technology Data Exchange (ETDEWEB)
Hashimoto, Yukio; Iwasawa, Kazuo [Tsukuba Univ., Ibaraki (Japan). Inst. of Physics; Tsukuma, Hidehiko; Sakata, Fumihiko
1998-03-01
The collective motion of atomic nuclei is closely coupled with the motion of nucleons, therefore, it is nonlinear, and the contents of the motion change largely with the increase of its amplitude. As the framework which describes the collective motion accompanied by the change of internal structure, time-dependent Hurtley Fock (TDHF) method is suitable. At present, the authors try to make the method for studying the large region structure in quantum system by utilizing the features of the TDHF phase space. The studies made so far are briefed. In this report, the correspondence of the large region patterns appearing in the band structure chart of three-level model with the periodic orbit group in the TDHF phase space is described. The Husimi function is made, and it possesses the information on the form of respective corresponding intrinsic state. The method of making the band structure chart is explained. There are three kinds of the tendency in the intrinsic state group. The E-T charts are made for the band structure charts to quantitatively express the large region tendency. The E-T chart and the T{sub r}-T chart are drawn for a selected characteristic orbit group. It became to be known that the large region properties of the quantum intrinsic state group of three-level model can be forecast by examining the properties of the periodic orbit group in the TDHF phase space. (K.I.)
Periodic orbits and TDHF phase space structure
Energy Technology Data Exchange (ETDEWEB)
Hashimoto, Yukio; Iwasawa, Kazuo [Tsukuba Univ., Ibaraki (Japan). Inst. of Physics; Tsukuma, Hidehiko; Sakata, Fumihiko
1998-03-01
The collective motion of atomic nuclei is closely coupled with the motion of nucleons, therefore, it is nonlinear, and the contents of the motion change largely with the increase of its amplitude. As the framework which describes the collective motion accompanied by the change of internal structure, time-dependent Hurtley Fock (TDHF) method is suitable. At present, the authors try to make the method for studying the large region structure in quantum system by utilizing the features of the TDHF phase space. The studies made so far are briefed. In this report, the correspondence of the large region patterns appearing in the band structure chart of three-level model with the periodic orbit group in the TDHF phase space is described. The Husimi function is made, and it possesses the information on the form of respective corresponding intrinsic state. The method of making the band structure chart is explained. There are three kinds of the tendency in the intrinsic state group. The E-T charts are made for the band structure charts to quantitatively express the large region tendency. The E-T chart and the T{sub r}-T chart are drawn for a selected characteristic orbit group. It became to be known that the large region properties of the quantum intrinsic state group of three-level model can be forecast by examining the properties of the periodic orbit group in the TDHF phase space. (K.I.)
Scaling of the local quantum uncertainty at quantum phase transitions
Energy Technology Data Exchange (ETDEWEB)
Coulamy, I.B.; Warnes, J.H.; Sarandy, M.S., E-mail: msarandy@if.uff.br; Saguia, A.
2016-04-29
We investigate the local quantum uncertainty (LQU) between a block of L qubits and one single qubit in a composite system of n qubits driven through a quantum phase transition (QPT). A first-order QPT is analytically considered through a Hamiltonian implementation of the quantum search. In the case of second-order QPTs, we consider the transverse-field Ising chain via a numerical analysis through density matrix renormalization group. For both cases, we compute the LQU for finite-sizes as a function of L and of the coupling parameter, analyzing its pronounced behavior at the QPT. - Highlights: • LQU is suitable for the analysis of block correlations. • LQU exhibits pronounced behavior at quantum phase transitions. • LQU exponentially saturates in the quantum search. • Concavity of LQU indicates criticality in the Ising chain.
Free-space quantum key distribution
Buttler, W T; Kwiat, P G; Luther, G G; Morgan, G L; Nordholt, J E; Peterson, C G; Simmons, C M
1998-01-01
A working free-space quantum key distribution (QKD) system has been developed and tested over a 205-m indoor optical path at Los Alamos National Laboratory under fluorescent lighting conditions. Results show that free-space QKD can provide secure real-time key distribution between parties who have a need to communicate secretly.
Evolution of classical projected phase space density in billiards
Indian Academy of Sciences (India)
Debabrata Biswas
2005-04-01
The classical phase space density projected on to the configuration space offers a means of comparing classical and quantum evolution. In this alternate approach that we adopt here, we show that for billiards, the eigenfunctions of the coarse-grained projected classical evolution operator are identical to a first approximation to the quantum Neumann eigenfunctions. Moreover, there exists a correspondence between the respective eigenvalues although their time evolutions differ.
Space-time mechanics: Quantum causal structure and expansive force
Valenzuela, Mauricio
2015-01-01
Combining twistor space and phase space formulation of quantum mechanics we propose a new framework of quantization of geometries which incorporates Wigner functions for geometrical observables. Quantizing the light-cone in 2+1D and 3+1D results in one-sheet "quantum hyperboloids". We propose that the latter rule the causal structure of the space-time, yielding uncertainty of positions and space-time curvature. The quantum hyperboloid predicts accelerated propagation of signals and effective space expansion. These effects are noticeable at scales of the quantization parameter in twistor space and negligible at much larger scales since the hyperboloid is asymptotic to the light-cone. Due to space-time non-commutativity it is necessary to introduce notions of observers which are able to determine distances in specific directions. Thus, in the perspective of a time-observer, time and radius of spatial sections of the quantum hyperboloid become discrete and bounded from below. Hence the time is quantized and punc...
Density functional theory on phase space
Blanchard, Philippe; Várilly, Joseph C
2010-01-01
Forty-five years after the point de d\\'epart [1] of density functional theory, its applications in chemistry and the study of electronic structures keep steadily growing. However, the precise form of the "divine" energy functional in terms of the electron density [2] still eludes us --and possibly will do so forever [3]. In what follows we examine a formulation in the same spirit with phase-space variables. The validity of Hohenberg-Kohn-Levy-type theorems on phase space is recalled. We study the representability problem for reduced Wigner functions, and proceed to analyze properties of the new functional. Along the way, new results on states in the phase-space formalism of quantum mechanics are established. Natural Wigner orbital theory is developed in depth, with the final aim of constructing accurate correlation-exchange functionals on phase space. A new proof of the overbinding property of the Mueller functional is given. This exact theory supplies its home at long last to that illustrious ancestor, the T...
Quantum Fisher information as signature of superradiant quantum phase transition
Wang, T L; Yang, W; Jin, G R; Lambert, N; Nori, F
2013-01-01
The single-mode Dicke model is well-known to undergo a quantum phase transition from the so-called normal phase to the supperradiant phase (hereinafter called the "superradiant quantum phase transition"). Normally, quantum phase transitions are closely related to the critical behavior of quantities such as entanglement, quantum fluctuations, and fidelity. In this paper, we study quantum Fisher information (QFI) of the field mode and that of the atoms in the ground state of the Dicke Hamiltonian. For finite and large enough number of atoms N, our numerical results show that near the critical atom-field coupling, the QFIs of the atomic and the field subsystems can surpass the classical limits, due to the appearance of nonclassical squeezed states. As the coupling increases far beyond the critical point, the two subsystems are in highly mixed states, which degrade the QFI and hence the ultimate phase sensitivity. In the thermodynamic limit, we present analytical results of the QFIs and their relationships with t...
Conductor-insulator quantum phase transitions
Trivedi, Nandini; Valles, James M
2012-01-01
When many particles come together how do they organise themselves? And what destroys this organisation? Combining experiments and theory, this book describes intriguing quantum phases - metals, superconductors and insulators - and transitions between them.
Quantum Computers, Discrete Space, and Entanglement
Pavicic, M
2002-01-01
We consider algebras underlying Hilbert spaces used by quantum information algorithms. We show how one can arrive at equations on such algebras which define n-dimensional Hilbert space subspaces which in turn can simulate quantum systems on a quantum system. In doing so we use MMP diagrams and linear algorithms. MMP diagrams are tractable since an n-block of an MMP diagram has n elements while an n-block of a standard lattice diagram has 2^n elements. An immediate test for such an approach is a generation of minimal and arbitrary Kochen-Specker vectors and we present a minimal state-independent Kochen-Specker set of seven vectors from a Hilbert space with more than four dimensions.
Quantum discord in de Sitter space
Kanno, Sugumi; Soda, Jiro
2016-01-01
We study quantum discord between two free modes of a massive scalar field in a maximally entangled state in de Sitter space. We introduce two observers, one in a global chart and the other in an open chart of de Sitter space, and the observers determine the quantum discord created by each detecting one of the modes. This situation is analogous to the relationship between an observer in a Minkowski chart and another in one of the two Rindler charts in flat space. We find that the state becomes less entangled as the curvature of the open chart gets larger. In particular, for the cases of a massless, and a conformally coupled scalar field, the entanglement vanishes in the limit of infinite curvature. However, we find that the quantum discord never disappears even in the limit that entanglement disappears.
Towards testing quantum physics in deep space
Kaltenbaek, Rainer
2016-07-01
MAQRO is a proposal for a medium-sized space mission to use the unique environment of deep space in combination with novel developments in space technology and quantum technology to test the foundations of physics. The goal is to perform matter-wave interferometry with dielectric particles of up to 10^{11} atomic mass units and testing for deviations from the predictions of quantum theory. Novel techniques from quantum optomechanics with optically trapped particles are to be used for preparing the test particles for these experiments. The core elements of the instrument are placed outside the spacecraft and insulated from the hot spacecraft via multiple thermal shields allowing to achieve cryogenic temperatures via passive cooling and ultra-high vacuum levels by venting to deep space. In combination with low force-noise microthrusters and inertial sensors, this allows realizing an environment well suited for long coherence times of macroscopic quantum superpositions and long integration times. Since the original proposal in 2010, significant progress has been made in terms of technology development and in refining the instrument design. Based on these new developments, we submitted/will submit updated versions of the MAQRO proposal in 2015 and 2016 in response to Cosmic-Vision calls of ESA for a medium-sized mission. A central goal has been to address and overcome potentially critical issues regarding the readiness of core technologies and to provide realistic concepts for further technology development. We present the progress on the road towards realizing this ground-breaking mission harnessing deep space in novel ways for testing the foundations of physics, a technology pathfinder for macroscopic quantum technology and quantum optomechanics in space.
Entanglement and separability in the noncommutative phase-space scenario
Bernardini, Alex E; Bertolami, Orfeu; Dias, Nuno C; Prata, João N
2014-01-01
Quantumness and separability criteria for continuous variable systems are discussed for the case of a noncommutative (NC) phase-space. In particular, the quantum nature and the entanglement configuration of NC two-mode Gaussian states are examined. Two families of covariance matrices describing standard quantum mechanics (QM) separable states are deformed into a NC QM configuration and then investigated through the positive partial transpose criterium for identifying quantum entanglement. It is shown that the entanglement of Gaussian states may be exclusively induced by switching on the NC deformation. Extensions of some preliminary results are presented.
Quantum Holonomy Theory and Hilbert Space Representations
Aastrup, Johannes
2016-01-01
We present a new formulation of quantum holonomy theory, which is a candidate for a non-perturbative and background independent theory of quantum gravity coupled to matter and gauge degrees of freedom. The new formulation is based on a Hilbert space representation of the QHD(M) algebra, which is generated by holonomy-diffeomorphisms on a 3-dimensional manifold and by canonical translation operators on the underlying configuration space over which the holonomy-diffeomorphisms form a non-commutative C*-algebra. A proof that the state exist is left for later publications.
Longitudinal Phase Space Tomography with Space Charge
Hancock, S; Lindroos, M
2000-01-01
Tomography is now a very broad topic with a wealth of algorithms for the reconstruction of both qualitative and quantitative images. In an extension in the domain of particle accelerators, one of the simplest algorithms has been modified to take into account the non-linearity of large-amplitude synchrotron motion. This permits the accurate reconstruction of longitudinal phase space density from one-dimensional bunch profile data. The method is a hybrid one which incorporates particle tracking. Hitherto, a very simple tracking algorithm has been employed because only a brief span of measured profile data is required to build a snapshot of phase space. This is one of the strengths of the method, as tracking for relatively few turns relaxes the precision to which input machine parameters need to be known. The recent addition of longitudinal space charge considerations as an optional refinement of the code is described. Simplicity suggested an approach based on the derivative of bunch shape with the properties of...
Wigner function for discrete phase space: exorcising ghost images
Arg"uelles, A; Arg\\"uelles, Arturo; Dittrich, Thomas
2005-01-01
We construct, using simple geometrical arguments, a Wigner function defined on a discrete phase space of arbitrary integer Hilbert-space dimension that is free of redundancies. ``Ghost images'' plaguing other Wigner functions for discrete phase spaces are thus revealed as artifacts. It allows to devise a corresponding phase-space propagator in an unambiguous manner. We apply our definitions to eigenstates and propagator of the quantum baker map. Scars on unstable periodic points of the corresponding classical map become visible with unprecedented resolution.
Dynamical quantum Hall effect in the parameter space.
Gritsev, V; Polkovnikov, A
2012-04-24
Geometric phases in quantum mechanics play an extraordinary role in broadening our understanding of fundamental significance of geometry in nature. One of the best known examples is the Berry phase [M.V. Berry (1984), Proc. Royal. Soc. London A, 392:45], which naturally emerges in quantum adiabatic evolution. So far the applicability and measurements of the Berry phase were mostly limited to systems of weakly interacting quasi-particles, where interference experiments are feasible. Here we show how one can go beyond this limitation and observe the Berry curvature, and hence the Berry phase, in generic systems as a nonadiabatic response of physical observables to the rate of change of an external parameter. These results can be interpreted as a dynamical quantum Hall effect in a parameter space. The conventional quantum Hall effect is a particular example of the general relation if one views the electric field as a rate of change of the vector potential. We illustrate our findings by analyzing the response of interacting spin chains to a rotating magnetic field. We observe the quantization of this response, which we term the rotational quantum Hall effect.
Unification of Quantum and Gravity by Non Classical Information Entropy Space
Directory of Open Access Journals (Sweden)
Davide Fiscaletti
2013-09-01
Full Text Available A quantum entropy space is suggested as the fundamental arena describing the quantum effects. In the quantum regime the entropy is expressed as the superposition of many different Boltzmann entropies that span the space of the entropies before any measure. When a measure is performed the quantum entropy collapses to one component. A suggestive reading of the relational interpretation of quantum mechanics and of Bohm’s quantum potential in terms of the quantum entropy are provided. The space associated with the quantum entropy determines a distortion in the classical space of position, which appears as a Weyl-like gauge potential connected with Fisher information. This Weyl-like gauge potential produces a deformation of the moments which changes the classical action in such a way that Bohm’s quantum potential emerges as consequence of the non classical definition of entropy, in a non-Euclidean information space under the constraint of a minimum condition of Fisher information (Fisher Bohm- entropy. Finally, the possible quantum relativistic extensions of the theory and the connections with the problem of quantum gravity are investigated. The non classical thermodynamic approach to quantum phenomena changes the geometry of the particle phase space. In the light of the representation of gravity in ordinary phase space by torsion in the flat space (Teleparallel gravity, the change of geometry in the phase space introduces quantum phenomena in a natural way. This gives a new force to F. Shojai’s and A. Shojai’s theory where the geometry of space-time is highly coupled with a quantum potential whose origin is not the Schrödinger equation but the non classical entropy of a system of many particles that together change the geometry of the phase space of the positions (entanglement. In this way the non classical thermodynamic changes the classical geodetic as a consequence of the quantum phenomena and quantum and gravity are unified. Quantum
On Arbitrary Phases in Quantum Amplitude Amplification
Hoyer, P
2000-01-01
We consider the use of arbitrary phases in quantum amplitude amplification which is a generalization of quantum searching. We prove that the phase condition in amplitude amplification is given by $\\tan(\\phi/2)=\\tan(\\phi/2)(1-2a)$, where $\\phi$ and $\\phi$ are the phases used and where $a$ is the success probability of the given algorithm. Thus the choice of phases depends nontrivially and nonlinearly on the success probability. Utilizing this condition, we give methods for constructing quantum algorithms that succeed with certainty and for implementing arbitrary rotations. We also conclude that phase errors of order up to $\\frac{1}{\\sqrt{a}}$ can be tolerated in amplitude amplification.
Projective limits of state spaces II. Quantum formalism
Lanéry, Suzanne; Thiemann, Thomas
2017-06-01
In this series of papers, we investigate the projective framework initiated by Kijowski (1977) and Okołów (2009, 2014, 2013), which describes the states of a quantum theory as projective families of density matrices. A short reading guide to the series can be found in Lanéry (2016). After discussing the formalism at the classical level in a first paper (Lanéry, 2017), the present second paper is devoted to the quantum theory. In particular, we inspect in detail how such quantum projective state spaces relate to inductive limit Hilbert spaces and to infinite tensor product constructions (Lanéry, 2016, subsection 3.1) [1]. Regarding the quantization of classical projective structures into quantum ones, we extend the results by Okołów (2013), that were set up in the context of linear configuration spaces, to configuration spaces given by simply-connected Lie groups, and to holomorphic quantization of complex phase spaces (Lanéry, 2016, subsection 2.2) [1].
Beyond relativity and quantum mechanics: space physics
Lindner, Henry H.
2011-09-01
Albert Einstein imposed an observer-based epistemology upon physics. Relativity and Quantum Mechanics limit physics to describing and modeling the observer's sensations and measurements. Their "underlying reality" consists only of ideas that serve to model the observer's experience. These positivistic models cannot be used to form physical theories of Cosmic phenomena. To do this, we must again remove the observer from the center of physics. When we relate motion to Cosmic space instead of to observers and we attempt to explain the causes of Cosmic phenomena, we are forced to admit that Cosmic space is a substance. We need a new physics of space. We can begin by replacing Relativity with a modified Lorentzian-Newtonian model of spatial flow, and Quantum Mechanics with a wave-based theory of light and electrons. Space physics will require the reinterpretation of all known phenomena, concepts, and mathematical models.
FREE-SPACE QUANTUM CRYPTOGRAPHY IN DAYLIGHT
Energy Technology Data Exchange (ETDEWEB)
Hughes, R.J.; Buttler, W.T. [and others
2000-01-01
Quantum cryptography is an emerging technology in which two parties may simultaneously generate shared, secret cryptographic key material using the transmission of quantum states of light. The security of these transmissions is based on the inviolability of the laws of quantum mechanics and information-theoretically secure post-processing methods. An adversary can neither successfully tap the quantum transmissions, nor evade detection, owing to Heisenberg's uncertainty principle. In this paper we describe the theory of quantum cryptography, and the most recent results from our experimental free-space system with which we have demonstrated for the first time the feasibility of quantum key generation over a point-to-point outdoor atmospheric path in daylight. We achieved a transmission distance of 0.5 km, which was limited only by the length of the test range. Our results provide strong evidence that cryptographic key material could be generated on demand between a ground station and a satellite (or between two satellites), allowing a satellite to be securely re-keyed on orbit. We present a feasibility analysis of surface-to-satellite quantum key generation.
Maximal-acceleration phase space relativity from Clifford algebras
Castro, C
2002-01-01
We present a new physical model that links the maximum speed of light with the minimal Planck scale into a maximal-acceleration Relativity principle in the spacetime tangent bundle and in phase spaces (cotangent bundle). Crucial in order to establish this link is the use of Clifford algebras in phase spaces. The maximal proper-acceleration bound is a = c^2/ \\Lambda in full agreement with the old predictions of Caianiello, the Finslerian geometry point of view of Brandt and more recent results in the literature. We present the reasons why an Extended Scale Relativity based on Clifford spaces is physically more appealing than those based on kappa-deformed Poincare algebras and the inhomogeneous quantum groups operating in quantum Minkowski spacetimes. The main reason being that the Planck scale should not be taken as a deformation parameter to construct quantum algebras but should exist already as the minimum scale in Clifford spaces.
Quantum Mechanics on discrete space and time
Lorente, M
2004-01-01
We propose the assumption of quantum mechanics on a discrete space and time, which implies the modification of mathematical expressions for some postulates of quantum mechanics. In particular we have a Hilbert space where the vectors are complex functions of discrete variable. As a concrete example we develop a discrete analog of the one-dimensional quantum harmonic oscillator, using the dependence of the Wigner functions in terms of Kravchuk polynomials. In this model the position operator has a discrete spectrum given by one index of the Wigner functions, in the same way that the energy eigenvalues are given by the other matricial index. Similar picture can be made for other models where the differential equation and their solutions correspond to the continuous limit of some difference operator and orthogonal polynomial of discrete variable.
Length and distance on a quantum space
Martinetti, Pierre
2012-01-01
This contribution is an introduction to the metric aspect of noncommutative geometry, with emphasize on the Moyal plane. Starting by questioning "how to define a standard meter in a space whose coordinates no longer commute?", we list several recent results regarding Connes's spectral distance calculated between eigenstates of the quantum harmonic oscillator arXiv:0912.0906, as well as between coherent states arXiv:1110.6164. We also question the difference (which remains hidden in the commutative case) between the spectral distance and the notion of quantum length inherited from the length operator defined in various models of noncommutative space-time (DFR and \\theta-Minkowski). We recall that a standard procedure in noncommutative geometry, consisting in doubling the spectral triple, allows to fruitfully confront the spectral distance with the quantum length. Finally we refine the idea of discrete vs. continuous geodesics in the Moyal plane, introduced in arXiv:1106.0261.
Relativistic phase space dimensional recurrences
Delbourgo, Robert
2003-01-01
We derive recurrence relations between phase space expressions in different dimensions by confining some of the coordinates to tori or spheres of radius $R$ and taking the limit as $R \\to \\infty$. These relations take the form of mass integrals, associated with extraneous momenta (relative to the lower dimension), and produce the result in the higher dimension.
Quantum mechanics as a measurement theory on biconformal space
Anderson, L B; Anderson, Lara B.; Wheeler, James T.
2004-01-01
Biconformal spaces contain the essential elements of quantum mechanics, making the independent imposition of quantization unnecessary. Based on three postulates characterizing motion and measurement in biconformal geometry, we derive standard quantum mechanics, and show how the need for probability amplitudes arises from the use of a standard of measurement. Additionally, we show that a postulate for unique, classical motion yields Hamiltonian dynamics with no measurable size changes, while a postulate for probabilistic evolution leads to physical dilatations manifested as measurable phase changes. Our results lead to the Feynman path integral formulation, from which follows the Schroedinger equation. We discuss the Heisenberg uncertainty relation and fundamental canonical commutation relations.
Energy Technology Data Exchange (ETDEWEB)
Parker, E.N. [Univ. of Chicago, IL (United States)
1994-10-01
Space science began with the indirect phase where the activity in space was inferred from such terrestrial phenomena as geomagnetic storms, ionospheric variations, and fluctuations in the cosmic ray intensity. The direct phase was initiated with spaceflight placing instruments directly in space and permitting the direct observation of UV and X rays, as well as precision observations of solar luminosity variations. The evidence from these many direct studies, together with the historical record of terrestrial conditions, shows that the variations of the luminosity of the Sun affect the terrestrial atmosphere at all levels, with devastating changes in climate tracking the major changes in the activity level and luminosity of the Sun. The quantification and understanding of this vital connection should be the first priority of space science and geophysics, from oceans and atmosphere through the ionosphere, magnetosphere, and all the way to the convective zone of the Sun. It becomes the vital phase of space science, focused on the basic science of the changing habitability of Earth. 13 refs.
Quantum mechanics in finite dimensional Hilbert space
de la Torre, A C
2002-01-01
The quantum mechanical formalism for position and momentum of a particle in a one dimensional cyclic lattice is constructively developed. Some mathematical features characteristic of the finite dimensional Hilbert space are compared with the infinite dimensional case. The construction of an unbiased basis for state determination is discussed.
Projective Loop Quantum Gravity I. State Space
Lanéry, Suzanne
2014-01-01
Instead of formulating the state space of a quantum field theory over one big Hilbert space, it has been proposed by Kijowski to describe quantum states as projective families of density matrices over a collection of smaller, simpler Hilbert spaces. Beside the physical motivations for this approach, it could help designing a quantum state space holding the states we need. In [Oko{\\l}\\'ow 2013, arXiv:1304.6330] the description of a theory of Abelian connections within this framework was developed, an important insight being to use building blocks labeled by combinations of edges and surfaces. The present work generalizes this construction to an arbitrary gauge group G (in particular, G is neither assumed to be Abelian nor compact). This involves refining the definition of the label set, as well as deriving explicit formulas to relate the Hilbert spaces attached to different labels. If the gauge group happens to be compact, we also have at our disposal the well-established Ashtekar-Lewandowski Hilbert space, wh...
Unconventional geometric quantum phase gates with a cavity QED system
Zheng, Shi-Biao
2004-11-01
We propose a scheme for realizing two-qubit quantum phase gates via an unconventional geometric phase shift with atoms in a cavity. In the scheme the atoms interact simultaneously with a highly detuned cavity mode and a classical field. The atoms undergo no transitions during the gate operation, while the cavity mode is displaced along a circle in the phase space, aquiring a geometric phase conditional upon the atomic state. Under certain conditions, the atoms are disentangled with the cavity mode and thus the gate is insensitive to both the atomic spontaneous emission and the cavity decay.
Quantum Phase Transitions in a Finite System
Leviatan, A
2006-01-01
A general procedure for studying finite-N effects in quantum phase transitions of finite systems is presented and applied to the critical-point dynamics of nuclei undergoing a shape-phase transition of second-order (continuous), and of first-order with an arbitrary barrier.
Crystal Phase Quantum Well Emission with Digital Control.
Assali, S; Lähnemann, J; Vu, T T T; Jöns, K D; Gagliano, L; Verheijen, M A; Akopian, N; Bakkers, E P A M; Haverkort, J E M
2017-09-18
One of the major challenges in the growth of quantum well and quantum dot heterostructures is the realization of atomically sharp interfaces. Nanowires provide a new opportunity to engineer the band structure as they facilitate the controlled switching of the crystal structure between the zinc-blende (ZB) and wurtzite (WZ) phases. Such a crystal phase switching results in the formation of crystal phase quantum wells (CPQWs) and quantum dots (CPQDs). For GaP CPQWs, the inherent electric fields due to the discontinuity of the spontaneous polarization at the WZ/ZB junctions lead to the confinement of both types of charge carriers at the opposite interfaces of the WZ/ZB/WZ structure. This confinement leads to a novel type of transition across a ZB flat plate barrier. Here, we show digital tuning of the visible emission of WZ/ZB/WZ CPQWs in a GaP nanowire by changing the thickness of the ZB barrier. The energy spacing between the sharp emission lines is uniform and is defined by the addition of single ZB monolayers. The controlled growth of identical quantum wells with atomically flat interfaces at predefined positions featuring digitally tunable discrete emission energies may provide a new route to further advance entangled photons in solid state quantum systems.
Quantum Opportunities and Challenges for Fundamental Sciences in Space
Yu, Nan
2012-01-01
Space platforms offer unique environment for and measurements of quantum world and fundamental physics. Quantum technology and measurements enhance measurement capabilities in space and result in greater science returns.
Discord under the influence of a quantum phase transition
Institute of Scientific and Technical Information of China (English)
Wang Lin-cheng; Shen Jian; Yi Xue-Xi
2011-01-01
This paper studies the discord of a bipartite two-level system coupling to an XY spin-chain environment in a transverse field and investigates the relationship between the discord property and the environment's quantum phase transition. The results show that the quantum discord is also able to characterize the quantum phase transitions. We also discuss the difference between discord and entanglement, and show that quantum discord may reveal more general information than quantum entanglement for characterizing the environment's quantum phase transition.
Quantum mechanics in an evolving Hilbert space
Artacho, Emilio
2016-01-01
Many basis sets for electronic structure calculations evolve with varying external parameters, such as moving atoms in dynamic simulations, giving rise to extra derivative terms in the dynamical equations. Here we revisit these derivatives in the context of differential geometry, thereby obtaining a more transparent formalisation, and a geometrical perspective for better understanding the resulting equations. The effect of the evolution of the basis set within the spanned Hilbert space separates explicitly from the effect of the turning of the space itself when moving in parameter space, as the tangent space turns when moving in a curved space. New insights are obtained using familiar concepts in that context such as the Riemann curvature. The differential geometry is not strictly that for curved spaces as in general relativity, a more adequate mathematical framework being provided by fibre bundles. The language used here, however, will be restricted to tensors and basic quantum mechanics. The local gauge imp...
Longitudinal phase space tomography with space charge
Hancock, S.; Lindroos, M.; Koscielniak, S.
2000-12-01
Tomography is now a very broad topic with a wealth of algorithms for the reconstruction of both qualitative and quantitative images. In an extension in the domain of particle accelerators, one of the simplest algorithms has been modified to take into account the nonlinearity of large-amplitude synchrotron motion. This permits the accurate reconstruction of longitudinal phase space density from one-dimensional bunch profile data. The method is a hybrid one which incorporates particle tracking. Hitherto, a very simple tracking algorithm has been employed because only a brief span of measured profile data is required to build a snapshot of phase space. This is one of the strengths of the method, as tracking for relatively few turns relaxes the precision to which input machine parameters need to be known. The recent addition of longitudinal space charge considerations as an optional refinement of the code is described. Simplicity suggested an approach based on the derivative of bunch shape with the properties of the vacuum chamber parametrized by a single value of distributed reactive impedance and by a geometrical coupling coefficient. This is sufficient to model the dominant collective effects in machines of low to moderate energy. In contrast to simulation codes, binning is not an issue since the profiles to be differentiated are measured ones. The program is written in Fortran 90 with high-performance Fortran extensions for parallel processing. A major effort has been made to identify and remove execution bottlenecks, for example, by reducing floating-point calculations and recoding slow intrinsic functions. A pointerlike mechanism which avoids the problems associated with pointers and parallel processing has been implemented. This is required to handle the large, sparse matrices that the algorithm employs. Results obtained with and without the inclusion of space charge are presented and compared for proton beams in the CERN protron synchrotron booster. Comparisons
Cold atom quantum sensors for space
Singh, Yeshpal
2016-07-01
Quantum sensors based on cold atoms offer the opportunity to perform highly accurate measurements of physical phenomena related to time, gravity and rotation. The deployment of such technologies in the microgravity environment of space may enable further enhancement of their performance, whilst permitting the detection of these physical phenomena over much larger scales than is possible with a ground-based instrument. In this talk, I will present an overview of the activities of the UK National Quantum Hub in Sensors and Metrology in developing cold atoms technology for space. Our activities are focused in two main areas: optical clocks and atom interferometers. I will also discuss our contributions to recent initiatives including STE-QUEST and AI-GOAT, the ESA/NASA initiative aiming at an atom interferometer gravitational wave detector in space.
Memory assisted free space quantum communication
Jordaan, Bertus; Namazi, Mehdi; Goham, Connor; Shahrokhshahi, Reihaneh; Vallone, Giuseppe; Villoresi, Paolo; Figueroa, Eden
2016-05-01
A quantum memory assisted node between different quantum channels has the capability to modify and synchronize its output, allowing for easy connectivity, and advanced cryptography protocols. We present the experimental progress towards the storage of single photon level pulses carrying random polarization qubits into a dual rail room temperature quantum memory (RTQM) after ~ 20m of free space propagation. The RTQM coherently stores the input pulses through electromagnetically induced transparency (EIT) of a warm 87 Rb vapor and filters the output by polarization elements and temperature-controlled etalon resonators. This allows the characterization of error rates for each polarization basis and the testing of the synchronization ability of the quantum memory. This work presents a steppingstone towards quantum key distribution and quantum repeater networks. The work was supported by the US-Navy Office of Naval Research, Grant Number N00141410801 and the Simons Foundation, Grant Number SBF241180.B. J. acknowledges financial assistance of the National Research Foundation (NRF) of South Africa.
Mohrhoff, U
2001-01-01
Epistemic interpretations of quantum mechanics fail to address the puzzle posed by the occurrence of probabilities in a fundamental physical theory. This is a puzzle about the physical world, not a puzzle about our relation to the physical world. Its solution requires a new concept of physical space, presented in this article. An examination of how the mind and the brain construct the phenomenal world reveals the psychological and neurobiological reasons why we think about space in ways that are inadequate to the physical world. The resulting notion that space is an intrinsically partitioned expanse has up to now stood in the way of a consistent ontological interpretation.
Quantum singularities in static and conformally static space-times
Konkowski, D A; 10.1142/S0217751X11054334
2011-01-01
The definition of quantum singularity is extended from static space-times to conformally static space-times. After the usual definitions of classical and quantum singularities are reviewed, examples of quantum singularities in static space-times are given. These include asymptotically power-law space-times, space-times with diverging higher-order differential invariants, and a space-time with a 2-sphere singularity. The theory behind quantum singularities in conformally static space-times is followed by an example, a Friedmann-Robertson-Walker space-time with cosmic string. The paper concludes by discussing areas of future research.
Phase space embedding of electrocardiograms
Richter, M; Richter, Marcus; Schreiber, Thomas
1998-01-01
We study properties of the human electrocardiogram under the working hypothesis that fluctuations beyond the regular structure of single cardiac cycles are unpredictable. On this background we discuss the possibility to use the phase space embedding method for this kind of signal. In particular, the specific nature of the stochastic or high dimensional component allows to use phase space embeddings for certain signal processing tasks. As practical applications, we discuss noise filtering, fetal ECG extraction, and the automatic detection of clinically relevant features. The main purpose of the paper is to connect results of embedding theory which had not been previously applied in practise, and practical applications which had not yet been justified theoretically.
High Quantum Efficiency Type II SLS FPAs for Space-Based Applications Project
National Aeronautics and Space Administration — This Phase I SBIR proposes to develop high quantum efficiency (QE) and low dark current infrared epitaxy materials based on Type II Strained Layer Superlattice (SLS)...
High Quantum Efficiency Type II SLS FPAs for Space-Based Applications Project
National Aeronautics and Space Administration — This Phase II SBIR proposes to develop high quantum efficiency (QE) and low dark current infrared epitaxy materials based on Type II Strained Layer Superlattice...
Scaling and Universality at Dynamical Quantum Phase Transitions.
Heyl, Markus
2015-10-02
Dynamical quantum phase transitions (DQPTs) at critical times appear as nonanalyticities during nonequilibrium quantum real-time evolution. Although there is evidence for a close relationship between DQPTs and equilibrium phase transitions, a major challenge is still to connect to fundamental concepts such as scaling and universality. In this work, renormalization group transformations in complex parameter space are formulated for quantum quenches in Ising models showing that the DQPTs are critical points associated with unstable fixed points of equilibrium Ising models. Therefore, these DQPTs obey scaling and universality. On the basis of numerical simulations, signatures of these DQPTs in the dynamical buildup of spin correlations are found with an associated power-law scaling determined solely by the fixed point's universality class. An outlook is given on how to explore this dynamical scaling experimentally in systems of trapped ions.
Research on Quantum Searching Algorithms Based on Phase Shifts
Institute of Scientific and Technical Information of China (English)
ZHONG Pu-Cha; BAO Wan-Su
2008-01-01
@@ One iterative in Grover's original quantum search algorithm consists of two Hadamard-Walsh transformations, a selective amplitude inversion and a diffusion amplitude inversion. We concentrate on the relation among the probability of success of the algorithm, the phase shifts, the number of target items and the number of iterations via replacing the two amplitude inversions by phase shifts of an arbitrary φ = ψ(0 ≤φ, ψ≤ 2π). Then, according to the relation we find out the optimal phase shifts when the number of iterations is given. We present a new quantum search algorithm based on the optimal phase shifts of 1.018 after 0.5π /√M/N iterations. The new algorithm can obtain either a single target item or multiple target items in the search space with the probability of success at least 93.43%.
Quantum phase transitions in the noncommutative Dirac Oscillator
Panella, O
2014-01-01
We study the (2+1) dimensional Dirac oscillator in a homogeneous magnetic field in the non-commutative plane. It is shown that the effect of non-commutativity is twofold: $i$) momentum non commuting coordinates simply shift the critical value ($B_{\\text{cr}}$) of the magnetic field at which the well known left-right chiral quantum phase transition takes place (in the commuting phase); $ii$) non-commutativity in the space coordinates induces a new critical value of the magnetic field, $B_{\\text{cr}}^*$, where there is a second quantum phase transition (right-left), --this critical point disappears in the commutative limit--. The change in chirality associated with the magnitude of the magnetic field is examined in detail for both critical points. The phase transitions are described in terms of the magnetisation of the system. Possible applications to the physics of silicene and graphene are briefly discussed.
The geometric phase in quantum physics
Energy Technology Data Exchange (ETDEWEB)
Bohm, A.
1993-03-01
After an explanatory introduction, a quantum system in a classical time-dependent environment is discussed; an example is a magnetic moment in a classical magnetic field. At first, the general abelian case is discussed in the adiabatic approximation. Then the geometric phase for nonadiabatic change of the environment (Anandan--Aharonov phase) is introduced, and after that general cyclic (nonadiabatic) evolution is discussed. The mathematics of fiber bundles is introduced, and some of its results are used to describe the relation between the adiabatic Berry phase and the geometric phase for general cyclic evolution of a pure state. The discussion is restricted to the abelian, U(1) phase.
Hilbert Space Operators in Quantum Physics
Blank, Jiří; Havlíček, Miloslav
2008-01-01
The second edition of this course-tested book provides a detailed and in-depth discussion of the foundations of quantum theory as well as its applications to various systems. The exposition is self-contained; in the first part the reader finds the mathematical background in chapters about functional analysis, operators on Hilbert spaces and their spectral theory, as well as operator sets and algebras. This material is used in the second part to a systematic explanation of the foundations, in particular, states and observables, properties of canonical variables, time evolution, symmetries and various axiomatic approaches. In the third part, specific physical systems and situations are discussed. Two chapters analyze Schrödinger operators and scattering, two others added in the second edition are devoted to new important topics, quantum waveguides and quantum graphs. Some praise for the previous edition: "I really enjoyed reading this work. It is very well written, by three real experts in the field. It stands...
Energy Technology Data Exchange (ETDEWEB)
Vargas-MartInez, J M; Moya-Cessa, H [INAOE, Coordinacion de Optica, Apartado Postal 51 y 216, 72000 Puebla (Mexico)
2004-03-01
Based on the phase operator introduced by Turski we present a formalism for phase that passes Barnett-Pegg's acid test giving the correct phase variance for a number state. We show that this formalism is in fact the radially integrated Q-function formalism that is used to obtain phase properties. It is also shown that depending on the commutation relation used for phase and number, the phase fluctuations for a coherent state obtained from the integrated Q-function tend to the 1/2{rho}{sup 2} limit while for the Pegg-Barnett formalism they tend to 1/(4{rho}{sup 2}+3/{pi}{sup 2}) just like the fluctuations from the integrated Wigner function, where {rho} is the amplitude of the coherent state00.
Hilbert space for quantum mechanics on superspace
Coulembier, Kevin
2011-01-01
In superspace a realization of sl2 is generated by the super Laplace operator and the generalized norm squared. In this paper, an inner product on superspace for which this representation is skew-symmetric is considered. This inner product was already defined for spaces of weighted polynomials (see [K. Coulembier, H. De Bie and F. Sommen, Orthogonality of Hermite polynomials in superspace and Mehler type formulae, arXiv:1002.1118]). In this article, it is proven that this inner product can be extended to the super Schwartz space, but not to the space of square integrable functions. Subsequently, the correct Hilbert space corresponding to this inner product is defined and studied. A complete basis of eigenfunctions for general orthosymplectically invariant quantum problems is constructed for this Hilbert space. Then the integrability of the sl2-representation is proven. Finally the Heisenberg uncertainty principle for the super Fourier transform is constructed.
Hilbert space for quantum mechanics on superspace
Coulembier, K.; De Bie, H.
2011-06-01
In superspace a realization of {sl}_2 is generated by the super Laplace operator and the generalized norm squared. In this paper, an inner product on superspace for which this representation is skew-symmetric is considered. This inner product was already defined for spaces of weighted polynomials (see [K. Coulembier, H. De Bie, and F. Sommen, Orthogonality of Hermite polynomials in superspace and Mehler type formulae, Proc. London Math. Soc. (accepted) arXiv:1002.1118]). In this article, it is proven that this inner product can be extended to the super Schwartz space, but not to the space of square integrable functions. Subsequently, the correct Hilbert space corresponding to this inner product is defined and studied. A complete basis of eigenfunctions for general orthosymplectically invariant quantum problems is constructed for this Hilbert space. Then the integrability of the {sl}_2-representation is proven. Finally, the Heisenberg uncertainty principle for the super Fourier transform is constructed.
Energy Technology Data Exchange (ETDEWEB)
Klimov, Andrei B [Departamento de FIsica, Universidad de Guadalajara, Revolucion 1500, 44420 Guadalajara, Jalisco (Mexico); Sanchez-Soto, Luis L [Departamento de Optica, Facultad de FIsica, Universidad Complutense, 28040 Madrid (Spain); Guise, Hubert de [Department of Physics, Lakehead University, Thunder Bay, Ontario P7B 5E1 (Canada); Bjoerk, Gunnar [Department of Microelectronics and Information Technology, Royal Institute of Technology (KTH), Electrum 229, SE-164 40 Kista (Sweden)
2004-04-02
We consider various approaches to treat the phases of a qutrit. Although it is possible to represent qutrits in a convenient geometrical manner by resorting to a generalization of the Poincare sphere, we argue that the appropriate way of dealing with this problem is through phase operators associated with the algebra su(3). The rather unusual properties of these phases are caused by the small dimension of the system and are explored in detail. We also examine the positive operator-valued measures that can describe the qutrit phase properties.
Quantum elements of time and space
Marks, Dennis
2017-01-01
Space-times of any number of spaces and times can be generated as tensor products of a time-like unit vector T and a space-like unit vector S. T is a 2 × 2 real anti-symmetric, hence trace-free, matrix squaring to - I ; S is a 2 × 2 real symmetric trace-free matrix squaring to + I . T is unique up to sign, corresponding to particles and antiparticles. S is a qubit whose eigenvalues are the bits + 1 and - 1 . Thus the quantization of space is rotationally invariant in 2 d and Lorentz invariant in 4 d . Use S instead of complex numbers C to geometrize quantum mechanics. The simplest space-time is the Minkowskian plane with vectors T and S, which generate a geometric algebra {I,T,S,ST}, where the bivector ST is space-like. It can be used as vector X for the Euclidean plane, along with Y=S. They generate a geometric algebra {I,X,Y,YX}. The bivector YX is T. The Minkowskian plane and the Euclidean plane have different geometries but the same geometric algebra, which is thus the foundation of both general relativity and quantum mechanics.
Disappearance and emergence of space and time in quantum gravity
Oriti, Daniele
2013-01-01
We discuss the hints for the disappearance of continuum space and time at microscopic scale. These include arguments for a discrete nature of them or for a fundamental non-locality, in a quantum theory of gravity. We discuss how these ideas are realized in specific quantum gravity approaches. Turning then the problem around, we consider the emergence of continuum space and time from the collective behaviour of discrete, pre-geometric atoms of quantum space, and for understanding spacetime as a kind of "condensate", and we present the case for this emergence process being the result of a phase transition, dubbed "geometrogenesis". We discuss some conceptual issues of this scenario and of the idea of emergent spacetime in general. As a concrete example, we outline the GFT framework for quantum gravity, and illustrate a tentative procedure for the emergence of spacetime in this framework. Last, we re-examine the conceptual issues raised by the emergent spacetime scenario in light of this concrete example.
Quantum holonomy theory and Hilbert space representations
Energy Technology Data Exchange (ETDEWEB)
Aastrup, Johannes [Mathematisches Institut, Universitaet Hannover (Germany); Moeller Grimstrup, Jesper [QHT Gruppen, Copenhagen Area (Denmark)
2016-11-15
We present a new formulation of quantum holonomy theory, which is a candidate for a non-perturbative and background independent theory of quantum gravity coupled to matter and gauge degrees of freedom. The new formulation is based on a Hilbert space representation of the QHD(M) algebra, which is generated by holonomy-diffeomorphisms on a 3-dimensional manifold and by canonical translation operators on the underlying configuration space over which the holonomy-diffeomorphisms form a non-commutative C*-algebra. A proof that the state that generates the representation exist is left for later publications. (copyright 2016 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Robust quantum data locking from phase modulation
Lupo, Cosmo; Wilde, Mark M.; Lloyd, Seth
2014-08-01
Quantum data locking is a uniquely quantum phenomenon that allows a relatively short key of constant size to (un)lock an arbitrarily long message encoded in a quantum state, in such a way that an eavesdropper who measures the state but does not know the key has essentially no information about the message. The application of quantum data locking in cryptography would allow one to overcome the limitations of the one-time pad encryption, which requires the key to have the same length as the message. However, it is known that the strength of quantum data locking is also its Achilles heel, as the leakage of a few bits of the key or the message may in principle allow the eavesdropper to unlock a disproportionate amount of information. In this paper we show that there exist quantum data locking schemes that can be made robust against information leakage by increasing the length of the key by a proportionate amount. This implies that a constant size key can still lock an arbitrarily long message as long as a fraction of it remains secret to the eavesdropper. Moreover, we greatly simplify the structure of the protocol by proving that phase modulation suffices to generate strong locking schemes, paving the way to optical experimental realizations. Also, we show that successful data locking protocols can be constructed using random code words, which very well could be helpful in discovering random codes for data locking over noisy quantum channels.
Quantum Fourier Transform and Phase Estimation in Qudit System
Institute of Scientific and Technical Information of China (English)
CAO Ye; PENG Shi-Guo; ZHENG Chao; LONG Gui-Lu
2011-01-01
The quantum Fourier transform and quantum phase estimation are the key components for many quantum algorithms, such as order-finding, factoring, and etc.In this article, the general procedure of quantum Fourier transform and phase estimation are investigated for high dimensional case.They can be seen as subroutines in a main program run in a qudit quantum computer, and the quantum circuits are given.
Fu, Jian; Xu, Yingying; Dong, Hongtao
2010-01-01
We demonstrate that n classical fields modulated with n different pseudorandom phase sequences can constitute a 2^n-dimensional Hilbert space that contains tensor product structure. By using classical fields modulated with pseudorandom phase sequences, we discuss effective simulation of Bell states and GHZ state, and apply both correlation analysis and von Neumann entropy to characterize the simulation. We obtain similar results with the cases in quantum mechanics and find that the conclusions can be easily generalized to n quantum particles. The research on simulation of quantum entanglement may be important, for it not only provides useful insights into fundamental features of quantum entanglement, but also yields new insights into quantum computation.
Coherent spaces, Boolean rings and quantum gates
Vourdas, A.
2016-10-01
Coherent spaces spanned by a finite number of coherent states, are introduced. Their coherence properties are studied, using the Dirac contour representation. It is shown that the corresponding projectors resolve the identity, and that they transform into projectors of the same type, under displacement transformations, and also under time evolution. The set of these spaces, with the logical OR and AND operations is a distributive lattice, and with the logical XOR and AND operations is a Boolean ring (Stone's formalism). Applications of this Boolean ring into classical CNOT gates with n-ary variables, and also quantum CNOT gates with coherent states, are discussed.
Entanglement due to noncommutativity in the phase-space
Bastos, Catarina; Bertolami, Orfeu; Dias, Nuno Costa; Prata, João Nuno
2013-01-01
The entanglement criterion for continuous variable systems and the conditions under which the uncertainty relations are fulfilled are generalized to the case of a noncommutative (NC) phase-space. The quantum nature and the separability of NC two-mode Gaussian states are examined. It is shown that the entanglement of Gaussian states may be exclusively induced by switching on the noncommutative deformation.
A Gaussian measure of quantum phase noise
Schleich, Wolfgang P.; Dowling, Jonathan P.
1992-01-01
We study the width of the semiclassical phase distribution of a quantum state in its dependence on the average number of photons (m) in this state. As a measure of phase noise, we choose the width, delta phi, of the best Gaussian approximation to the dominant peak of this probability curve. For a coherent state, this width decreases with the square root of (m), whereas for a truncated phase state it decreases linearly with increasing (m). For an optimal phase state, delta phi decreases exponentially but so does the area caught underneath the peak: all the probability is stored in the broad wings of the distribution.
Exotic quantum phase transitions of strongly interacting topological insulators
Slagle, Kevin; You, Yi-Zhuang; Xu, Cenke
2015-03-01
Using determinant quantum Monte Carlo simulations, we demonstrate that an extended Hubbard model on a bilayer honeycomb lattice has two novel quantum phase transitions. The first is a quantum phase transition between the weakly interacting gapless Dirac fermion phase and a strongly interacting fully gapped and symmetric trivial phase, which cannot be described by the standard Gross-Neveu model. The second is a quantum critical point between a quantum spin Hall insulator with spin Sz conservation and the previously mentioned strongly interacting fully gapped phase. At the latter quantum critical point the single-particle excitations remain gapped, while spin and charge gaps both close. We argue that the first quantum phase transition is related to the Z16 classification of the topological superconductor 3He-B phase with interactions, while the second quantum phase transition is a topological phase transition described by a bosonic O (4 ) nonlinear sigma model field theory with a Θ term.
Quantum Nucleation of Phase Slips in 1-d Superfluids
Arovas, Daniel
1998-03-01
The rate for quantum nucleation of phase slips past an impurity in a one-dimensional superfluid is computed. Real time evolution of the nonlinear Schrödinger equation shows that there is a critical velocity vc below which solutions are time-independent [1,2]; this is the regime of quantum phase slip nucleation. We start with the Gross-Pitaevskii model in the presence of an impurity potential, and derive the Euclidean action for a space-time vortex-antivortex pair, which describes a phase slip event. The action is computed as a function of the superfluid velocity v and the impurity potential width and depth.l [1] V. Hakim, Phys. Rev. E 55, 2835 (1997).l [1] J. A. Freire, D. P. Arovas, and H. Levine, Phys. Rev. Lett (in press, 1997).l
Free space relativistic quantum cryptography with faint laser pulses
Molotkov, S. N.; Potapova, T. A.
2013-07-01
A new protocol for quantum key distribution through empty space is proposed. Apart from the quantum mechanical restrictions on distinguishability of non-orthogonal states, the protocol employs additional restrictions imposed by special relativity. The protocol ensures generation of a secure key even for the source generating non-strictly single-photon quantum states and for arbitrary losses in quantum communication channel.
Passive longitudinal phase space linearizer
Directory of Open Access Journals (Sweden)
P. Craievich
2010-03-01
Full Text Available We report on the possibility to passively linearize the bunch compression process in electron linacs for the next generation x-ray free electron lasers. This can be done by using the monopole wakefields in a dielectric-lined waveguide. The optimum longitudinal voltage loss over the length of the bunch is calculated in order to compensate both the second-order rf time curvature and the second-order momentum compaction terms. Thus, the longitudinal phase space after the compression process is linearized up to a fourth-order term introduced by the convolution between the bunch and the monopole wake function.
Interacting Quantum Fields on de Sitter Space
Barata, João C A; Mund, Jen
2016-01-01
In 1975 Figari, H{\\o}egh-Krohn and Nappi constructed the ${\\mathscr P}(\\varphi)_2$ model on the two-dimensional de Sitter space. Here we complement their work with a number of new results. In particular, we show that $i.)$ the unitary irreducible representations of $SO_0(1,2)$ for both the principal and the complementary series can be formulated on the Hilbert space spanned by wave functions supported on the Cauchy surface; $ii.)$ physical infrared problems are absent on de Sitter space; $iii.)$ the interacting quantum fields satisfy the equations of motion in their covariant form; $iv.)$ the generators of the boosts and the rotations for the interacting quantum field theory arise by contracting the stress-energy tensor with the relevant Killing vector fields and integrating over the relevant line segments. They generate a reducible, unitary representation of the Lorentz group on the Fock space for the free field. We establish also relations to the modular objects of (relative) Tomita-Takesaki theory. In addi...
de Gosson, Maurice A
2011-01-01
Quantum blobs are the smallest phase space units of phase space compatible with the uncertainty principle of quantum mechanics and having the symplectic group as group of symmetries. Quantum blobs are in a bijective correspondence with the squeezed coherent states from standard quantum mechanics, of which they are a phase space picture. This allows us to propose a substitute for phase space in quantum mechanics. We study the relationship between quantum blobs with a certain class of level sets defined by Fermi for the purpose of representing geometrically quantum states.
Faint laser pulses versus a single-photon source in free space quantum cryptography
Molotkov, S. N.; Potapova, T. A.
2016-03-01
In this letter we present estimates for the distance of secret key transmission through free space for three different protocols of quantum key distribution: for BB84 and phase time-coding protocols in the case of a strictly single-photon source, and for the relativistic quantum key distribution protocol in the case of faint laser pulses.
A general formalism for phase space calculations
Norbury, John W.; Deutchman, Philip A.; Townsend, Lawrence W.; Cucinotta, Francis A.
1988-01-01
General formulas for calculating the interactions of galactic cosmic rays with target nuclei are presented. Methods for calculating the appropriate normalization volume elements and phase space factors are presented. Particular emphasis is placed on obtaining correct phase space factors for 2-, and 3-body final states. Calculations for both Lorentz-invariant and noninvariant phase space are presented.
Quantum phase transitions with dynamical flavors
Bea, Yago; Ramallo, Alfonso V
2016-01-01
We study the properties of a D6-brane probe in the ABJM background with smeared massless dynamical quarks in the Veneziano limit. Working at zero temperature and non-vanishing charge density, we show that the system undergoes a quantum phase transition in which the topology of the brane embedding changes from a black hole to a Minkowski embedding. In the unflavored background the phase transition is of second order and takes place when the charge density vanishes. We determine the corresponding critical exponents and show that the scaling behavior near the quantum critical point has multiplicative logarithmic corrections. In the background with dynamical quarks the phase transition is of first order and occurs at non-zero charge density. In this case we compute the discontinuity of several physical quantities as functions of the number $N_f$ of unquenched quarks of the background.
Quantum phase transitions with dynamical flavors
Bea, Yago; Jokela, Niko; Ramallo, Alfonso V.
2016-07-01
We study the properties of a D6-brane probe in the Aharony-Bergman-Jafferis-Maldacena (ABJM) background with smeared massless dynamical quarks in the Veneziano limit. Working at zero temperature and nonvanishing charge density, we show that the system undergoes a quantum phase transition in which the topology of the brane embedding changes from a black hole to a Minkowski embedding. In the unflavored background the phase transition is of second order and takes place when the charge density vanishes. We determine the corresponding critical exponents and show that the scaling behavior near the quantum critical point has multiplicative logarithmic corrections. In the background with dynamical quarks the phase transition is of first order and occurs at nonzero charge density. In this case we compute the discontinuity of several physical quantities as functions of the number Nf of unquenched quarks of the background.
General Phase Matching Condition for Quantum Searching
Long, G L; Sun, Y; Long, Gui-Lu; Xiao, Li; Sun, Yang
2001-01-01
We present a general phase matching condition for the quantum search algorithm with arbitrary unitary transformation and arbitrary phase rotations. We show by an explicit expression that the phase matching condition depends both on the unitary transformation U and the initial state. Assuming that the initial amplitude distribution is an arbitrary superposition sin\\theta_0 |1> + cos\\theta_0 e^{i\\delta} |2> with |1> = {1 / sin\\beta} \\sum_k |\\tau_k> and |2> = {1 / cos\\beta} \\sum_{i \
Emergence of Decoherence as Phenomenon in Quantum Phase Transition
Quan, H T; Liu, X F; Sun, C P
2005-01-01
We consider the intrinsic relation between the appearance of classicality of a quantum system and the occurrence of quantum phase transition (QPT) in the environment surrounding this system, and study in detail the novel mechanism of quantum decoherence based on QPT with a generalized Hepp-Coleman model where the quantum system is a two level system and the environment is the Ising spin chain interacting with the quantum system. It is discovered that, the quantum decoherence of the quantum system can be accompanied by the quantum critical phenomenon induced by the effective transverse back-action of the quantum system on the environment.
Optimisation of a quantum pair space thruster
Directory of Open Access Journals (Sweden)
Valeriu DRAGAN
2012-06-01
Full Text Available The paper addresses the problem of propulsion for long term space missions. Traditionally a space propulsion unit has a propellant mass which is ejected trough a nozzle to generate thrust; this is also the case with inert gases energized by an on-board power unit. Unconventional methods for propulsion include high energy LASERs that rely on the momentum of photons to generate thrust. Anti-matter has also been proposed for energy storage. Although the momentum of ejected gas is significantly higher, the LASER propulsion offers the perspective of unlimited operational time – provided there is a power source. The paper will propose the use of the quantum pair formation for generating a working mass, this is different than conventional anti-matter thrusters since the material particles generated are used as propellant not as energy storage.Two methods will be compared: LASER and positron-electron, quantum pair formation. The latter will be shown to offer better momentum above certain energy levels.For the demonstrations an analytical solution is obtained and provided in the form of various coefficients. The implications are, for now, theoretical however the practicality of an optimized thruster using such particles is not to be neglected for long term space missions.
Quantum correlations with vacuum ambiguity in de Sitter space
Feng, Jun; Yang, Wen-Li; Zhang, Yao-Zhong; Fan, Heng
2012-01-01
We study the quantum correlations of free scalar field with vacuum ambiguity of de Sitter space. We show the occurrence of degradation of quantum entanglement and quantum discord between field modes for inertial observer in curved space due to the radiation associated with cosmological horizon. In particular, we find that quantum correlations can be used to encode infinite de Sitter invariant vacua, which correspond to infinite set of possible physical worlds. This may provide a superselection rule of physical vacuum via quantum information tasks. We also discuss the simulation of such quantum effects of vacuum ambiguity in ion trap experiments.
Quantum Field Theory on Noncommutative Spaces
Szabó, R J
2003-01-01
A pedagogical and self-contained introduction to noncommutative quantum field theory is presented, with emphasis on those properties that are intimately tied to string theory and gravity. Topics covered include the Weyl-Wigner correspondence, noncommutative Feynman diagrams, UV/IR mixing, noncommutative Yang-Mills theory on infinite space and on the torus, Morita equivalences of noncommutative gauge theories, twisted reduced models, and an in-depth study of the gauge group of noncommutative Yang-Mills theory. Some of the more mathematical ideas and techniques of noncommutative geometry are also briefly explained.
Phase Diagram in Quantum Chromodynamics
Apostol, M
2013-01-01
It is suggested that the hadronization of the quark-gluon plasma is a first-order phase transition described by a critical curve in the temperature-(quark) density plane which terminates in a critical point. Such a critical curve is derived from the van der Waals equation and its parameters are estimated by using the theoretical approach given in M. Apostol, Roum. Reps. Phys. 59 249 (2007); Mod. Phys. Lett. B21 893 (2007). The main assumption is that quark-gluon plasma created by high-energy nucleus-nucleus collisions is a gas of ultrarelativistic quarks in equilibrium with gluons (vanishing chemical potential, indefinite number of quarks). This plasma expands, gets cool and dilute and hadronizes at a certain transition temperature and transition density. The transition density is very close to the saturation density of the nuclear matter and, it is suggested that both these points are very close to the critical point n~1fm^{-3} (quark density) and T~200MeV (temperature).
Quantum Space-Time and Reference Frames in Gravity and Flat Space-Time
Mayburov, S
2000-01-01
The quantum space-time model which accounts material Reference Frames (RF) quantum effects considered for flat space-time and ADM canonical gravity. As was shown by Aharonov for RF - free material object its c.m. nonrelativistic motion in vacuum described by Schrodinger wave packet evolution which modify space coordinate operator of test particle in this RF and changes its Heisenberg uncertainty relations. In the relativistic case we show that Lorentz transformations between two RFs include the quantum corrections for RFs momentum uncertainty and in general can be formulated as the quantum space-time transformations. As the result for moving RF its Lorentz time boost acquires quantum fluctuations which calculated solving relativistic Heisenberg equations for the quantum clocks models. It permits to calculate RF proper time for the arbitrary RF quantum motion including quantum gravity metrics fluctuations. Space-time structure of canonical Quantum Gravity and its observables evolution for RF proper time discus...
Practical free-space quantum cryptography
Energy Technology Data Exchange (ETDEWEB)
Hughes, R.J.; Buttler, W.T.; Kwiat, P.G.; Lamoreaux, S.K.; Luther, G.G.; Morgan, G.L.; Nordholt, J.E.; Peterson, C.G.; Simmons, C.M.
1998-12-01
An experimental free-space quantum key distribution (QKD) system has been tested over an outdoor optical path of {approx} 1 km under nighttime conditions at Los Alamos National Laboratory. This system employs the Bennett 92 protocol; here the authors give a brief overview of this protocol, and describe the experimental implementation of it. An analysis of the system efficiency is presented, as well as a description of the error detection protocol, which employs a two-dimensional parity check scheme. Finally, the susceptibility of this system to eavesdropping by various techniques is determined, and the effectiveness of privacy amplification procedures is discussed. The conclusions are that free-space QKD is both effective and secure; possible applications include the rekeying of satellites in low earth orbit.
Quantum phase transition and entanglement in Li atom system
Institute of Scientific and Technical Information of China (English)
2008-01-01
By use of the exact diagonalization method, the quantum phase transition and en- tanglement in a 6-Li atom system are studied. It is found that entanglement appears before the quantum phase transition and disappears after it in this exactly solvable quantum system. The present results show that the von Neumann entropy, as a measure of entanglement, may reveal the quantum phase transition in this model.
Phase diagram of quantum square ice
Henry, Louis-Paul; Holdsworth, Peter; Mila, Frederic; Roscilde, Tommaso
2013-03-01
We have investigated the ground-state and finite-temperature phase diagram of quantum square ice - realized by the transverse-field Ising model on a checkerboard lattice - using both linear spin-wave (LSW) theory and quantum Monte Carlo (QMC). We generalize the model with different couplings between nearest (J1) and next-to-nearest (J2) neighbors on the checkerboard lattice. Our QMC approach generalizes the loop algorithm - very efficient in the study of constrained classical systems - to a ``brane algorithm'' for quantum systems. At the LSW level the vast degeneracy of the ground-state for J1 =J2 and J2 >J1 remains intact; moreover LSW theory breaks down in extended regions of the phase diagram, pointing at non-classical states. Our QMC study goes beyond perturbative schemes and addresses directly the nature of the low-temperature phases. We have critically examined the possibility of a resonating-plaquette state for J1 =J2 , suggested by degenerate perturbation theory on the ice-rule manifold for weak fields. Our QMC results for finite fields confirm the absence of Néel or collinear order, but they do not confirm the presence of resonating-plaquette order, pointing at a possibly more complex non-classical state.
Quantum Mechanics as an Approximation to Classical Mechanics in Hilbert Space
Bracken, A. J.
2002-01-01
Classical mechanics is formulated in complex Hilbert space with the introduction of a commutative product of operators, an antisymmetric bracket, and a quasidensity operator. These are analogues of the star product, the Moyal bracket, and the Wigner function in the phase space formulation of quantum mechanics. Classical mechanics can now be viewed as a deformation of quantum mechanics. The forms of semiquantum approximations to classical mechanics are indicated.
Quantum dynamic of massive particle On 1+3 De Sitter space-time
Directory of Open Access Journals (Sweden)
A Rabeie
2012-09-01
Full Text Available The phase space which is related to the motion of massive particle on 1+3- De sitter space is a 3-dimensional complex sphere. Our main aim in this study is discribing this movement in the frame quantum mechanics. Transfering from classical mechanic to quantum mechanics is possible by means of coherent states. Thus, after determination of this state, we quantize some of the classical observables.
Quantum dynamic of massive particle On 1+3 De Sitter space-time
2012-01-01
The phase space which is related to the motion of massive particle on 1+3- De sitter space is a 3-dimensional complex sphere. Our main aim in this study is discribing this movement in the frame quantum mechanics. Transfering from classical mechanic to quantum mechanics is possible by means of coherent states. Thus, after determination of this state, we quantize some of the classical observables.
Harmonic oscillator in Snyder space: The classical case and the quantum case
Indian Academy of Sciences (India)
Carlos Leiva
2010-02-01
The harmonic oscillator in Snyder space is investigated in its classical and quantum versions. The classical trajectory is obtained and the semiclassical quantization from the phase space trajectories is discussed. An effective cut-off to high frequencies is found. The quantum version is developed and an equivalent usual harmonic oscillator is obtained through an effective mass and an effective frequency introduced in the model. This modified parameters give us a modified energy spectrum also.
Phase Transition in Loop Quantum Gravity
Mäkelä, Jarmo
2016-01-01
We point out that with a specific counting of states loop quantum gravity implies that black holes perform a phase transition at a certain characteristic temperature $T_C$. In this phase transition the punctures of the spin network on the stretched horizon of the black hole jump, in effect, from the vacuum to the excited states. The characteristic temperature $T_C$ may be regarded as the lowest possible temperature of the hole. From the point of view of a distant observer at rest with respect to the hole the characteristic temperature $T_C$ corresponds to the Hawking temperature of the hole.
Uniform approximation from symbol calculus on a spherical phase space
Energy Technology Data Exchange (ETDEWEB)
Yu Liang, E-mail: liangyu@wigner.berkeley.edu [Department of Physics, University of California, Berkeley, CA 94720 (United States)
2011-12-16
We use symbol correspondence and quantum normal form theory to develop a more general method for finding uniform asymptotic approximations. We then apply this method to derive a result we announced in an earlier paper, namely the uniform approximation of the 6j-symbol in terms of the rotation matrices. The derivation is based on the Stratonovich-Weyl symbol correspondence between matrix operators and functions on a spherical phase space. The resulting approximation depends on a canonical, or area-preserving, map between two pairs of intersecting level sets on the spherical phase space. (paper)
Quantum and thermal phase escape in extended Josephson systems
Energy Technology Data Exchange (ETDEWEB)
Kemp, A.
2006-07-12
In this work I examine phase escape in long annular Josephson tunnel junctions. The sine-Gordon equation governs the dynamics of the phase variable along the junction. This equation supports topological soliton solutions, which correspond to quanta of magnetic flux trapped in the junction barrier. For such Josephson vortices an effective potential is formed by an external magnetic field, while a bias current acts as a driving force. Both together form a metastable potential well, which the vortex is trapped in. When the driving force exceeds the pinning force of the potential, the vortex escapes and the junction switches to the voltage state. At a finite temperature the driving force fluctuates. If the junction's energy scale is small, the phase variable can undergo a macroscopic quantum tunneling (MQT) process at temperatures below the crossover temperature. Without a vortex trapped, the metastable state is not a potential minimum in space, but a potential minimum at zero phase difference. (orig.)
Three qubit quantum phase gate based on cavity QED
Chang, Juntao; Zubairy, M. Suhail
2004-10-01
We describe a three qubit quantum phase gate in which the three qubits are represented by the photons in a three-modes optical cavity. This gate is implemented by passing a four-level atom in a cascade configuration through the cavity. We shall discuss the application of such a quantum phase gate to quantum searching.
Quantum Phase Imaging using Spatial Entanglement
Lu, Chien-Hung; Sun, Xiaohang; Fleischer, Jason W
2015-01-01
Entangled photons have the remarkable ability to be more sensitive to signal and less sensitive to noise than classical light. Joint photons can sample an object collectively, resulting in faster phase accumulation and higher spatial resolution, while common components of noise can be subtracted. Even more, they can accomplish this while physically separate, due to the nonlocal properties of quantum mechanics. Indeed, nearly all quantum optics experiments rely on this separation, using individual point detectors that are scanned to measure coincidence counts and correlations. Scanning, however, is tedious, time consuming, and ill-suited for imaging. Moreover, the separation of beam paths adds complexity to the system while reducing the number of photons available for sampling, and the multiplicity of detectors does not scale well for greater numbers of photons and higher orders of entanglement. We bypass all of these problems here by directly imaging collinear photon pairs with an electron-multiplying CCD cam...
Experimental Bayesian Quantum Phase Estimation on a Silicon Photonic Chip.
Paesani, S; Gentile, A A; Santagati, R; Wang, J; Wiebe, N; Tew, D P; O'Brien, J L; Thompson, M G
2017-03-10
Quantum phase estimation is a fundamental subroutine in many quantum algorithms, including Shor's factorization algorithm and quantum simulation. However, so far results have cast doubt on its practicability for near-term, nonfault tolerant, quantum devices. Here we report experimental results demonstrating that this intuition need not be true. We implement a recently proposed adaptive Bayesian approach to quantum phase estimation and use it to simulate molecular energies on a silicon quantum photonic device. The approach is verified to be well suited for prethreshold quantum processors by investigating its superior robustness to noise and decoherence compared to the iterative phase estimation algorithm. This shows a promising route to unlock the power of quantum phase estimation much sooner than previously believed.
Duality, Phase Structures and Dilemmas in Symmetric Quantum Games
Ichikawa, T; Ichikawa, Tsubasa; Tsutsui, Izumi
2006-01-01
Symmetric quantum games for 2-player, 2-qubit strategies are analyzed in detail by using a scheme in which all pure states in the 2-qubit Hilbert space are utilized for strategies. We consider two different types of symmetric games exemplified by the familiar games, the Battle of the Sexes (BoS) and the Prisoners' Dilemma (PD). These two types of symmetric games are shown to be related by a duality map, which ensures that they share common phase structures with respect to the equilibria of the strategies. We find eight distinct phase structures possible for the symmetric games, which are determined by the classical payoff matrices from which the quantum games are defined. We also discuss the possibility of resolving the dilemmas in the classical BoS, PD and the Stag Hunt (SH) game based on the phase structures obtained in the quantum games. It is observed that quantization cannot resolve the dilemma fully for the BoS, while it generically can for the PD and SH if appropriate correlations for the strategies of...
Bundles over Quantum RealWeighted Projective Spaces
Directory of Open Access Journals (Sweden)
Tomasz Brzeziński
2012-09-01
Full Text Available The algebraic approach to bundles in non-commutative geometry and the definition of quantum real weighted projective spaces are reviewed. Principal U(1-bundles over quantum real weighted projective spaces are constructed. As the spaces in question fall into two separate classes, the negative or odd class that generalises quantum real projective planes and the positive or even class that generalises the quantum disc, so do the constructed principal bundles. In the negative case the principal bundle is proven to be non-trivial and associated projective modules are described. In the positive case the principal bundles turn out to be trivial, and so all the associated modules are free. It is also shown that the circle (coactions on the quantum Seifert manifold that define quantum real weighted projective spaces are almost free.
Quantum Computing in Fock Space Systems
Berezin, Alexander A.
1997-04-01
Fock space system (FSS) has unfixed number (N) of particles and/or degrees of freedom. In quantum computing (QC) main requirement is sustainability of coherent Q-superpositions. This normally favoured by low noise environment. High excitation/high temperature (T) limit is hence discarded as unfeasible for QC. Conversely, if N is itself a quantized variable, the dimensionality of Hilbert basis for qubits may increase faster (say, N-exponentially) than thermal noise (likely, in powers of N and T). Hence coherency may win over T-randomization. For this type of QC speed (S) of factorization of long integers (with D digits) may increase with D (for 'ordinary' QC speed polynomially decreases with D). This (apparent) paradox rests on non-monotonic bijectivity (cf. Georg Cantor's diagonal counting of rational numbers). This brings entire aleph-null structurality ("Babylonian Library" of infinite informational content of integer field) to superposition determining state of quantum analogue of Turing machine head. Structure of integer infinititude (e.g. distribution of primes) results in direct "Platonic pressure" resembling semi-virtual Casimir efect (presure of cut-off vibrational modes). This "effect", the embodiment of Pythagorean "Number is everything", renders Godelian barrier arbitrary thin and hence FSS-based QC can in principle be unlimitedly efficient (e.g. D/S may tend to zero when D tends to infinity).
Realization of Quantum Circuits in Fock Space
Institute of Scientific and Technical Information of China (English)
MA Lei; LI Yun
2004-01-01
In this letter, by using the method we offered in our paper [L. Ma and Y.D. Zhang, Commun. Theor. Phys.(Beijing, China) 36 (2001) 119], some extended quantum logic gates, such as quantum counter, quantum adder, are studied and their expressions are given. It may be useful for us to study the more complicated quantum logic circuits deeply.
Phase Space Approach to Laser-driven Electronic Wavepacket Propagation
Takemoto, Norio; Tannor, David J
2012-01-01
We propose a phase space method to propagate a quantum wavepacket driven by a strong external field. The method employs the so-called biorthogonal von Neumann basis recently introduced for the calculation of the energy eigenstates of time-independent quantum systems [A. Shimshovitz and D.J. Tannor, arXiv:1201.2299v1]. While the individual elements in this basis set are time-independent, a small subset is chosen in a time-dependent manner to adapt to the evolution of the wavepacket in phase space. We demonstrate the accuracy and efficiency of the present propagation method by calculating the electronic wavepacket in a one-dimensional soft-core atom interacting with a superposition of an intense, few-cycle, near-infrared laser pulse and an attosecond extreme-ultraviolet laser pulse.
Optically induced phase transition of excitons in coupled quantum dots
Institute of Scientific and Technical Information of China (English)
Chen Zi-Dong
2008-01-01
The weak classical light excitations in many semiconductor quantum dots have been chosen as important solidstate quantum systems for processing quantum information and implementing quantum computing. For strong classical light we predict theoretically a novel phase transition as a function of magnitude of this classical light from the deformed to the normal phases in resonance case, and the essential features of criticality such as the scaling behaviour, critical exponent and universality are also present in this paper.
Nonperturbative studies of quantum field theories on noncommutative spaces
Energy Technology Data Exchange (ETDEWEB)
Volkholz, J.
2007-11-16
This work deals with three quantum field theories on spaces with noncommuting position operators. Noncommutative models occur in the study of string theories and quantum gravity. They usually elude treatment beyond the perturbative level. Due to the technique of dimensional reduction, however, we are able to investigate these theories nonperturbatively. This entails translating the action functionals into a matrix language, which is suitable for numerical simulations. First we explore the {lambda}{phi}{sup 4} model on a noncommutative plane. We investigate the continuum limit at fixed noncommutativity, which is known as the double scaling limit. Here we focus especially on the fate of the striped phase, a phase peculiar to the noncommutative version of the regularized {lambda}{phi}{sup 4} model. We find no evidence for its existence in the double scaling limit. Next we examine the U(1) gauge theory on a four-dimensional spacetime, where two spatial directions are noncommutative. We examine the phase structure and find a new phase with a spontaneously broken translation symmetry. In addition we demonstrate the existence of a finite double scaling limit which confirms the renormalizability of the theory. Furthermore we investigate the dispersion relation of the photon. In the weak coupling phase our results are consistent with an infrared instability predicted by perturbation theory. If the translational symmetry is broken, however, we find a dispersion relation corresponding to a massless particle. Finally, we investigate a supersymmetric theory on the fuzzy sphere, which features scalar neutral bosons and Majorana fermions. The supersymmetry is exact in the limit of infinitely large matrices. We investigate the phase structure of the model and find three distinct phases. Summarizing, we study noncommutative field theories beyond perturbation theory. Moreover, we simulate a supersymmetric theory on the fuzzy sphere, which might provide an alternative to attempted
Quantum Dynamics of Magnetic and Electric Dipoles and Berry's Phase
Furtado, C; Furtado, Claudio
2003-01-01
We study the quantum dynamics of neutral particle that posseses a permanent magnetic and electric dipole moments in the presence of an electromagnetic field. The analysis of this dynamics demonstrates the appearance of a quantum phase that combines the Aharonov-Casher effect and the He-Mckellar-Wilkens effect. We demonstrate that this phase is a special case of the Berry's quantum phase. A series of field configurations where this phase would be found are presented. A generalized Casella-type effect is found in one these configurations. A physical scenario for the quantum phase in an interferometric experiment is proposed.
Dynamical phase transitions in quantum mechanics
Directory of Open Access Journals (Sweden)
Rotter Ingrid
2012-02-01
Full Text Available The nucleus is described as an open many-body quantum system with a non-Hermitian Hamilton operator the eigenvalues of which are complex, in general. The eigenvalues may cross in the complex plane (exceptional points, the phases of the eigenfunctions are not rigid in approaching the crossing points and the widths bifurcate. By varying only one parameter, the eigenvalue trajectories usually avoid crossing and width bifurcation occurs at the critical value of avoided crossing. An analog spectroscopic redistribution takes place for discrete states below the particle decay threshold. By this means, a dynamical phase transition occurs in the many-level system starting at a critical value of the level density. Hence the properties of the low-lying nuclear states (described well by the shell model and those of highly excited nuclear states (described by random ensembles differ fundamentally from one another. The statement of Niels Bohr on the collective features of compound nucleus states at high level density is therefore not in contradiction to the shell-model description of nuclear (and atomic states at low level density. Dynamical phase transitions are observed experimentally in different quantum mechanical systems by varying one or two parameters.
Quantum Vacuum Instability of 'Eternal' de Sitter Space
Anderson, Paul R
2013-01-01
The Euclidean or Bunch-Davies O(4,1) invariant 'vacuum' state of quantum fields in global de Sitter space is shown to be unstable to small perturbations, even for a massive free field with no self-interactions. There are perturbations of this state with arbitrarily small energy density at early times that is exponentially blueshifted in the contracting phase of 'eternal' de Sitter space, and becomes large enough to disturb the classical geometry through the semiclassical Einstein eqs. at later times. In the closely analogous case of a constant, uniform electric field, a time symmetric state equivalent to the de Sitter invariant one is constructed, which is also not a stable vacuum state under perturbations. The role of a quantum anomaly in the growth of perturbations and symmetry breaking is emphasized in both cases. In de Sitter space, the same results are obtained either directly from the renormalized stress tensor of a massive scalar field, or for massless conformal fields of any spin, more directly from t...
Classical Analog of Extended Phase Space SUSY and Its Breaking
Gagik Ter-Kazarian
2013-01-01
We derive the classical analog of the extended phase space quantum mechanics of the particle with odd degrees of freedom which gives rise to (N=2)-realization of supersymmetry (SUSY) algebra. By means of an iterative procedure, we find the approximate groundstate solutions to the extended Schr\\"{o}dinger-like equation and use these solutions further to calculate the parameters which measure the breaking of extended SUSY such as the groundstate energy. Consequently, we calculate a more practic...
Torus as phase space: Weyl quantization, dequantization, and Wigner formalism
Energy Technology Data Exchange (ETDEWEB)
Ligabò, Marilena, E-mail: marilena.ligabo@uniba.it [Dipartimento di Matematica, Università di Bari, I-70125 Bari (Italy)
2016-08-15
The Weyl quantization of classical observables on the torus (as phase space) without regularity assumptions is explicitly computed. The equivalence class of symbols yielding the same Weyl operator is characterized. The Heisenberg equation for the dynamics of general quantum observables is written through the Moyal brackets on the torus and the support of the Wigner transform is characterized. Finally, a dequantization procedure is introduced that applies, for instance, to the Pauli matrices. As a result we obtain the corresponding classical symbols.
Experimental Trapped-ion Quantum Simulation of the Kibble-Zurek dynamics in momentum space
Cui, Jin-Ming; Huang, Yun-Feng; Wang, Zhao; Cao, Dong-Yang; Wang, Jian; Lv, Wei-Min; Luo, Le; del Campo, Adolfo; Han, Yong-Jian; Li, Chuan-Feng; Guo, Guang-Can
2016-01-01
The Kibble-Zurek mechanism is the paradigm to account for the nonadiabatic dynamics of a system across a continuous phase transition. Its study in the quantum regime is hindered by the requisite of ground state cooling. We report the experimental quantum simulation of critical dynamics in the transverse-field Ising model by a set of Landau-Zener crossings in pseudo-momentum space, that can be probed with high accuracy using a single trapped ion. We test the Kibble-Zurek mechanism in the quantum regime in the momentum space and find the measured scaling of excitations is in accordance with the theoretical prediction. PMID:27633087
Experimental Trapped-ion Quantum Simulation of the Kibble-Zurek dynamics in momentum space
Cui, Jin-Ming; Huang, Yun-Feng; Wang, Zhao; Cao, Dong-Yang; Wang, Jian; Lv, Wei-Min; Luo, Le; Del Campo, Adolfo; Han, Yong-Jian; Li, Chuan-Feng; Guo, Guang-Can
2016-09-01
The Kibble-Zurek mechanism is the paradigm to account for the nonadiabatic dynamics of a system across a continuous phase transition. Its study in the quantum regime is hindered by the requisite of ground state cooling. We report the experimental quantum simulation of critical dynamics in the transverse-field Ising model by a set of Landau-Zener crossings in pseudo-momentum space, that can be probed with high accuracy using a single trapped ion. We test the Kibble-Zurek mechanism in the quantum regime in the momentum space and find the measured scaling of excitations is in accordance with the theoretical prediction.
Hamilton geometry: Phase space geometry from modified dispersion relations
Barcaroli, Leonardo; Gubitosi, Giulia; Loret, Niccoló; Pfeifer, Christian
2015-01-01
We describe the Hamilton geometry of the phase space of particles whose motion is characterised by general dispersion relations. In this framework spacetime and momentum space are naturally curved and intertwined, allowing for a simultaneous description of both spacetime curvature and non-trivial momentum space geometry. We consider as explicit examples two models for Planck-scale modified dispersion relations, inspired from the $q$-de Sitter and $\\kappa$-Poincar\\'e quantum groups. In the first case we find the expressions for the momentum and position dependent curvature of spacetime and momentum space, while for the second case the manifold is flat and only the momentum space possesses a nonzero, momentum dependent curvature. In contrast, for a dispersion relation that is induced by a spacetime metric, as in General Relativity, the Hamilton geometry yields a flat momentum space and the usual curved spacetime geometry with only position dependent geometric objects.
Topology-driven magnetic quantum phase transition in topological insulators.
Zhang, Jinsong; Chang, Cui-Zu; Tang, Peizhe; Zhang, Zuocheng; Feng, Xiao; Li, Kang; Wang, Li-Li; Chen, Xi; Liu, Chaoxing; Duan, Wenhui; He, Ke; Xue, Qi-Kun; Ma, Xucun; Wang, Yayu
2013-03-29
The breaking of time reversal symmetry in topological insulators may create previously unknown quantum effects. We observed a magnetic quantum phase transition in Cr-doped Bi2(SexTe1-x)3 topological insulator films grown by means of molecular beam epitaxy. Across the critical point, a topological quantum phase transition is revealed through both angle-resolved photoemission measurements and density functional theory calculations. We present strong evidence that the bulk band topology is the fundamental driving force for the magnetic quantum phase transition. The tunable topological and magnetic properties in this system are well suited for realizing the exotic topological quantum phenomena in magnetic topological insulators.
Photon Cascade from a Single Crystal Phase Nanowire Quantum Dot
DEFF Research Database (Denmark)
Bouwes Bavinck, Maaike; Jöns, Klaus D; Zieliński, Michal
2016-01-01
unprecedented potential to be controlled with atomic layer accuracy without random alloying. We show for the first time that crystal phase quantum dots are a source of pure single-photons and cascaded photon-pairs from type II transitions with excellent optical properties in terms of intensity and line width...... quantum optical properties for single photon application and quantum optics.......We report the first comprehensive experimental and theoretical study of the optical properties of single crystal phase quantum dots in InP nanowires. Crystal phase quantum dots are defined by a transition in the crystallographic lattice between zinc blende and wurtzite segments and therefore offer...
The Phase Space Elementary Cell in Classical and Generalized Statistics
Directory of Open Access Journals (Sweden)
Piero Quarati
2013-10-01
Full Text Available In the past, the phase-space elementary cell of a non-quantized system was set equal to the third power of the Planck constant; in fact, it is not a necessary assumption. We discuss how the phase space volume, the number of states and the elementary-cell volume of a system of non-interacting N particles, changes when an interaction is switched on and the system becomes or evolves to a system of correlated non-Boltzmann particles and derives the appropriate expressions. Even if we assume that nowadays the volume of the elementary cell is equal to the cube of the Planck constant, h3, at least for quantum systems, we show that there is a correspondence between different values of h in the past, with important and, in principle, measurable cosmological and astrophysical consequences, and systems with an effective smaller (or even larger phase-space volume described by non-extensive generalized statistics.
Chaotic systems in complex phase space
Bender, Carl M; Hook, Daniel W; Weir, David J
2008-01-01
This paper examines numerically the complex classical trajectories of the kicked rotor and the double pendulum. Both of these systems exhibit a transition to chaos, and this feature is studied in complex phase space. Additionally, it is shown that the short-time and long-time behaviors of these two PT-symmetric dynamical models in complex phase space exhibit strong qualitative similarities.
Grassmann phase space methods for fermions. II. Field theory
Energy Technology Data Exchange (ETDEWEB)
Dalton, B.J., E-mail: bdalton@swin.edu.au [Centre for Quantum and Optical Science, Swinburne University of Technology, Melbourne, Victoria 3122 (Australia); Jeffers, J. [Department of Physics, University of Strathclyde, Glasgow G4ONG (United Kingdom); Barnett, S.M. [School of Physics and Astronomy, University of Glasgow, Glasgow G12 8QQ (United Kingdom)
2017-02-15
In both quantum optics and cold atom physics, the behaviour of bosonic photons and atoms is often treated using phase space methods, where mode annihilation and creation operators are represented by c-number phase space variables, with the density operator equivalent to a distribution function of these variables. The anti-commutation rules for fermion annihilation, creation operators suggests the possibility of using anti-commuting Grassmann variables to represent these operators. However, in spite of the seminal work by Cahill and Glauber and a few applications, the use of Grassmann phase space methods in quantum-atom optics to treat fermionic systems is rather rare, though fermion coherent states using Grassmann variables are widely used in particle physics. This paper presents a phase space theory for fermion systems based on distribution functionals, which replace the density operator and involve Grassmann fields representing anti-commuting fermion field annihilation, creation operators. It is an extension of a previous phase space theory paper for fermions (Paper I) based on separate modes, in which the density operator is replaced by a distribution function depending on Grassmann phase space variables which represent the mode annihilation and creation operators. This further development of the theory is important for the situation when large numbers of fermions are involved, resulting in too many modes to treat separately. Here Grassmann fields, distribution functionals, functional Fokker–Planck equations and Ito stochastic field equations are involved. Typical applications to a trapped Fermi gas of interacting spin 1/2 fermionic atoms and to multi-component Fermi gases with non-zero range interactions are presented, showing that the Ito stochastic field equations are local in these cases. For the spin 1/2 case we also show how simple solutions can be obtained both for the untrapped case and for an optical lattice trapping potential.
Isometric Coactions of Compact Quantum Groups on Compact Quantum Metric Spaces
Indian Academy of Sciences (India)
Johan Quaegebeur; Marie Sabbe
2012-08-01
We propose a notion of isometric coaction of a compact quantum group on a compact quantum metric space in the framework of Rieffel, where the metric structure is given by a Lipnorm. Within this setting we study the problem of the existence of a quantum isometry group.
Quantum Phase from the Twin Paradox
Ord, G. N.
2012-05-01
The modern concept of spacetime usually emerges from the consideration of moving clocks on the assumption that world-lines are continuous. In this paper we start with the assumption that natural clocks are digital and that events are discrete. By taking different continuum limits we show that the phase of non-relativistic quantum mechanics and the odd metric of spacetime both emerge from the consideration of discrete clocks in relative motion. From this perspective, the continuum limit that manifests itself in 'spacetime' is an infinite mass limit. The continuum limit that gives rise to the Schrödinger equation retains a finite mass as a beat frequency superimposed on the 'Zitterbewegung' at the Compton frequency. We illustrate this in a simple model in which a Poisson process drives a relativistic clock that gives rise to a Feynman path integral, where the phase is a manifestation of the twin paradox. The example shows that the non-Euclidean character of spacetime and the wave-particle duality of quantum mechanics share a common origin. They both emerge from the necessity that clocks age at rates that are path dependent.
Symmetries of Nonrelativistic Phase Space and the Structure of Quark-Lepton Generation
Zenczykowski, Piotr
2009-01-01
According to the Hamiltonian formalism, nonrelativistic phase space may be considered as an arena of physics, with momentum and position treated as independent variables. Invariance of x^2+p^2 constitutes then a natural generalization of ordinary rotational invariance. We consider Dirac-like linearization of this form, with position and momentum satisfying standard commutation relations. This leads to the identification of a quantum-level structure from which some phase space properties might emerge. Genuine rotations and reflections in phase space are tied to the existence of new quantum numbers, unrelated to ordinary 3D space. Their properties allow their identification with the internal quantum numbers characterising the structure of a single quark-lepton generation in the Standard Model. In particular, the algebraic structure of the Harari-Shupe preon model of fundamental particles is reproduced exactly and without invoking any subparticles. Analysis of the Clifford algebra of nonrelativistic phase space ...
Transverse phase space and its multipole decomposition
Lorcé, Cédric
2016-01-01
Relativistic phase space distributions are very interesting objects as they allow one to gather the information extracted from various types of experiments into a single coherent picture. Focusing on the four-dimensional transverse phase space, we identified all the possible angular correlations providing at the same time a clear physical interpretation of all the leading-twist generalized and transverse-momentum dependent parton distributions. We also developed a convenient representation of this four-dimensional space.
Hydrogen Atom Spectrum in Noncommutative Phase Space
Institute of Scientific and Technical Information of China (English)
LI Kang; CHAMOUN Nidal
2006-01-01
@@ We study the energy levels of the hydrogen atom in the noncommutative phase space with simultaneous spacespace and momentum-momentum noncommutative relations. We find new terms compared to the case that only noncommutative space-space relations are assumed. We also present some comments on a previous paper [Alavi S A hep-th/0501215].
The Way to Phase Space Crystals
Guo, Lingzhen; Michael, Marthaler; Schön, Gerd
A novel way to create a band structure of the quasienergy spectrum for driven systems is proposed based on the discrete symmetry in phase space. The system, e.g., an ion or ultracold atom trapped in a potential, shows no spatial periodicity, but it is driven by a time-dependent field. Under rotating wave approximation, the system can produce a periodic lattice structure in phase space. The band structure in quasienergy arises as a consequence of the n-fold discrete periodicity in phase space induced by this driving field. We propose explicit models to realize such a phase space crystal and analyze its band structure in the frame of a tightbinding approximation. The phase space lattice differs fundamentally from a lattice in real space, because its coordinate system, i.e., phase space, has a noncommutative geometry. The phase space crystal opens new ways to engineer energy band structures, with the added advantage that its properties can be changed in situ by tuning the driving field's parameters. Carl-Zeiss Stiftung.
Phase-space noncommutative formulation of Ozawa's uncertainty principle
Bastos, Catarina; Bernardini, Alex E.; Bertolami, Orfeu; Costa Dias, Nuno; Prata, João Nuno
2014-08-01
Ozawa's measurement-disturbance relation is generalized to a phase-space noncommutative extension of quantum mechanics. It is shown that the measurement-disturbance relations have additional terms for backaction evading quadrature amplifiers and for noiseless quadrature transducers. Several distinctive features appear as a consequence of the noncommutative extension: measurement interactions which are noiseless, and observables which are undisturbed by a measurement, or of independent intervention in ordinary quantum mechanics, may acquire noise, become disturbed by the measurement, or no longer be an independent intervention in noncommutative quantum mechanics. It is also found that there can be states which violate Ozawa's universal noise-disturbance trade-off relation, but verify its noncommutative deformation.
Quantum mechanics on a curved Snyder space
Mignemi, S
2015-01-01
We study the representations of the three-dimensional Euclidean Snyder-de Sitter algebra. This algebra generates the symmetries of a model admitting two fundamental scales (Planck mass and cosmological constant) and is invariant under the Born reciprocity for exchange of positions and momenta. Its representations can be obtained starting from those of the Snyder algebra, and exploiting the geometrical properties of the phase space, that can be identified with a Grassmannian manifold. Both the position and momentum operators turn out to have a discrete spectrum.
Quantum Mechanics on a Curved Snyder Space
Directory of Open Access Journals (Sweden)
Salvatore Mignemi
2016-01-01
Full Text Available We study the representations of the three-dimensional Euclidean Snyder-de Sitter algebra. This algebra generates the symmetries of a model admitting two fundamental scales (Planck mass and cosmological constant and is invariant under the Born reciprocity for exchange of positions and momenta. Its representations can be obtained starting from those of the Snyder algebra and exploiting the geometrical properties of the phase space that can be identified with a Grassmannian manifold. Both the position and momentum operators turn out to have a discrete spectrum.
Phase-selective reversible quantum decoherence in cavity QED experiment
Filip, R
2001-01-01
New feasible cavity QED experiment is proposed to analyse reversible quantum decoherence in consequence of quantum complementarity and entanglement. Utilizing the phase selective manipulations with enviroment, it is demonstrated how the complementarity particularly induces a preservation of visibility, whereas quantum decoherence is more progressive due to pronounced entanglement between system and enviroment. This effect can be directly observed using the proposed cavity QED measurements.
Directory of Open Access Journals (Sweden)
T.H. Seligman
2006-02-01
Full Text Available Thermalization in highly excited quantum many-body system does not necessarily mean a complete memory loss of the way the system was formed. This effect may pave a way for a quantum computing, with a large number of qubits $nsimeq 100-1000$, far beyond the quantum chaos border. One of the manifestations of such a thermalized non-equilibrated matter is revealed by a strongasymmetry around 90$^circ $ c.m. of evaporating proton yield in the Bi($gamma$,p photonuclear reaction. The effect is described in terms of anomalously slow cross symmetry phase relaxation in highly excited quantum many-body systems withexponentially large Hilbert space dimensions. In the above reaction this phase relaxation is about eight orders of magnitude slower than energy relaxation (thermalization.
Bienert, M.; Flores, J.; Kun, S. Yu.; Seligman, T. H.
2006-02-01
Thermalization in highly excited quantum many-body system does not necessarily mean a complete memory loss of the way the system was formed. This effect may pave a way for a quantum computing, with a large number of qubits n ≈ 100-1000, far beyond the quantum chaos border. One of the manifestations of such a thermalized non-equilibrated matter is revealed by a strong asymmetry around 90° c.m. of evaporating proton yield in the Bi(γ,p) photonuclear reaction. The effect is described in terms of anomalously slow cross symmetry phase relaxation in highly excited quantum many-body systems with exponentially large Hilbert space dimensions. In the above reaction this phase relaxation is about eight orders of magnitude slower than energy relaxation (thermalization).
Bienert, M; Kun, S Yu; Seligman, T H
2006-01-01
Thermalization in highly excited quantum many-body system does not necessarily mean a complete memory loss of the way the system was formed. This effect may pave a way for a quantum computing, with a large number of qubits $n\\simeq 100$--1000, far beyond the quantum chaos border. One of the manifestations of such a thermalized non-equilibrated matter is revealed by a strong asymmetry around 90$^\\circ $ c.m. of evaporating proton yield in the Bi($\\gamma$,p) photonuclear reaction. The effect is described in terms of anomalously slow cross symmetry phase relaxation in highly excited quantum many-body systems with exponentially large Hilbert space dimensions. In the above reaction this phase relaxation is about eight orders of magnitude slower than energy relaxation (thermalization).
PT phase transition in multidimensional quantum systems
Bender, Carl M
2012-01-01
Non-Hermitian PT-symmetric quantum-mechanical Hamiltonians generally exhibit a phase transition that separates two parametric regions, (i) a region of unbroken PT symmetry in which the eigenvalues are all real, and (ii) a region of broken PT symmetry in which some of the eigenvalues are complex. This transition has recently been observed experimentally in a variety of physical systems. Until now, theoretical studies of the PT phase transition have generally been limited to one-dimensional models. Here, four nontrivial coupled PT-symmetric Hamiltonians, $H=p^2/2+x^2/2+q^2/2+y^2/2+igx^2y$, $H=p^2/2+x^2/2+q^2/2+y^2+igx^2y$, $H=p^2/2+x^2/2+q^2/2+y^2/2+r^2/2+z^2/2+igxyz$, and $H=p^2/2+x^2/2+q^2/2+y^2+r^2/2+3z^2/2+igxyz$ are examined. Based on extensive numerical studies, this paper conjectures that all four models exhibit a phase transition. The transitions are found to occur at $g\\approx 0.1$, $g\\approx 0.04$, $g\\approx 0.1$, and $g\\approx 0.05$. These results suggest that the PT phase transition is a robust phen...
Elementary particles and emergent phase space
Zenczykowski, Piotr
2014-01-01
The Standard Model of elementary particles, although very successful, contains various elements that are put in by hand. Understanding their origin requires going beyond the model and searching for ""new physics"". The present book elaborates on one particular proposal concerning such physics. While the original conception is 50 years old, it has not lost its appeal over time. Its basic idea is that space - an arena of events treated in the Standard Model as a classical background - is a concept which emerges from a strictly discrete quantum layer in the limit of large quantum numbers. This bo
κ-Poincaré–Hopf algebra and Hopf algebroid structure of phase space from twist
Energy Technology Data Exchange (ETDEWEB)
Jurić, Tajron, E-mail: Tajron.Juric@irb.hr [Rudjer Bošković Institute, Bijenička c.54, HR-10002 Zagreb (Croatia); Meljanac, Stjepan, E-mail: meljanac@irb.hr [Rudjer Bošković Institute, Bijenička c.54, HR-10002 Zagreb (Croatia); Štrajn, Rina, E-mail: r.strajn@jacobs-university.de [Jacobs University Bremen, 28759 Bremen (Germany)
2013-11-15
We unify κ-Poincaré algebra and κ-Minkowski spacetime by embedding them into quantum phase space. The quantum phase space has Hopf algebroid structure to which we apply the twist in order to get κ-deformed Hopf algebroid structure and κ-deformed Heisenberg algebra. We explicitly construct κ-Poincaré–Hopf algebra and κ-Minkowski spacetime from twist. It is outlined how this construction can be extended to κ-deformed super-algebra including exterior derivative and forms. Our results are relevant for constructing physical theories on noncommutative spacetime by twisting Hopf algebroid phase space structure.
Alternative Approach to Noncommutative Quantum Mechanics on a Curved Space
Nakamura, M
2015-01-01
Starting with the first-order singular Lagrangian containing the redundant variables, the noncommutative quantum mechanics on a curved space is investigated by the constraint star-product quantization formalism of the projection operator method. Imposing the additional constraints to eliminate the reduntant degrees of freedom, the noncommutative quantum system with noncommutativity among the coordinates on the curved space is exactly constructed. Then, it is shown that the resultant Hamiltonian contains the quantum corrections in the exact form. We further discuss the additional constraints to realize the noncommutativities both of coordinates and momenta on the curved space.
Spinor calculus for q-deformed quantum spaces I
Schmidt, Alexander
2007-01-01
The article is dedi. to q-deformed versions of spinor calculus. As a kind of review, the most relevant properties of the two-dimensional quantum plane are summarized. Additionally, the relationship between the quantum plane and higher-dimensional quantum spaces like the q-deformed Euclidean space in four dimensions or the q-deformed Minkowski space is outlined. These considerations are continued by introducing q-analogs of the Pauli matrices. Their main properties are discussed in detail and numerous relations that could prove useful in physical applications are presented. In this respect, q-deformed versions of the important Fierz identities are written down.
A conditional quantum phase gate between two 3-state atoms
Yi, X X; You, L
2002-01-01
We propose a scheme for conditional quantum logic between two 3-state atoms that share a quantum data-bus such as a single mode optical field in cavity QED systems, or a collective vibrational state of trapped ions. Making use of quantum interference, our scheme achieves successful conditional phase evolution without any real transitions of atomic internal states or populating the quantum data-bus. In addition, it only requires common addressing of the two atoms by external laser fields.
Conditional quantum phase gate between two 3-state atoms.
Yi, X X; Su, X H; You, L
2003-03-07
We propose a scheme for conditional quantum logic between two 3-state atoms that share a quantum data bus such as a single mode optical field in cavity QED systems, or a collective vibrational state of trapped ions. Making use of quantum interference, our scheme achieves successful conditional phase evolution without any real transitions of atomic internal states or populating the quantum data bus. In addition, it requires only common addressing of the two atoms by external laser fields.
Hilbert space structure in quantum gravity: an algebraic perspective
Giddings, Steven B
2015-01-01
If quantum gravity respects the principles of quantum mechanics, suitably generalized, it may be that a more viable approach to the theory is through identifying the relevant quantum structures rather than by quantizing classical spacetime. This viewpoint is supported by difficulties of such quantization, and by the apparent lack of a fundamental role for locality. In finite or discrete quantum systems, important structure is provided by tensor factorizations of the Hilbert space. However, even in local quantum field theory properties of the generic type III von Neumann algebras and of long range gauge fields indicate that factorization of the Hilbert space is problematic. Instead it is better to focus on on the structure of the algebra of observables, and in particular on its subalgebras corresponding to regions. This paper suggests that study of analogous algebraic structure in gravity gives an important perspective on the nature of the quantum theory. Significant departures from the subalgebra structure of...
Surface waves on a quantum plasma half-space
Lázár, M; Smolyakov, A
2007-01-01
Surface modes are coupled electromagnetic/electrostatic excitations of free electrons near the vacuum-plasma interface and can be excited on a sufficiently dense plasma half-space. They propagate along the surface plane and decay in either sides of the boundary. In such dense plasma models, which are of interest in electronic signal transmission or in some astrophysical applications, the dynamics of the electrons is certainly affected by the quantum effects. Thus, the dispersion relation for the surface wave on a quantum electron plasma half-space is derived by employing the quantum hydrodynamical (QHD) and Maxwell-Poison equations. The QHD include quantum forces involving the Fermi electron temperature and the quantum Bohm potential. It is found that, at room temperature, the quantum effects are mainly relevant for the electrostatic surface plasma waves in a dense gold metallic plasma.
Nuclear Binding Near a Quantum Phase Transition
Elhatisari, Serdar; Li, Ning; Rokash, Alexander; Alarcón, Jose Manuel; Du, Dechuan; Klein, Nico; Lu, Bing-nan; Meißner, Ulf-G.; Epelbaum, Evgeny; Krebs, Hermann; Lähde, Timo A.; Lee, Dean; Rupak, Gautam
2016-09-01
How do protons and neutrons bind to form nuclei? This is the central question of ab initio nuclear structure theory. While the answer may seem as simple as the fact that nuclear forces are attractive, the full story is more complex and interesting. In this work we present numerical evidence from ab initio lattice simulations showing that nature is near a quantum phase transition, a zero-temperature transition driven by quantum fluctuations. Using lattice effective field theory, we perform Monte Carlo simulations for systems with up to twenty nucleons. For even and equal numbers of protons and neutrons, we discover a first-order transition at zero temperature from a Bose-condensed gas of alpha particles (4He nuclei) to a nuclear liquid. Whether one has an alpha-particle gas or nuclear liquid is determined by the strength of the alpha-alpha interactions, and we show that the alpha-alpha interactions depend on the strength and locality of the nucleon-nucleon interactions. This insight should be useful in improving calculations of nuclear structure and important astrophysical reactions involving alpha capture on nuclei. Our findings also provide a tool to probe the structure of alpha cluster states such as the Hoyle state responsible for the production of carbon in red giant stars and point to a connection between nuclear states and the universal physics of bosons at large scattering length.
Nuclear binding near a quantum phase transition
Elhatisari, Serdar; Rokash, Alexander; Alarcón, Jose Manuel; Du, Dechuan; Klein, Nico; Lu, Bing-nan; Meißner, Ulf-G; Epelbaum, Evgeny; Krebs, Hermann; Lähde, Timo A; Lee, Dean; Rupak, Gautam
2016-01-01
How do protons and neutrons bind to form nuclei? This is the central question of ab initio nuclear structure theory. While the answer may seem as simple as the fact that nuclear forces are attractive, the full story is more complex and interesting. In this work we present numerical evidence from ab initio lattice simulations showing that nature is near a quantum phase transition, a zero-temperature transition driven by quantum fluctuations. Using lattice effective field theory, we perform Monte Carlo simulations for systems with up to twenty nucleons. For even and equal numbers of protons and neutrons, we discover a first-order transition at zero temperature from a Bose-condensed gas of alpha particles (4He nuclei) to a nuclear liquid. Whether one has an alpha-particle gas or nuclear liquid is determined by the strength of the alpha-alpha interactions, and we show that the alpha-alpha interactions depend on the strength and locality of the nucleon-nucleon interactions. The existence of the nearby first-order ...
Implementing phase-covariant cloning in circuit quantum electrodynamics
Energy Technology Data Exchange (ETDEWEB)
Zhu, Meng-Zheng [School of Physics and Material Science, Anhui University, Hefei 230039 (China); School of Physics and Electronic Information, Huaibei Normal University, Huaibei 235000 (China); Ye, Liu, E-mail: yeliu@ahu.edu.cn [School of Physics and Material Science, Anhui University, Hefei 230039 (China)
2016-10-15
An efficient scheme is proposed to implement phase-covariant quantum cloning by using a superconducting transmon qubit coupled to a microwave cavity resonator in the strong dispersive limit of circuit quantum electrodynamics (QED). By solving the master equation numerically, we plot the Wigner function and Poisson distribution of the cavity mode after each operation in the cloning transformation sequence according to two logic circuits proposed. The visualizations of the quasi-probability distribution in phase-space for the cavity mode and the occupation probability distribution in the Fock basis enable us to penetrate the evolution process of cavity mode during the phase-covariant cloning (PCC) transformation. With the help of numerical simulation method, we find out that the present cloning machine is not the isotropic model because its output fidelity depends on the polar angle and the azimuthal angle of the initial input state on the Bloch sphere. The fidelity for the actual output clone of the present scheme is slightly smaller than one in the theoretical case. The simulation results are consistent with the theoretical ones. This further corroborates our scheme based on circuit QED can implement efficiently PCC transformation.
Implementing phase-covariant cloning in circuit quantum electrodynamics
Zhu, Meng-Zheng; Ye, Liu
2016-10-01
An efficient scheme is proposed to implement phase-covariant quantum cloning by using a superconducting transmon qubit coupled to a microwave cavity resonator in the strong dispersive limit of circuit quantum electrodynamics (QED). By solving the master equation numerically, we plot the Wigner function and Poisson distribution of the cavity mode after each operation in the cloning transformation sequence according to two logic circuits proposed. The visualizations of the quasi-probability distribution in phase-space for the cavity mode and the occupation probability distribution in the Fock basis enable us to penetrate the evolution process of cavity mode during the phase-covariant cloning (PCC) transformation. With the help of numerical simulation method, we find out that the present cloning machine is not the isotropic model because its output fidelity depends on the polar angle and the azimuthal angle of the initial input state on the Bloch sphere. The fidelity for the actual output clone of the present scheme is slightly smaller than one in the theoretical case. The simulation results are consistent with the theoretical ones. This further corroborates our scheme based on circuit QED can implement efficiently PCC transformation.
Ensembles on configuration space classical, quantum, and beyond
Hall, Michael J W
2016-01-01
This book describes a promising approach to problems in the foundations of quantum mechanics, including the measurement problem. The dynamics of ensembles on configuration space is shown here to be a valuable tool for unifying the formalisms of classical and quantum mechanics, for deriving and extending the latter in various ways, and for addressing the quantum measurement problem. A description of physical systems by means of ensembles on configuration space can be introduced at a very fundamental level: the basic building blocks are a configuration space, probabilities, and Hamiltonian equations of motion for the probabilities. The formalism can describe both classical and quantum systems, and their thermodynamics, with the main difference being the choice of ensemble Hamiltonian. Furthermore, there is a natural way of introducing ensemble Hamiltonians that describe the evolution of hybrid systems; i.e., interacting systems that have distinct classical and quantum sectors, allowing for consistent descriptio...
Novel quantum behavior generated by traveling across a quantum phase transition
Acevedo, O. L.; Rodriguez, F. J.; Quiroga, L.; Johnson, N. F.
2012-02-01
We report novel dynamical behavior in a multi-qubit--light system described by the Dicke model, which is being driven across its thermodynamic quantum-phase boundary. Analyzing the system's quantum fidelity, we find that the near-adiabatic regime exhibits the richest phenomena, with a strong asymmetry in the internal collective dynamics depending on which phase is the starting point. Depending on the quenching regime a highly non-trivial behavior emerges in both the qubit and radiation subsystems. For the former, we find that for some paths in parameter space the final fidelity of the near-adiabatic process does not depend on the direction of the trajectory, but depends only on the speed at which the path is traveled. This behavior is contrasted with Landau-Zener tunneling and the Kibble-Zurek mechanism. Furthermore, for some qubit subsystems, we identify purification and screening effects which could be used for quantum control. By contrast, the evolution of the Wigner function shows the radiation subsystem exhibits the emergence of complexity and non-classicality. These findings could be experimentally tested in several condensed matter scenarios -- for example, diamond-NV centers and superconductor qubits in confined radiation environments.
Phase transitions in open quantum systems
Jung, C; Rotter, I
1999-01-01
We consider the behaviour of open quantum systems in dependence on the coupling to one decay channel by introducing the coupling parameter $\\alpha$ being proportional to the average degree of overlapping. Under critical conditions, a reorganization of the spectrum takes place which creates a bifurcation of the time scales with respect to the lifetimes of the resonance states. We derive analytically the conditions under which the reorganization process can be understood as a second-order phase transition and illustrate our results by numerical investigations. The conditions are fulfilled e.g. for a picket fence with equal coupling of the states to the continuum. Energy dependencies within the system are included. We consider also the generic case of an unfolded Gaussian Orthogonal Ensemble. In all these cases, the reorganization of the spectrum occurs at the critical value $\\alpha_{crit}$ of the control parameter globally over the whole energy range of the spectrum. All states act cooperatively.
Quantum Key Distribution Network Based on Differential Phase Shift
Institute of Scientific and Technical Information of China (English)
WANG Wan-Ying; WANG Chuan; WEN Kai; LONG Gui-Lu
2007-01-01
Using a series of quantum correlated photon pairs, we propose a theoretical scheme for any-to-any multi-user quantum key distribution network based on differential phase shift. The differential phase shift and the different detection time slots ensure the security of our scheme against eavesdropping. We discuss the security under the intercept-resend attack and the source replacement attack.
Quantum restoration of broken symmetry in onedimensional loop space
Indian Academy of Sciences (India)
Pinaki Patra; Tanmay Mandal; Jyoti Prasad Saha
2014-06-01
For one-dimensional loop space, a nonlinear nonlocal transformation of fields is given to make the action of the self-interacting quantum field to the free one. A specific type of classically broken symmetry is restored in quantum theory. One-dimensional sine-Gordon system and sech interactions are treated as the explicit examples.
Euclidean Quantum Field Theory on Commutative and Noncommutative Spaces
Wulkenhaar, R.
I give an introduction to Euclidean quantum field theory from the point of view of statistical physics, with emphasis both on Feynman graphs and on the Wilson-Polchinski approach to renormalisation. In the second part I discuss attempts to renormalise quantum field theories on noncommutative spaces.
Quantum electrodynamics with arbitrary charge on a noncommutative space
Institute of Scientific and Technical Information of China (English)
ZHOU Wan-Ping; CAI Shao-Hong; LONG Zheng-Wen
2009-01-01
Using the Seiberg-Witten map,we obtain a quantum electrodynamics on a noncommutative space,which has arbitrary charge and keep the gauge invariance to at the leading order in theta.The one-loop divergence and Compton scattering are reinvestigated.The uoncommutative effects are larger than those in ordinary noncommutative quantum electrodynamics.
Curved noncommutative tori as Leibniz quantum compact metric spaces
Energy Technology Data Exchange (ETDEWEB)
Latrémolière, Frédéric, E-mail: frederic@math.du.edu [Department of Mathematics, University of Denver, Denver, Colorado 80208 (United States)
2015-12-15
We prove that curved noncommutative tori are Leibniz quantum compact metric spaces and that they form a continuous family over the group of invertible matrices with entries in the image of the quantum tori for the conjugation by modular conjugation operator in the regular representation, when this group is endowed with a natural length function.
Curved noncommutative tori as Leibniz quantum compact metric spaces
Latrémolière, Frédéric
2015-12-01
We prove that curved noncommutative tori are Leibniz quantum compact metric spaces and that they form a continuous family over the group of invertible matrices with entries in the image of the quantum tori for the conjugation by modular conjugation operator in the regular representation, when this group is endowed with a natural length function.
Yeh, Leehwa
1993-01-01
The phase-space-picture approach to quantum non-equilibrium statistical mechanics via the characteristic function of infinite-mode squeezed coherent states is introduced. We use quantum Brownian motion as an example to show how this approach provides an interesting geometrical interpretation of quantum non-equilibrium phenomena.
Universal Quantum Gates Based on Both Geometric and Dynamic Phases in Quantum Dots
Institute of Scientific and Technical Information of China (English)
杨开宇; 朱诗亮; 汪子丹
2003-01-01
A large-scalable quantum computer model, whose qubits are represented by the subspace subtended by the ground state and the single exciton state on semiconductor quantum dots, is proposed. A universal set of quantum gates in this system may be achieved by a mixed approach, composed of dynamic evolution and nonadiabatic geometric phase.
Quantum phase transition of light as a control of the entanglement between interacting quantum dots
Barragan, Angela; Vera-Ciro, Carlos; Mondragon-Shem, Ian
We study coupled quantum dots arranged in a photonic crystal, interacting with light which undergoes a quantum phase transition. At the mean-field level for the infinite lattice, we compute the concurrence of the quantum dots as a measure of their entanglement. We find that this quantity smoothly
Quantum Moduli Spaces of Linear and Ring Mooses
Hailu, G
2003-01-01
Quantum moduli spaces of four dimensional $SU(2)^{r}$ linear and ring mooses with $\\mathcal{N}=1$ supersymmetry and link chiral superfields in the fundamental representation are produced starting from simple pure gauge theories of disconnected nodes.
Towards an axiomatic noncommutative geometry of quantum space and time
Kiselev, Arthemy V
2013-01-01
By exploring a possible physical realisation of the geometric concept of noncommutative tangent bundle, we outline an axiomatic quantum picture of space as topological manifold and time as a count of its reconfiguration events.
The Dirac operator and gamma matrices for quantum Minkowski spaces
1997-01-01
Gamma matrices for quantum Minkowski spaces are found. The invariance of the corresponding Dirac operator is proven. We introduce momenta for spin 1/2 particles and get (in certain cases) formal solutions of the Dirac equation.
Chaotic systems in complex phase space
Indian Academy of Sciences (India)
Carl M Bender; Joshua Feinberg; Daniel W Hook; David J Weir
2009-09-01
This paper examines numerically the complex classical trajectories of the kicked rotor and the double pendulum. Both of these systems exhibit a transition to chaos, and this feature is studied in complex phase space. Additionally, it is shown that the short-time and long-time behaviours of these two $\\mathcal{PT}$ -symmetric dynamical models in complex phase space exhibit strong qualitative similarities.
Phase Space Distribution of Riemann Zeros
Dutta, Parikshit
2016-01-01
We present the partition function of a most generic $U(N)$ single plaquette model in terms of representations of unitary group. Extremising the partition function in large N limit we obtain a relation between eigenvalues of unitary matrices and number of boxes in the most dominant Young tableaux distribution. Since, eigenvalues of unitary matrices behave like coordinates of free fermions whereas, number of boxes in a row is like conjugate momenta of the same, a relation between them allows us to provide a phase space distribution for different phases of the unitary model under consideration. This proves a universal feature that all the phases of a generic unitary matrix model can be described in terms of topology of free fermi phase space distribution. Finally, using this result and analytic properties of resolvent that satisfy Dyson-Schwinger equation, we present a phase space distribution of unfolded zeros of Riemann zeta function.
Theoretical Study of Quantum Bit Rate in Free-Space Quantum Cryptography
Institute of Scientific and Technical Information of China (English)
MA Jing; ZHANG Guang-Yu; TAN Li-Ying
2006-01-01
The quantum bit rate is an important operating parameter in free-space quantum key distribution. We introduce the measuring factor and the sifting factor, and present the expressions of the quantum bit rate based on the ideal single-photon sources and the single-photon sources with Poisson distribution. The quantum bit rate is studied in the numerical simulation for the laser links between a ground station and a satellite in a low earth orbit. The results show that it is feasible to implement quantum key distribution between a ground station and a satellite in a low earth orbit.
Attractive and repulsive quantum forces from dimensionality of space
DEFF Research Database (Denmark)
Bialynicki-Birula, I.; Cirone, M.A.; Dahl, Jens Peder
2002-01-01
Two particles of identical mass attract and repel each other even when there exist no classical external forces and their average relative momentum vanishes. This quantum force depends crucially on the number of dimensions of space.......Two particles of identical mass attract and repel each other even when there exist no classical external forces and their average relative momentum vanishes. This quantum force depends crucially on the number of dimensions of space....
The static hyperpolarizability of space-fractional quantum systems
Dawson, Nathan J
2016-01-01
The nonlinear response is investigated for a space-fractional quantum mechanical system subject to a static electric field. Expressions for the polarizability and hyperpolarizability are derived from the fractional Schrodinger equation in the particle-centric view under the three-level ansatz. Two types of asymmetric single-particle quantum systems are studied and both the linear and first nonlinear response to the perturbing field are analyzed with respect to the space-fractional parameter.
Simple procedure for phase-space measurement and entanglement validation
Rundle, R. P.; Mills, P. W.; Tilma, Todd; Samson, J. H.; Everitt, M. J.
2017-08-01
It has recently been shown that it is possible to represent the complete quantum state of any system as a phase-space quasiprobability distribution (Wigner function) [Phys. Rev. Lett. 117, 180401 (2016), 10.1103/PhysRevLett.117.180401]. Such functions take the form of expectation values of an observable that has a direct analogy to displaced parity operators. In this work we give a procedure for the measurement of the Wigner function that should be applicable to any quantum system. We have applied our procedure to IBM's Quantum Experience five-qubit quantum processor to demonstrate that we can measure and generate the Wigner functions of two different Bell states as well as the five-qubit Greenberger-Horne-Zeilinger state. Because Wigner functions for spin systems are not unique, we define, compare, and contrast two distinct examples. We show how the use of these Wigner functions leads to an optimal method for quantum state analysis especially in the situation where specific characteristic features are of particular interest (such as for spin Schrödinger cat states). Furthermore we show that this analysis leads to straightforward, and potentially very efficient, entanglement test and state characterization methods.
Energy Technology Data Exchange (ETDEWEB)
Hui, Ning-Ju [Department of Applied Physics, Xi' an University of Technology, Xi' an 710054 (China); Xu, Yang-Yang; Wang, Jicheng; Zhang, Yixin [Jiangsu Provincial Research Center of Light Industrial Optoelectronic Engineering and Technology, School of Science, Jiangnan University, Wuxi 214122 (China); Hu, Zheng-Da, E-mail: huyuanda1112@jiangnan.edu.cn [Jiangsu Provincial Research Center of Light Industrial Optoelectronic Engineering and Technology, School of Science, Jiangnan University, Wuxi 214122 (China)
2017-04-01
We investigate the properties of geometric quantum coherence in the XY spin-1/2 chain with staggered Dzyaloshinsky-Moriya interaction via the quantum renormalization-group approach. It is shown that the geometric quantum coherence and its coherence susceptibility are effective to detect the quantum phase transition. In the thermodynamic limit, the geometric quantum coherence exhibits a sudden jump. The coherence susceptibilities versus the anisotropy parameter and the Dzyaloshinsky-Moriya interaction are infinite and vanishing, respectively, illustrating the distinct roles of the anisotropy parameter and the Dzyaloshinsky-Moriya interaction in quantum phase transition. Moreover, we also explore the finite-size scaling behaviors of the coherence susceptibilities. For a finite-size chain, the coherence susceptibility versus the phase-transition parameter is always maximal at the critical point, indicating the dramatic quantum fluctuation. Besides, we show that the correlation length can be revealed by the scaling exponent for the coherence susceptibility versus the Dzyaloshinsky-Moriya interaction.
Hui, Ning-Ju; Xu, Yang-Yang; Wang, Jicheng; Zhang, Yixin; Hu, Zheng-Da
2017-04-01
We investigate the properties of geometric quantum coherence in the XY spin-1/2 chain with staggered Dzyaloshinsky-Moriya interaction via the quantum renormalization-group approach. It is shown that the geometric quantum coherence and its coherence susceptibility are effective to detect the quantum phase transition. In the thermodynamic limit, the geometric quantum coherence exhibits a sudden jump. The coherence susceptibilities versus the anisotropy parameter and the Dzyaloshinsky-Moriya interaction are infinite and vanishing, respectively, illustrating the distinct roles of the anisotropy parameter and the Dzyaloshinsky-Moriya interaction in quantum phase transition. Moreover, we also explore the finite-size scaling behaviors of the coherence susceptibilities. For a finite-size chain, the coherence susceptibility versus the phase-transition parameter is always maximal at the critical point, indicating the dramatic quantum fluctuation. Besides, we show that the correlation length can be revealed by the scaling exponent for the coherence susceptibility versus the Dzyaloshinsky-Moriya interaction.
Compact phase space, cosmological constant, discrete time
Rovelli, Carlo
2015-01-01
We study the quantization of geometry in the presence of a cosmological constant, using a discretiza- tion with constant-curvature simplices. Phase space turns out to be compact and the Hilbert space finite dimensional for each link. Not only the intrinsic, but also the extrinsic geometry turns out to be discrete, pointing to discreetness of time, in addition to space. We work in 2+1 dimensions, but these results may be relevant also for the physical 3+1 case.
Adaptive Optical Phase Estimation Using Time-Symmetric Quantum Smoothing
Wheatley, T A; Yonezawa, H; Nakane, D; Arao, H; Pope, D T; Ralph, T C; Wiseman, H M; Furusawa, A; Huntington, E H
2009-01-01
Quantum parameter estimation has many applications, from gravitational wave detection to quantum key distribution. We present the first experimental demonstration of the time-symmetric technique of quantum smoothing. We consider both adaptive and non-adaptive quantum smoothing, and show that both are better than their well-known time-asymmetric counterparts (quantum filtering). For the problem of estimating a stochastically varying phase shift on a coherent beam, our theory predicts that adaptive quantum smoothing (the best scheme) gives an estimate with a mean-square error up to $2\\sqrt{2}$ times smaller than that from non-adaptive quantum filtering (the standard quantum limit). The experimentally measured improvement is $2.24 \\pm 0.14$.
Quantum spin Hall phase in 2D trigonal lattice
Wang, Z. F.; Jin, Kyung-Hwan; Liu, Feng
2016-09-01
The quantum spin Hall (QSH) phase is an exotic phenomena in condensed-matter physics. Here we show that a minimal basis of three orbitals (s, px, py) is required to produce a QSH phase via nearest-neighbour hopping in a two-dimensional trigonal lattice. Tight-binding model analyses and calculations show that the QSH phase arises from a spin-orbit coupling (SOC)-induced s-p band inversion or p-p bandgap opening at Brillouin zone centre (Γ point), whose topological phase diagram is mapped out in the parameter space of orbital energy and SOC. Remarkably, based on first-principles calculations, this exact model of QSH phase is shown to be realizable in an experimental system of Au/GaAs(111) surface with an SOC gap of ~73 meV, facilitating the possible room-temperature measurement. Our results will extend the search for substrate supported QSH materials to new lattice and orbital types.
Quantization as Asymptotics of Diffusion Processes in the Phase Space
Beniaminov, E M
2008-01-01
This work is an extended version of the paper arXiv:0803.2669v1[math-ph], in which the main results were announced. We consider certain classical diffusion process for a wave function on the phase space. It is shown that at the time of order $10^{-11}$ {\\it sec} this process converges to a process considered by quantum mechanics and described by the Schrodinger equation. This model studies the probability distributions in the phase space corresponding to the wave functions of quantum mechanics. We estimate the parameters of the model using the Lamb--Retherford experimental data on shift in the spectrum of hydrogen atom and the assumption on the heat reason of the considered diffusion process. In the paper it is shown that the quantum mechanical description of the processes can arise as an approximate description of more exact models. For the model considered in this paper, this approximation arises when the Hamilton function changes slowly under deviations of coordinates, momenta, and time on intervals whose ...
Dynamical tunneling in systems with a mixed phase space
Energy Technology Data Exchange (ETDEWEB)
Loeck, Steffen
2010-04-22
Tunneling is one of the most prominent features of quantum mechanics. While the tunneling process in one-dimensional integrable systems is well understood, its quantitative prediction for systems with a mixed phase space is a long-standing open challenge. In such systems regions of regular and chaotic dynamics coexist in phase space, which are classically separated but quantum mechanically coupled by the process of dynamical tunneling. We derive a prediction of dynamical tunneling rates which describe the decay of states localized inside the regular region towards the so-called chaotic sea. This approach uses a fictitious integrable system which mimics the dynamics inside the regular domain and extends it into the chaotic region. Excellent agreement with numerical data is found for kicked systems, billiards, and optical microcavities, if nonlinear resonances are negligible. Semiclassically, however, such nonlinear resonance chains dominate the tunneling process. Hence, we combine our approach with an improved resonance-assisted tunneling theory and derive a unified prediction which is valid from the quantum to the semiclassical regime. We obtain results which show a drastically improved accuracy of several orders of magnitude compared to previous studies. (orig.)
Dissipative quantum trajectories in complex space: Damped harmonic oscillator
Chou, Chia-Chun
2016-10-01
Dissipative quantum trajectories in complex space are investigated in the framework of the logarithmic nonlinear Schrödinger equation. The logarithmic nonlinear Schrödinger equation provides a phenomenological description for dissipative quantum systems. Substituting the wave function expressed in terms of the complex action into the complex-extended logarithmic nonlinear Schrödinger equation, we derive the complex quantum Hamilton-Jacobi equation including the dissipative potential. It is shown that dissipative quantum trajectories satisfy a quantum Newtonian equation of motion in complex space with a friction force. Exact dissipative complex quantum trajectories are analyzed for the wave and solitonlike solutions to the logarithmic nonlinear Schrödinger equation for the damped harmonic oscillator. These trajectories converge to the equilibrium position as time evolves. It is indicated that dissipative complex quantum trajectories for the wave and solitonlike solutions are identical to dissipative complex classical trajectories for the damped harmonic oscillator. This study develops a theoretical framework for dissipative quantum trajectories in complex space.
String theory, quantum phase transitions, and the emergent Fermi liquid.
Cubrović, Mihailo; Zaanen, Jan; Schalm, Koenraad
2009-07-24
A central problem in quantum condensed matter physics is the critical theory governing the zero-temperature quantum phase transition between strongly renormalized Fermi liquids as found in heavy fermion intermetallics and possibly in high-critical temperature superconductors. We found that the mathematics of string theory is capable of describing such fermionic quantum critical states. Using the anti-de Sitter/conformal field theory correspondence to relate fermionic quantum critical fields to a gravitational problem, we computed the spectral functions of fermions in the field theory. By increasing the fermion density away from the relativistic quantum critical point, a state emerges with all the features of the Fermi liquid.
Quantum processes, space-time representation and brain dynamics
Roy, Sisir; Roy, Sisir; Kafatos, Menas
2003-01-01
The recent controversy of applicability of quantum formalism to brain dynamics has been critically analysed. The prerequisites for any type of quantum formalism or quantum field theory is to investigate whether the anatomical structure of brain permits any kind of smooth geometric notion like Hilbert structure or four dimensional Minkowskian structure for quantum field theory. The present understanding of brain function clearly denies any kind of space-time representation in Minkowskian sense. However, three dimensional space and one time can be assigned to the neuromanifold and the concept of probabilistic geometry is shown to be appropriate framework to understand the brain dynamics. The possibility of quantum structure is also discussed in this framework.
Preon model and cosmological quantum-hyperchromodynamic phase transition
Nishimura, H.; Hayashi, Y.
1987-05-01
From the cosmological viewpoint, we investigate whether or not recent preon models are compatible with the picture of the first-order phase transition from the preon phase to the composite quark-lepton phase. It is shown that the current models accepting the 't Hooft anomaly-matching condition together with quantum hyperchromodynamics are consistent with the cosmological first-order phase transition.
Decorated defect condensate, a window to unconventional quantum phase transitions in Weyl semimetals
You, Yizhi
2016-01-01
We investigate the unconventional quantum phase transitions in Weyl semimetals. The emergent boson fields, coupling with the Weyl fermion bilinears, contain a Wess-Zumino-Witten term or topological $\\Theta$ term inherited from the momentum space monopoles carried by Weyl points. Three types of unconventional quantum critical points will be studied in order: (1) The transition between two distinct symmetry breaking phases whose criticality is beyond Landau's paradigm. (2) The transition between a symmetry breaking state to a topological ordered state. (3) The transition between $3d$ topological order phase to trivial disordered phase whose criticality could be traced back to a $Z_2$ symmetry breaking transition in $4d$. The essence of these unconventional critical points lies in the fact that the topological defect of an order parameter carries either a nontrivial quantum number or a topological term so the condensation of the defects would either break some symmetry or give rise to a topological order phase w...
Decorated defect condensate: A window to unconventional quantum phases in Weyl semimetals
You, Yizhi
2016-11-01
We investigate the unconventional quantum phases in Weyl semimetals. The emergent boson fields, coupling with the Weyl fermion bilinears, contain a Wess-Zumino-Witten term or topological Θ term inherited from the momentum space monopoles carried by Weyl points. Three types of unconventional quantum critical points will be studied in the following order. (1) The transition between two distinct symmetry breaking phases whose criticality is beyond Landau's paradigm. (2) The transition between a symmetry breaking state to a topological ordered state. (3) The transition between 3 d topological order phase to trivial disordered phase whose criticality could be traced back to a Z2 symmetry breaking transition in 4 d . The essence of these unconventional critical points lies in the fact that the topological defect of an order parameter carries either a nontrivial quantum number or a topological term so the condensation of the defects would either break some symmetry or give rise to a topological order phase with nontrivial braiding statistics.
Frobenius manifolds, quantum cohomology, and moduli spaces
Manin, Yuri I
1999-01-01
This is the first monograph dedicated to the systematic exposition of the whole variety of topics related to quantum cohomology. The subject first originated in theoretical physics (quantum string theory) and has continued to develop extensively over the last decade. The author's approach to quantum cohomology is based on the notion of the Frobenius manifold. The first part of the book is devoted to this notion and its extensive interconnections with algebraic formalism of operads, differential equations, perturbations, and geometry. In the second part of the book, the author describes the con
Abdelmadjid Maireche
2016-01-01
In this research paper, we consider full phase-space noncommutativity in the Schrödinger equation (SE), we apply Boopp’s shift method and standard perturbation theory to the modified (SE) in order to obtain exactly new modified energy eigenvalues in noncommutative two dimensional real space-phase NC-2D: RSP for prolonged isotropic Harmonic oscillator plus inverse quadratic potential (PCIHOIQ potential) (central singular even-power potential (CSEP potential)) with novel two parts and , it is ...
Phase locking and quantum statistics in a parametrically driven nonlinear resonator
Hovsepyan, G. H.; Shahinyan, A. R.; Chew, Lock Yue; Kryuchkyan, G. Yu.
2016-04-01
We discuss phase-locking phenomenon at low-level of quanta and quantum statistics for parametrically driven nonlinear Kerr resonator (PDNR). Oscillatory mode of PDNR is created in the process of a degenerate down-conversion of photons under interaction with a train of external Gaussian pulses. We calculate the distribution of photon-number states, the second-order correlation function of photons, the Wigner functions of cavity mode showing two-fold symmetry in phase space, and we analyze formation of phase-locked states in the regular as well as the quantum chaotic regime of the PDNR.
Energy Technology Data Exchange (ETDEWEB)
Ye, Jinwu, E-mail: jy306@ccs.msstate.edu [Beijing Key Laboratory for Terahertz Spectroscopy and Imaging, Key Laboratory of Terahertz Optoelectronics, Ministry of Education, Department of Physics, Capital Normal University, Beijing 100048 (China); Department of Physics and Astronomy, Mississippi State University, P.O. Box 5167, MS 39762 (United States); Chen, Yan, E-mail: yanchen99@gmail.com [Department of Physics, Surface Physics Laboratory (National Key Laboratory) and Lab of Advanced Materials, Fudan University, Shanghai (China)
2013-04-11
By using the dual vortex method (DVM), we develop systematically a simple and effective scheme to use the vortex degree of freedoms on dual lattices to characterize the symmetry breaking patterns of the boson insulating states in the direct lattices. Then we apply our scheme to study quantum phases and phase transitions in an extended boson Hubbard model slightly away from 1/3 (2/3) filling on frustrated lattices such as triangular and Kagome lattice. In a triangular lattice at 1/3, we find a X-CDW, a stripe CDW phase which was found previously by a density operator formalism (DOF). Most importantly, we also find a new CDW-VB phase which has both local CDW and local VB orders, in sharp contrast to a bubble CDW phase found previously by the DOF. In the Kagome lattice at 1/3, we find a VBS phase and a 6-fold CDW phase. Most importantly, we also identify a CDW-VB phase which has both local CDW and local VB orders which was found in previous QMC simulations. We also study several other phases which are not found by the DVM. By analyzing carefully the saddle point structures of the dual gauge fields in the translational symmetry breaking sides and pushing the effective actions slightly away from the commensurate filling f=1/3(2/3), we classified all the possible types of supersolids and analyze their stability conditions. In a triangular lattice, there are X-CDW supersolid, stripe CDW supersolid, but absence of any valence bond supersolid (VB-SS). There are also a new kind of supersolid: CDW-VB supersolid. In a Kagome lattice, there are 6-fold CDW supersolid, stripe CDW supersolid, but absence of any valence bond supersolid (VB-SS). There are also a new kind of supersolid: CDW-VB supersolid. We show that independent of the types of the SS, the quantum phase transitions from solids to supersolids driven by a chemical potential are in the same universality class as that from a Mott insulator to a superfluid, therefore have exact exponents z=2, ν=1/2, η=0 (with
Spinor calculus for q-deformed quantum spaces II
Schmidt, Alexander
2007-01-01
This is the second part of an article about q-deformed analogs of spinor calculus. The considerations refer to quantum spaces of physical interest, i.e. q-deformed Euclidean space in three or four dimensions as well as q-deformed Minkowski space. The Clifford algebras corresponding to these quantum spaces are treated. Especially, their commutation relations and their Hopf structures are written down. Bases of the four-dimensional Clifford algebras are constructed and their properties are discussed. Matrix representations of the Clifford algebras lead to q-deformed Dirac-matrices for the four-dimensional quantum spaces. Moreover, q-analogs of the four-dimensional spin matrices are presented. A very complete set of trace relations and rearrangement formulae concerning spin and Dirac-matrices is given. Dirac spinors together with their bilinear covariants are defined. Their behavior under q-deformed Lorentz transformation is discussed in detail.
Towards Quantum Communication in Free-Space Seawater
Ji, Ling; Yang, Ai-Lin; Feng, Zhen; Zhang, Chen; Jiang, Xiao; Lin, Xiao-Feng; Li, Hong-Gen; Jin, Xian-Min
2016-01-01
Long-distance quantum channels capable of transferring quantum states faithfully for unconditionally secure quantum communication have been so far confirmed feasible in both fiber and free-space air. However, it remains unclear whether seawater, which covers more than 70% of the earth, can also be utilized, leaving global quantum communication incomplete. Here we experimentally demonstrate that polarization quantum states including general qubits and entangled states can well survive after travelling through seawater. We performed experiments in a 3.3-meter-long tube filled with seawater samples collected in a range of 36 kilometers in Yellow sea, which conforms to Jerlov water type I. For single photons at 405 nm in blue-green window, we obtained average process fidelity above 98%. For entangled photons at 810 nm, even with high loss, we observe violation of Bell inequality with 33 standard deviations. This work confirms feasibility of seawater quantum channel, representing the first step towards underwater ...
Quantum mechanics: why complex Hilbert space?
Cassinelli, G; Lahti, P
2017-11-13
We outline a programme for an axiomatic reconstruction of quantum mechanics based on the statistical duality of states and effects that combines the use of a theorem of Solér with the idea of symmetry. We also discuss arguments favouring the choice of the complex field.This article is part of the themed issue 'Second quantum revolution: foundational questions'. © 2017 The Author(s).
Phase space representation of quantum mechanics
DEFF Research Database (Denmark)
Henriksen, Niels Engholm; Billing, G. D.; Hansen, Flemming Yssing
1988-01-01
The accuracy of the Wigner propagation method is studied for stationary as well as non-stationary states of Morse oscillators. We investigate the possibility of improving the approach by introducing an effective potential. We find that the Wigner propagation method is accurate only for the ground...
Quantum Phase Transitions in Conventional Matrix Product Systems
Zhu, Jing-Min; Huang, Fei; Chang, Yan
2017-02-01
For matrix product states(MPSs) of one-dimensional spin-1/2 chains, we investigate a new kind of conventional quantum phase transition(QPT). We find that the system has two different ferromagnetic phases; on the line of the two ferromagnetic phases coexisting equally, the system in the thermodynamic limit is in an isolated mediate-coupling state described by a paramagnetic state and is in the same state as the renormalization group fixed point state, the expectation values of the physical quantities are discontinuous, and any two spin blocks of the system have the same geometry quantum discord(GQD) within the range of open interval (0,0.25) and the same classical correlation(CC) within the range of open interval (0,0.75) compared to any phase having no any kind of correlation. We not only realize the control of QPTs but also realize the control of quantum correlation of quantum many-body systems on the critical line by adjusting the environment parameters, which may have potential application in quantum information fields and is helpful to comprehensively and deeply understand the quantum correlation, and the organization and structure of quantum correlation especially for long-range quantum correlation of quantum many-body systems.
Hybird of Quantum Phases for Induced Dipole Moments
Ma, Kai
2016-01-01
The quantum phase effects for induced electric and magnetic dipole moments are investigated. It is shown that the phase shift received by induced electric dipole has the same form with the one induced by magnetic dipole moment, therefore the total phase is a hybrid of these two types of phase. This feature indicates that in order to have a decisive measurement on either one of these two phases, it is necessary to measure the velocity dependence of the observed phase.
Classical analog of extended phase space SUSY and its breaking
Ter-Kazarian, Gagik
2013-01-01
We derive the classical analog of the extended phase space quantum mechanics of the particle with odd degrees of freedom which gives rise to (N=2)-realization of supersymmetry (SUSY) algebra. By means of an iterative procedure, we find the approximate groundstate solutions to the extended Schr\\"{o}dinger-like equation and use these solutions further to calculate the parameters which measure the breaking of extended SUSY such as the groundstate energy. Consequently, we calculate a more practical measure for the SUSY breaking which is the expectation value of an auxiliary field. We analyze non-perturbative mechanism for extended phase space SUSY breaking in the instanton picture and show that this has resulted from tunneling between the classical vacua of the theory. Particular attention is given to the algebraic properties of shape invariance and spectrum generating algebra.
Quantum electrodynamic effects in finite space
Dobiasch, P.; Walther, H.
The modifications of various quantum properties due to a discrete structure of the modes of the vacuum electromagnetic field are discussed. In contrast to the usual case of a continuous spectrum of the free space fluctuations, we consider physical systems in a resonator or in a wave guide. It is shown that the relaxation time of the system can be increased ot decreased, by increasing or decreasing the density of modes with respect to the case of unperturbed vacuum. On the other hand, we predict level shifts due to the reduced mass of the electron and deviations from the Lambshift for hydrogen in a wave guide, which can be detected with the presently feasible high resolution spectroscopy. We propose an experimental set-up. Nous discutons les modifications de diverses propriétés quantiques sous l'influence d'une structure de modes discrets du champ électromagnétique dans le vide. En comparaison du cas habituel d'un spectre continu des fluctuations du vide dans l'espace libre, nous considérons ici des systèmes physiques dans un résonateur ou un guide d'ondes. Il est démontré que le temps de relaxation du système peut être prolongé ou raccourci, ceci en augmentant ou diminuant la densité des modes par rapport à sa valeur dans le vide non-perturbé. D'autre part, nous prédisons des déplacements de niveau dus à la masse réduite de l'électron et des déviations du Lamb shift pour des atomes d'hydrogène dans un guide d'ondes, qui peuvent être détectées grâce à la haute résolution accessible actuellement en spectroscopie. Nous présentons un dispositif expérimental.
Poincaré series of quantum matrix bialgebras determined by a pair of quantum spaces
Hai, P H
1994-01-01
The dimension of the third components of the quantum matrix bialgebras determined by a pair of quantum spaces is calculated. The Poincaré series of some deformations of GL(n) is calculated. A new deformation of G(3) is given.
The time-dependent forced anisotropic oscillator in noncommutative phase space
Energy Technology Data Exchange (ETDEWEB)
Liang Mailin; Chen Qian, E-mail: mailinliang@yahoo.com.cn, E-mail: mailinliang@tju.edu.cn [Physics Department, School of Science, Tianjin University, Tianjin 300072 (China)
2011-07-01
Wave functions of the time-dependent forced anisotropic harmonic oscillator in noncommutative phase space are derived using the linear transformation and unitary transformation methods. The energy spectrum is given for the stationary system. Further, quantum fluctuations and the squeezing effect are investigated. It is found that the anisotropic property of the harmonic oscillator in noncommutative space has the squeezing effect.
Non-equilibrium quantum phase transition via entanglement decoherence dynamics
Lin, Yu-Chen; Yang, Pei-Yun; Zhang, Wei-Min
2016-01-01
We investigate the decoherence dynamics of continuous variable entanglement as the system-environment coupling strength varies from the weak-coupling to the strong-coupling regimes. Due to the existence of localized modes in the strong-coupling regime, the system cannot approach equilibrium with its environment, which induces a nonequilibrium quantum phase transition. We analytically solve the entanglement decoherence dynamics for an arbitrary spectral density. The nonequilibrium quantum phase transition is demonstrated as the system-environment coupling strength varies for all the Ohmic-type spectral densities. The 3-D entanglement quantum phase diagram is obtained. PMID:27713556
Phase space reduction and vortex statistics: An anyon quantization ambiguity
Energy Technology Data Exchange (ETDEWEB)
Allen, T.J.; Bordner, A.J.; Crossley, D.B. (Department of Physics, University of Wisconsin, 1150 University Avenue, Madison, Wisconsin 53706 (United States))
1994-06-15
We examine the quantization of the motion of two charged vortices in a Ginzburg-Landau theory for the fractional quantum Hall effect recently proposed by the first two authors. The system has two second-class constraints which can be implemented either in the reduced phase space or Dirac-Gupta-Bleuler formalism. Using the intrinsic formulation of statistics, we show that these two ways of implementing the constraints are inequivalent unless the vortices are quantized with conventional statistics, either fermionic or bosonic.
Plane Pendulum and Beyond by Phase Space Geometry
Klee, Bradley
2016-01-01
By careful analysis, the simple harmonic approximation leads to a wildly inaccurate prediction for the period of a simple plane pendulum. We make a perturbation ansatz for the phase space trajectory of a one-dimensional, anharmonic oscillator and apply conservation of energy to set undetermined functions. Iteration of the algorithm yields, to arbitrary precision, a solution to the equations of motion and the period of oscillation. Comparison with Jacobian elliptic functions leads to multidimensional applications such as the construction of approximate Seiffert spirals. Throughout we develop a quantum/classical analogy for the purpose of comparing time-independent perturbation theories.
Quantum decoherence of subcritical bubble in electroweak phase transition
Shiromizu, T
1995-01-01
In a weakly first order phase transition the typical scale of a subcritical bubble calculated in our previous papers turned out to be too small. At this scale quantum fluctuations may dominate and our previous classical result may be altered. So we examine the critical size of a subcritical bubble where quantum-to-classical transition occurs through quantum decoherence. We show that this critical size is almost equal to the typical scale which we previously obtained.
Curved momentum spaces from quantum groups with cosmological constant
Ballesteros, Á.; Gubitosi, G.; Gutiérrez-Sagredo, I.; Herranz, F. J.
2017-10-01
We bring the concept that quantum symmetries describe theories with nontrivial momentum space properties one step further, looking at quantum symmetries of spacetime in presence of a nonvanishing cosmological constant Λ. In particular, the momentum space associated to the κ-deformation of the de Sitter algebra in (1 + 1) and (2 + 1) dimensions is explicitly constructed as a dual Poisson-Lie group manifold parametrized by Λ. Such momentum space includes both the momenta associated to spacetime translations and the 'hyperbolic' momenta associated to boost transformations, and has the geometry of (half of) a de Sitter manifold. Known results for the momentum space of the κ-Poincaré algebra are smoothly recovered in the limit Λ → 0, where hyperbolic momenta decouple from translational momenta. The approach here presented is general and can be applied to other quantum deformations of kinematical symmetries, including (3 + 1)-dimensional ones.
Observability of relative phases of macroscopic quantum states
Pati, A K
1998-01-01
After a measurement, to observe the relative phases of macroscopically distinguishable states we have to ``undo'' a quantum measurement. We generalise an earlier model of Peres from two state to N-state quantum system undergoing measurement process and discuss the issue of observing relative phases of different branches. We derive an inequality which is satisfied by the relative phases of macroscopically distinguishable states and consequently any desired relative phases can not be observed in interference setups. The principle of macroscopic complementarity is invoked that might be at ease with the macroscopic world. We illustrate the idea of limit on phase observability in Stern-Gerlach measurements and the implications are discussed.
Coulomb analogy for non-Hermitian degeneracies near quantum phase transitions.
Cejnar, Pavel; Heinze, Stefan; Macek, Michal
2007-09-07
Degeneracies near the real axis in a complex-extended parameter space of a Hermitian Hamiltonian are studied. We present a method to measure distributions of such degeneracies on the Riemann sheet of a selected level and apply it in classification of quantum phase transitions. The degeneracies are shown to behave similarly as complex zeros of a partition function.
Quantum phase transition of a magnet in a spin bath
DEFF Research Database (Denmark)
Rønnow, H.M.; Parthasarathy, R.; Jensen, J.;
2005-01-01
The excitation spectrum of a model magnetic system, LiHoF(4), was studied with the use of neutron spectroscopy as the system was tuned to its quantum critical point by an applied magnetic field. The electronic mode softening expected for a quantum phase transition was forestalled by hyperfine...
Phase-modulation transmission system for quantum cryptography.
Mérolla, J M; Mazurenko, Y; Goedgebuer, J P; Porte, H; Rhodes, W T
1999-01-15
We describe a new method for quantum key distribution that utilizes phase modulation of sidebands of modulation by use of integrated electro-optic modulators at the transmitting and receiving modules. The system is shown to produce constructive or destructive interference with unity visibility, which should allow quantum cryptography to be carried out with high flexibility by use of conventional devices.
Noether symmetries in the phase space
Díaz, Bogar; Galindo-Linares, Elizabeth; Ramírez-Romero, Cupatitzio; Silva-Ortigoza, Gilberto; Suárez-Xique, Román; Torres del Castillo, Gerardo F.; Velázquez, Mercedes
2014-09-01
The constants of motion of a mechanical system with a finite number of degrees of freedom are related to the variational symmetries of a Lagrangian constructed from the Hamiltonian of the original system. The configuration space for this Lagrangian is the phase space of the original system. The symmetries considered in this manner include transformations of the time and may not be canonical in the standard sense.
Noether symmetries in the phase space
Directory of Open Access Journals (Sweden)
Bogar Díaz
2014-09-01
Full Text Available The constants of motion of a mechanical system with a finite number of degrees of freedom are related to the variational symmetries of a Lagrangian constructed from the Hamiltonian of the original system. The configuration space for this Lagrangian is the phase space of the original system. The symmetries considered in this manner include transformations of the time and may not be canonical in the standard sense.
Positive phase space distributions and uncertainty relations
Kruger, Jan
1993-01-01
In contrast to a widespread belief, Wigner's theorem allows the construction of true joint probabilities in phase space for distributions describing the object system as well as for distributions depending on the measurement apparatus. The fundamental role of Heisenberg's uncertainty relations in Schroedinger form (including correlations) is pointed out for these two possible interpretations of joint probability distributions. Hence, in order that a multivariate normal probability distribution in phase space may correspond to a Wigner distribution of a pure or a mixed state, it is necessary and sufficient that Heisenberg's uncertainty relation in Schroedinger form should be satisfied.
Identifying Phase Space Boundaries with Voronoi Tessellations
Debnath, Dipsikha; Kilic, Can; Kim, Doojin; Matchev, Konstantin T.; Yang, Yuan-Pao
2016-11-24
Determining the masses of new physics particles appearing in decay chains is an important and longstanding problem in high energy phenomenology. Recently it has been shown that these mass measurements can be improved by utilizing the boundary of the allowed region in the fully differentiable phase space in its full dimensionality. Here we show that the practical challenge of identifying this boundary can be solved using techniques based on the geometric properties of the cells resulting from Voronoi tessellations of the relevant data. The robust detection of such phase space boundaries in the data could also be used to corroborate a new physics discovery based on a cut-and-count analysis.
Identifying Phase Space Boundaries with Voronoi Tessellations
Debnath, Dipsikha; Kilic, Can; Kim, Doojin; Matchev, Konstantin T; Yang, Yuan-Pao
2016-01-01
Determining the masses of new physics particles appearing in decay chains is an important and longstanding problem in high energy phenomenology. Recently it has been shown that these mass measurements can be improved by utilizing the boundary of the allowed region in the fully differentiable phase space in its full dimensionality. Here we show that the practical challenge of identifying this boundary can be solved using techniques based on the geometric properties of the cells resulting from Voronoi tessellations of the relevant data. The robust detection of such phase space boundaries in the data could also be used to corroborate a new physics discovery based on a cut-and-count analysis.
Grassmann phase space theory for fermions
Energy Technology Data Exchange (ETDEWEB)
Dalton, Bryan J. [Centre for Quantum and Optical Science, Swinburne University of Technology, Melbourne, Victoria, 3122 (Australia); Jeffers, John [Department of Physics, University of Strathclyde, Glasgow, G4 ONG (United Kingdom); Barnett, Stephen M. [School of Physics and Astronomy, University of Glasgow, Glasgow, G12 8QQ (United Kingdom)
2017-06-15
A phase space theory for fermions has been developed using Grassmann phase space variables which can be used in numerical calculations for cold Fermi gases and for large fermion numbers. Numerical calculations are feasible because Grassmann stochastic variables at later times are related linearly to such variables at earlier times via c-number stochastic quantities. A Grassmann field version has been developed making large fermion number applications possible. Applications are shown for few mode and field theory cases. (copyright 2016 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Braiding and Berry's phases in non-Abelian quantum hall states
Zikos, Georgios
universal set of quantum gates (the quantum analogs of Boolean logic gates) by braiding them. I then focus in particular on my work developing algorithms for performing brute force searches over the space of braids to find braids which produce unitary operations close to any desired operation. These brute force searches are a crucial part of our quantum gate construction, and I show that by using a so-called "load balanced" bidirectional search I can find braids which approximate any desired operation to an accuracy of 1 part in 105. I then turn to my work calculating the Berry's phase obtained when quasiparticles are moved around one another in the Moore-Read state, a non Abelian state generally believed to describe the nu = 5/2 quantum Hall effect. This work is done using variational Monte Carlo, a method which allows one to numerically evaluate the Berry's phase for finite size systems. By exploiting certain properties of the Moore-Read state I have been able to study systems consisting of as many as 150 electrons. In so doing I have verified the conjectured connection between the Berry's phase produced by physically moving quasiparticles around one another and the mathematical phase one obtains by simply analytically continuing the quasiparticle coordinates. An added benefit of these calculations is that we can deduce the length scale which determines the size of the quasiparticles. This length scale dictates how far apart the quasiparticles must be in order to prevent errors when they are used for topological quantum computation.
Grassmann phase space methods for fermions. I. Mode theory
Dalton, B. J.; Jeffers, J.; Barnett, S. M.
2016-07-01
In both quantum optics and cold atom physics, the behaviour of bosonic photons and atoms is often treated using phase space methods, where mode annihilation and creation operators are represented by c-number phase space variables, with the density operator equivalent to a distribution function of these variables. The anti-commutation rules for fermion annihilation, creation operators suggest the possibility of using anti-commuting Grassmann variables to represent these operators. However, in spite of the seminal work by Cahill and Glauber and a few applications, the use of Grassmann phase space methods in quantum-atom optics to treat fermionic systems is rather rare, though fermion coherent states using Grassmann variables are widely used in particle physics. The theory of Grassmann phase space methods for fermions based on separate modes is developed, showing how the distribution function is defined and used to determine quantum correlation functions, Fock state populations and coherences via Grassmann phase space integrals, how the Fokker-Planck equations are obtained and then converted into equivalent Ito equations for stochastic Grassmann variables. The fermion distribution function is an even Grassmann function, and is unique. The number of c-number Wiener increments involved is 2n2, if there are n modes. The situation is somewhat different to the bosonic c-number case where only 2 n Wiener increments are involved, the sign of the drift term in the Ito equation is reversed and the diffusion matrix in the Fokker-Planck equation is anti-symmetric rather than symmetric. The un-normalised B distribution is of particular importance for determining Fock state populations and coherences, and as pointed out by Plimak, Collett and Olsen, the drift vector in its Fokker-Planck equation only depends linearly on the Grassmann variables. Using this key feature we show how the Ito stochastic equations can be solved numerically for finite times in terms of c-number stochastic
Torre, Amalia
2005-01-01
Ray, wave and quantum concepts are central to diverse and seemingly incompatible models of light. Each model particularizes a specific ''manifestation'' of light, and then corresponds to adequate physical assumptions and formal approximations, whose domains of applicability are well-established. Accordingly each model comprises its own set of geometric and dynamic postulates with the pertinent mathematical means.At a basic level, the book is a complete introduction to the Wigner optics, which bridges between ray and wave optics, offering the optical phase space as the ambience and the Wigner f
Fano, Guido
2017-01-01
This book is designed to make accessible to nonspecialists the still evolving concepts of quantum mechanics and the terminology in which these are expressed. The opening chapters summarize elementary concepts of twentieth century quantum mechanics and describe the mathematical methods employed in the field, with clear explanation of, for example, Hilbert space, complex variables, complex vector spaces and Dirac notation, and the Heisenberg uncertainty principle. After detailed discussion of the Schrödinger equation, subsequent chapters focus on isotropic vectors, used to construct spinors, and on conceptual problems associated with measurement, superposition, and decoherence in quantum systems. Here, due attention is paid to Bell’s inequality and the possible existence of hidden variables. Finally, progression toward quantum computation is examined in detail: if quantum computers can be made practicable, enormous enhancements in computing power, artificial intelligence, and secure communication will result...
Free space quantum key distribution: Towards a real life application
Weier, H.; Schmitt-Manderbach, T.; Regner, N.; Kurtsiefer, Ch.; Weinfurter, H.
2006-08-01
Quantum key distribution (QKD) [1] is the first method of quantum information science that will find its way into our everyday life. It employs fundamental laws of quantum physics to ensure provably secure symmetric key generation between two parties. The key can then be used to encrypt and decrypt sensitive data with unconditional security. Here, we report on a free space QKD implementation using strongly attenuated laser pulses over a distance of 480 m. It is designed to work continuously without human interaction. Until now, it produces quantum keys unattended at night for more than 12 hours with a sifted key rate of more than 50 kbit/s and a quantum bit error rate between 3% and 5%.
Space-Like Motions of Quantum Zero Mass Neutrinos
Widom, A; Srivastava, Y N
2011-01-01
Recent experimental reports of super-luminal velocity neutrinos moving between Geneva and Gran Sasso in no way contradict the special relativity considerations of conventional quantum field theory. A neutrino exchanged between Geneva and Gran Sasso is both virtual and space-like. The Lorentz invariant space-like distance $L$ and the Lorentz invariant space-like four momentum transfered $\\varpi $ between Geneva and Gran Sasso can be extracted from experimental data as will be shown in this work.
Quantum phase gate based on electromagnetically induced transparency in optical cavities
Borges, Halyne S.; Villas-Bôas, Celso J.
2016-11-01
We theoretically investigate the implementation of a quantum controlled-phase gate in a system constituted by a single atom inside an optical cavity, based on the electromagnetically induced transparency effect. First we show that a probe pulse can experience a π phase shift due to the presence or absence of a classical control field. Considering the interplay of the cavity-EIT effect and the quantum memory process, we demonstrated a controlled-phase gate between two single photons. To this end, first one needs to store a (control) photon in the ground atomic states. In the following, a second (target) photon must impinge on the atom-cavity system. Depending on the atomic state, this second photon will be either transmitted or reflected, acquiring different phase shifts. This protocol can then be easily extended to multiphoton systems, i.e., keeping the control photon stored, it may induce phase shifts in several single photons, thus enabling the generation of multipartite entangled states. We explore the relevant parameter space in the atom-cavity system that allows the implementation of quantum controlled-phase gates using the recent technologies. In particular, we have found a lower bound for the cooperativity of the atom-cavity system which enables the implementation of phase shift on single photons. The induced shift on the phase of a photonic qubit and the controlled-phase gate between single photons, combined with optical devices, enable one to perform universal quantum computation.
Integrability and Quantum Phase Transitions in Interacting Boson Models
Dukelsky, J; García-Ramos, J E; Pittel, S
2003-01-01
The exact solution of the boson pairing hamiltonian given by Richardson in the sixties is used to study the phenomena of level crossings and quantum phase transitions in the integrable regions of the sd and sdg interacting boson models.
Quantum theory of space charge limited current in solids
Energy Technology Data Exchange (ETDEWEB)
González, Gabriel, E-mail: gabriel.gonzalez@uaslp.mx [Cátedras Conacyt, Universidad Autónoma de San Luis Potosí, San Luis Potosí 78000, Mexico and Coordinación para la Innovación y la Aplicación de la Ciencia y la Tecnología, Universidad Autónoma de San Luis Potosí, San Luis Potosí 78000 (Mexico)
2015-02-28
We present a quantum model of space charge limited current transport inside trap-free solids with planar geometry in the mean field approximation. We use a simple transformation which allows us to find the exact analytical solution for the steady state current case. We use our approach to find a Mott-Gurney like behavior and the mobility for single charge carriers in the quantum regime in solids.
Quantum Currents in the Coset Space SU(2)/U(1)
Institute of Scientific and Technical Information of China (English)
DING Xiang-Mao; HOU Bo-Yu; ZHAO Liu
2002-01-01
We propose a rational quantum deformed nonlocal currents in the homogeneous space SU(2)k/U(1), and in terms of it and a free boson field a representation for the Drinfeld currents of Yangian double at a general level k = c is obtained. In the classical limit h → 0, the quantum nonlocal currents become SU(2)k parafermion, and the realization of Yangian double becomes the parafermion realization of SU(2)k current algebra.
Quantum Phase Transitions in Odd-Mass Nuclei
Leviatan, A; Iachello, F
2011-01-01
Quantum shape-phase transitions in odd-even nuclei are investigated in the framework of the interacting boson-fermion model. Classical and quantum analysis show that the presence of the odd fermion strongly influences the location and nature of the phase transition, especially near the critical point. Experimental evidence for the occurrence of spherical to axially-deformed transitions in odd-proton nuclei Pm, Eu and Tb (Z=61, 63, 65) is presented.
Experimental quantum-enhanced estimation of a lossy phase shift
Kacprowicz, M; Wasilewski, W; Banaszek, K; Walmsley, I A
2009-01-01
When standard light sources are employed, the precision of the phase determination is limited by the shot noise. Quantum entanglement provides means to exceed this limit with the celebrated example of N00N states that saturate the ultimate Heisenberg limit on precision, but at the same time are extremely fragile to losses. In contrast, we provide experimental evidence that appropriately engineered quantum states outperform both standard and N00N states in the precision of phase estimation when losses are present.
Quantum chaos inside space-temporal Sinai billiards
Addazi, Andrea
2016-01-01
We discuss general aspects of non-relativistic quantum chaos theory of scattering of a quantum particle on a system of a large number of naked singularities. We define such a system space-temporal Sinai billiard We dis- cuss the problem in semiclassical approach. We show that in semiclassical regime the formation of trapped periodic semiclassical orbits inside the sys- tem is unavoidable. This leads to general expression of survival probabilities and scattering time delays, expanded to the chaotic Pollicott-Ruelle reso- nances. Finally, we comment on possible generalizations of these aspects to relativistic quantum field theory.
Hilbert space structure in quantum gravity: an algebraic perspective
Giddings, Steven B.
2015-12-01
If quantum gravity respects the principles of quantum mechanics, suitably generalized, it may be that a more viable approach to the theory is through identifying the relevant quantum structures rather than by quantizing classical spacetime. This viewpoint is supported by difficulties of such quantization, and by the apparent lack of a fundamental role for locality. In finite or discrete quantum systems, important structure is provided by tensor factorizations of the Hilbert space. However, even in local quantum field theory properties of the generic type III von Neumann algebras and of long range gauge fields indicate that factorization of the Hilbert space is problematic. Instead it is better to focus on the structure of the algebra of observables, and in particular on its subalgebras corresponding to regions. This paper suggests that study of analogous algebraic structure in gravity gives an important perspective on the nature of the quantum theory. Significant departures from the subalgebra structure of local quantum field theory are found, working in the correspondence limit of long-distances/low-energies. Particularly, there are obstacles to identifying commuting algebras of localized operators. In addition to suggesting important properties of the algebraic structure, this and related observations pose challenges to proposals of a fundamental role for entanglement.
Beyond peaceful coexistence the emergence of space, time and quantum
2016-01-01
Beyond Peaceful Coexistence: The Emergence of Space, Time and Quantum brings together leading academics in mathematics and physics to address going beyond the 'peaceful coexistence' of space-time descriptions (local and continuous ones) and quantum events (discrete and non-commutative ones). Formidable challenges waiting beyond the Standard Model require a new semantic consistency within the theories in order to build new ways of understanding, working and relating to them. The original A. Shimony meaning of the peaceful coexistence (the collapse postulate and non-locality) appear to be just the tip of the iceberg in relation to more serious fundamental issues across physics as a whole.Chapters in this book present perspectives on emergent, discrete, geometrodynamic and topological approaches, as well as a new interpretative spectrum of quantum theories after Copenhagen, discrete time theories, time-less approaches and 'super-fluid' pictures of space-time.As well as stimulating further research among establis...
Formation of Ion Phase-Space Vortexes
DEFF Research Database (Denmark)
Pécseli, Hans; Trulsen, J.; Armstrong, R. J.
1984-01-01
The formation of ion phase space vortexes in the ion two stream region behind electrostatic ion acoustic shocks are observed in a laboratory experiment. A detailed analysis demonstrates that the evolution of such vortexes is associated with ion-ion beam instabilities and a nonlinear equation for ...
A precise error bound for quantum phase estimation.
Directory of Open Access Journals (Sweden)
James M Chappell
Full Text Available Quantum phase estimation is one of the key algorithms in the field of quantum computing, but up until now, only approximate expressions have been derived for the probability of error. We revisit these derivations, and find that by ensuring symmetry in the error definitions, an exact formula can be found. This new approach may also have value in solving other related problems in quantum computing, where an expected error is calculated. Expressions for two special cases of the formula are also developed, in the limit as the number of qubits in the quantum computer approaches infinity and in the limit as the extra added qubits to improve reliability goes to infinity. It is found that this formula is useful in validating computer simulations of the phase estimation procedure and in avoiding the overestimation of the number of qubits required in order to achieve a given reliability. This formula thus brings improved precision in the design of quantum computers.
Quantum phase transitions with parity-symmetry breaking and hysteresis
Trenkwalder, A.; Spagnolli, G.; Semeghini, G.; Coop, S.; Landini, M.; Castilho, P.; Pezzè, L.; Modugno, G.; Inguscio, M.; Smerzi, A.; Fattori, M.
2016-09-01
Symmetry-breaking quantum phase transitions play a key role in several condensed matter, cosmology and nuclear physics theoretical models. Its observation in real systems is often hampered by finite temperatures and limited control of the system parameters. In this work we report, for the first time, the experimental observation of the full quantum phase diagram across a transition where the spatial parity symmetry is broken. Our system consists of an ultracold gas with tunable attractive interactions trapped in a spatially symmetric double-well potential. At a critical value of the interaction strength, we observe a continuous quantum phase transition where the gas spontaneously localizes in one well or the other, thus breaking the underlying symmetry of the system. Furthermore, we show the robustness of the asymmetric state against controlled energy mismatch between the two wells. This is the result of hysteresis associated with an additional discontinuous quantum phase transition that we fully characterize. Our results pave the way to the study of quantum critical phenomena at finite temperature, the investigation of macroscopic quantum tunnelling of the order parameter in the hysteretic regime and the production of strongly quantum entangled states at critical points.
Using the Phase Space to Design Complexity
DEFF Research Database (Denmark)
Heinrich, Mary Katherine; Ayres, Phil
2016-01-01
Architecture that is responsive, adaptive, or interactive can contain active architectural elements or robotic sensor-actuator systems. The consideration of architectural robotic elements that utilize distributed control and distributed communication allows for self-organization, emergence......, and evolution on site in real-time. The potential complexity of behaviors in such architectural robotic systems requires design methodology able to encompass a range of possible outcomes, rather than a single solution. We present an approach of adopting an aspect of complexity science and applying...... it to the realm of computational design in architecture, specifically by considering the phase space and related concepts. We consider the scale and predictability of certain design characteristics, and originate the concept of a formation space extension to the phase space, for design to deal directly...
Thermodynamic Products in the Extended Phase Space
Pradhan, Parthapratim
2016-01-01
We have examined the thermodynamic properties of spherically symmetric charged-AdS black hole, charged AdS BH surrounded by quintessence and charged AdS BH in $f(R)$ gravity in the extended phase-space. Where the cosmological constant should be treated as thermodynamic pressure and its conjugate parameter as thermodynamic volume. Then they should behave as a analog of Van der Waal like systems. In the extended phase space we have calculated the \\emph{entropy product} and \\emph{thermodynamic volume product} of all horizons. The mass(or enthalpy) independent nature of the said products signals they are "universal" quantities. Various types of pictorial diagram of the specific heat is given. The divergence of the specific heat indicates that the second order phase transition occurs under certain condition.
A Representation of Quantum Measurement in Order-Unit Spaces
Niestegge, Gerd
2010-01-01
A certain generalization of the mathematical formalism of quantum mechanics beyond operator algebras is considered. The approach is based on the concept of conditional probability and the interpretation of the Lueders - von Neumann quantum measurement as a probability conditionalization rule. A major result shows that the operator algebras must be replaced by order-unit spaces with some specific properties in the generalized approach, and it is analyzed under which conditions these order-unit spaces become Jordan algebras. An application of this result provides a characterization of the projection lattices in operator algebras.
Relativistic quantum level-spacing statistics in chaotic graphene billiards.
Huang, Liang; Lai, Ying-Cheng; Grebogi, Celso
2010-05-01
An outstanding problem in quantum nonlinear dynamics concerns about the energy-level statistics in experimentally accessible relativistic quantum systems. We demonstrate, using chaotic graphene confinements where electronic motions are governed by the Dirac equation in the low-energy regime, that the level-spacing statistics are those given by Gaussian orthogonal ensemble (GOE) random matrices. Weak magnetic field can change the level-spacing statistics to those of Gaussian unitary ensemble for electrons in graphene. For sufficiently strong magnetic field, the GOE statistics are restored due to the appearance of Landau levels.
Active phase compensation of quantum key distribution system
Institute of Scientific and Technical Information of China (English)
CHEN Wei; HAN ZhengFu; MO XiaoFan; XU FangXing; WEI Guo; GUO GuangCan
2008-01-01
Quantum key distribution (QKD) system must be robust enough in practical communication. Besides birefringence of fiber, system performance is notably affected by phase drift. The Faraday-Michelson QKD system can auto-compensate the birefringence of fiber, but phase shift is still a serious problem in its practical operation. In this paper, the major reason of phase drift and its effect on Faraday-Michel-son QKD system is analyzed and an effective active phase compensation scheme is proposed. By this means, we demonstrate a quantum key distribution system which can stably run over 37-km fiber in practical working condition with the long-time averaged quantum bit error rate of 1.59% and the stan-dard derivation of 0.46%. This result shows that the active phase compensation scheme is suitable to be used in practical QKD systems based on double asymmetric interferometers without additional de-vices and thermal controller.
Quantum like representation of aSpiral Phase Plate
Bovino, Fabio A
2011-01-01
We introduce a quantum like representation of a Spiral Phase Plate, acting on an electromagnetic field, as a two mode phase operator. The representation is based on the Newton binomial expansion and on properties of rational power of lowering and raising operators of quantum field. The correctness of this representation is proved by obtaining the same results of the Paul's operator in the single mode limit and comparing the results of two particular problems solved both in the classical and quantum picture: the action of a Spiral Phase Plate on a Gaussian Beam (corresponding to the vacuum state of the two-dimensional harmonic oscillator) and on a off-axis Gaussian Beam (corresponding to the displaced vacuum state in quantum picture).
Real Space Renormalization of Majorana Fermions in Quantum Nano-Wire Superconductors
Jafari, R.; Langari, A.; Akbari, Alireza; Kim, Ki-Seok
2017-02-01
We develop the real space quantum renormalization group (QRG) approach for majorana fermions. As an example we focus on the Kitaev chain to investigate the topological quantum phase transition (TQPT) in the one-dimensional spinless p-wave superconductor. Studying the behaviour of local compressibility and ground-state fidelity, show that the TQPT is signalled by the maximum of local compressibility at the quantum critical point tuned by the chemical potential. Moreover, a sudden drop of the ground-state fidelity and the divergence of fidelity susceptibility at the topological quantum critical point are used as proper indicators for the TQPT, which signals the appearance of Majorana fermions. Finally, we present the scaling analysis of ground-state fidelity near the critical point that manifests the universal information about the TQPT, which reveals two different scaling behaviors as we approach the critical point and thermodynamic limit.
A gauge theory of gravity in curved phase-spaces
Castro, Carlos
2016-06-01
After a cursory introduction of the basic ideas behind Born’s Reciprocal Relativity theory, the geometry of the cotangent bundle of spacetime is studied via the introduction of nonlinear connections associated with certain nonholonomic modifications of Riemann-Cartan gravity within the context of Finsler geometry. A novel gauge theory of gravity in the 8D cotangent bundle T∗M of spacetime is explicitly constructed and based on the gauge group SO(6, 2) ×sR8 which acts on the tangent space to the cotangent bundle T(x,p)T∗M at each point (x,p). Several gravitational actions involving curvature and torsion tensors and associated with the geometry of curved phase-spaces are presented. We conclude with a brief discussion of the field equations, the geometrization of matter, quantum field theory (QFT) in accelerated frames, T-duality, double field theory, and generalized geometry.
Ultrafast control of electron spin in a quantum dot using geometric phase
Malinovsky, V. S.; Rudin, S.
2012-12-01
We propose a scheme to perform arbitrary unitary operations on a single electron-spin qubit in a quantum dot. The design is solely based on the geometrical phase that the qubit state acquires after a cyclic evolution in the parameter space. The scheme is utilizing ultrafast linearly-chirped pulses providing adiabatic excitation of the qubit states and the geometric phase is fully controlled by the relative phase between pulses. The analytic expression of the evolution operator for the electron spin in a quantum dot, which provides a clear geometrical interpretation of the qubit dynamics is obtained. Using parameters of InGaN/GaN, GaN/AlN quantum dots we provide an estimate for the time scale of the qubit rotations and parameters of the external fields.
Tailoring Accelerating Beams in Phase Space
Wen, Yuanhui; Zhang, Yanfeng; Chen, Hui; Yu, Siyuan
2016-01-01
An appropriate design of wavefront will enable light fields propagating along arbitrary trajectories thus forming accelerating beams in free space. Previous ways of designing such accelerating beams mainly rely on caustic methods, which start from diffraction integrals and only deal with two-dimensional fields. Here we introduce a new perspective to construct accelerating beams in phase space by designing the corresponding Wigner distribution function (WDF). We find such a WDF-based method is capable of providing both the initial field distribution and the angular spectrum in need by projecting the WDF into the real space and the Fourier space respectively. Moreover, this approach applies to the construction of both two- and three-dimensional fields, greatly generalizing previous caustic methods. It may therefore open up a new route to construct highly-tailored accelerating beams and facilitate applications ranging from particle manipulation and trapping to optical routing as well as material processing.
Consistency of Scalar Potentials from Quantum de Sitter Space
Espinosa, José R; Trépanier, Maxime
2015-01-01
We derive constraints on the scalar potential of a quantum field theory in de Sitter space. The constraints, which we argue should be understood as consistency conditions for quantum field theories in dS space, originate from a consistent interpretation of quantum de Sitter space through its Coleman-De Luccia tunneling rate. Indeed, consistency of de Sitter space as a quantum theory of gravity with a finite number of degrees of freedom suggests the tunneling rates to vacua with negative cosmological constants be interpreted as Poincar\\'e recurrences. Demanding the tunneling rate to be a Poincar\\'e recurrence imposes two constraints, or consistency conditions, on the scalar potential. Although the exact consistency conditions depend on the shape of the scalar potential, generically they correspond to: the distance in field space between the de Sitter vacuum and any other vacuum with negative cosmological constant must be of the order of the reduced Planck mass or larger; and the fourth root of the vacuum energ...
Quantum Griffiths Phase Inside the Ferromagnetic Phase of Ni1 -xVx
Wang, Ruizhe; Gebretsadik, Adane; Ubaid-Kassis, Sara; Schroeder, Almut; Vojta, Thomas; Baker, Peter J.; Pratt, Francis L.; Blundell, Stephen J.; Lancaster, Tom; Franke, Isabel; Möller, Johannes S.; Page, Katharine
2017-06-01
We study by means of bulk and local probes the d -metal alloy Ni1 -xVx close to the quantum critical concentration, xc≈11.6 %, where the ferromagnetic transition temperature vanishes. The magnetization-field curve in the ferromagnetic phase takes an anomalous power-law form with a nonuniversal exponent that is strongly x dependent and mirrors the behavior in the paramagnetic phase. Muon spin rotation experiments demonstrate inhomogeneous magnetic order and indicate the presence of dynamic fluctuating magnetic clusters. These results provide strong evidence for a quantum Griffiths phase on the ferromagnetic side of the quantum phase transition.
Canonical quantum gravity on noncommutative space-time
Kober, Martin
2015-06-01
In this paper canonical quantum gravity on noncommutative space-time is considered. The corresponding generalized classical theory is formulated by using the Moyal star product, which enables the representation of the field quantities depending on noncommuting coordinates by generalized quantities depending on usual coordinates. But not only the classical theory has to be generalized in analogy to other field theories. Besides, the necessity arises to replace the commutator between the gravitational field operator and its canonical conjugated quantity by a corresponding generalized expression on noncommutative space-time. Accordingly the transition to the quantum theory has also to be performed in a generalized way and leads to extended representations of the quantum theoretical operators. If the generalized representations of the operators are inserted to the generalized constraints, one obtains the corresponding generalized quantum constraints including the Hamiltonian constraint as dynamical constraint. After considering quantum geometrodynamics under incorporation of a coupling to matter fields, the theory is transferred to the Ashtekar formalism. The holonomy representation of the gravitational field as it is used in loop quantum gravity opens the possibility to calculate the corresponding generalized area operator.
Lipschitz and Besov spaces in quantum calculus
Nemri, Akram; Selmi, Belgacem
2016-08-01
The purpose of this paper is to investigate the harmonic analysis on the time scale 𝕋q, q ∈ (0, 1) to introduce q-weighted Besov spaces subspaces of Lp(𝕋 q) generalizing the classical one. Further, using an example of q-weighted wα,β(.; q) which is introduced and studied. We give a new characterization of the q-Besov space using q-Poisson kernel and the g1 Littlewood-Paley operator.
Transmission Phase Through Two Quantum Dots Embedded in a Four-Terminal Quantum Ring
Sigrist, M.; Fuhrer, A; Ihn, T.; Ensslin, K.; Wegscheider, W.; Bichler, M.
2003-01-01
We use the Aharonov-Bohm effect in a four-terminal ring based on a Ga[Al]As heterostructure for the measurement of the relative transmission phase. In each of the two interfering paths we induce a quantum dot. The number of electrons in the two dots can be controlled independently. The transmission phase is measured as electrons are added to or taken away from the individual quantum dots.
Quantum effects of massive modes in a cosmological quantum space-time
Tavakoli, Yaser
2015-01-01
The quantum theory of a massive, minimally coupled scalar field on an isotropic cosmological quantum space-time is revisited. The interplay between the quantum background and the massive modes of the field, when disregarding their back-reaction effects, gives rise to a theory of quantum field on an effective, dressed space-time whose isotropy may be broken in the direction of the field propagation. On the resulting dressed geometry, evolution of the massive modes, by analyzing the solutions to the corresponding Klein-Gordon equation, is investigated. In particular, by computing the leading order contributions in adiabatic series, an approximate solution for the mode function is obtained. By using the adiabatic regularization, to the fourth order in expansion series, the renormalization of the stress-energy and Hamiltonian of the quantized field is studied. The problem of particle production is studied here in the light of the classical theory of wave propagation on the effective anisotropic background. To the...
Experimental realization of quantum cryptography communication in free space
Institute of Scientific and Technical Information of China (English)
WANG; Chuan; ZHANG; Jingfu; WANG; Pingxiao; DENG; Fuguo; A
2005-01-01
Utilizing linear optical devices, the principle of B92 quantum key distribution (QKD) protocol is demonstrated in free space with a distance of transmission of 2.2 meters. The faint laser pulses with 650 nm wavelength are used as the single photon sources. The experimental results show that the eavesdropping behavior in the signal transmission can be detected. We also discuss the problems and solutions in using the quantum cryptography communication practically. It is pointed out that one of the approaches to increasing the distance of the quantum communication is to overcome the attenuation of the single photon in transmission. This could not be solved by the use of single photon source, and new quantum communication protocols are needed to solve these problems.
Limited Holism and Real-Vector-Space Quantum Theory
Hardy, Lucien
2010-01-01
Quantum theory has the property of "local tomography": the state of any composite system can be reconstructed from the statistics of measurements on the individual components. In this respect the holism of quantum theory is limited. We consider in this paper a class of theories more holistic than quantum theory in that they are constrained only by "bilocal tomography": the state of any composite system is determined by the statistics of measurements on pairs of components. Under a few auxiliary assumptions, we derive certain general features of such theories. In particular, we show how the number of state parameters can depend on the number of perfectly distinguishable states. We also show that real-vector-space quantum theory, while not locally tomographic, is bilocally tomographic.
Limited Holism and Real-Vector-Space Quantum Theory
Hardy, Lucien; Wootters, William K.
2012-03-01
Quantum theory has the property of "local tomography": the state of any composite system can be reconstructed from the statistics of measurements on the individual components. In this respect the holism of quantum theory is limited. We consider in this paper a class of theories more holistic than quantum theory in that they are constrained only by "bilocal tomography": the state of any composite system is determined by the statistics of measurements on pairs of components. Under a few auxiliary assumptions, we derive certain general features of such theories. In particular, we show how the number of state parameters can depend on the number of perfectly distinguishable states. We also show that real-vector-space quantum theory, while not locally tomographic, is bilocally tomographic.
Hamiltonian and physical Hilbert space in polymer quantum mechanics
Corichi, A; Zapata, R J A; Corichi, Alejandro; Vukasinac, Tatjana; Zapata, Jose A.
2006-01-01
In this paper, a version of polymer quantum mechanics, which is inspired by loop quantum gravity, is considered and shown to be equivalent, in a precise sense, to the standard, experimentally tested, Schroedinger quantum mechanics. The kinematical cornerstone of our framework is the so called polymer representation of the Heisenberg-Weyl (H-W) algebra, which is the starting point of the construction. The dynamics is constructed as a continuum limit of effective theories characterized by a scale, and requires a renormalization of the inner product. The result is a physical Hilbert space in which the continuum Hamiltonian can be represented and that is unitarily equivalent to the Schroedinger representation of quantum mechanics. As a concrete implementation of our formalism, the simple harmonic oscillator is fully developed.
Practical Quantum Cryptography for Secure Free-Space Communications
Energy Technology Data Exchange (ETDEWEB)
Buttler, W.T.; Hughes, R.J.; Kwiat, P.G.; Lamoreaux, S.K.; Morgan, G.L.; Nordholt, J.E.; Peterson, C.G.
1999-02-01
Quantum cryptography is an emerging technology in which two parties may simultaneously generate shared, secret cryptographic key material using the transmission of quantum states of light. The security of these transmissions is based on the inviolability of the laws of quantum mechanics and information-theoretically secure post-processing methods. An adversary can neither successfully tap the quantum transmissions, nor evade detection, owing to Heisenberg's uncertainty principle. In this paper we describe the theory of quantum cryptography, and the most recent results from our experimental free-space system with which we have demonstrated for the first time the feasibility of quantum key generation over a point-to-point outdoor atmospheric path in daylight. We achieved a transmission distance of 0.5 km, which was limited only by the length of the test range. Our results provide strong evidence that cryptographic key material could be generated on demand between a ground station and a satellite (or between two satellites), allowing a satellite to be securely re-keyed on orbit. We present a feasibility analysis of surface-to-satellite quantum key generation.
On space of integrable quantum field theories
Smirnov, F A
2016-01-01
We study deformations of 2D Integrable Quantum Field Theories (IQFT) which preserve integrability (the existence of infinitely many local integrals of motion). The IQFT are understood as "effective field theories", with finite ultraviolet cutoff. We show that for any such IQFT there are infinitely many integrable deformations generated by scalar local fields $X_s$, which are in one-to-one correspondence with the local integrals of motion; moreover, the scalars $X_s$ are built from the components of the associated conserved currents in a universal way. The first of these scalars, $X_1$, coincides with the composite field $(T{\\bar T})$ built from the components of the energy-momentum tensor. The deformations of quantum field theories generated by $X_1$ are "solvable" in a certain sense, even if the original theory is not integrable. In a massive IQFT the deformations $X_s$ are identified with the deformations of the corresponding factorizable S-matrix via the CDD factor. The situation is illustrated by explicit...
On space of integrable quantum field theories
Directory of Open Access Journals (Sweden)
F.A. Smirnov
2017-02-01
Full Text Available We study deformations of 2D Integrable Quantum Field Theories (IQFT which preserve integrability (the existence of infinitely many local integrals of motion. The IQFT are understood as “effective field theories”, with finite ultraviolet cutoff. We show that for any such IQFT there are infinitely many integrable deformations generated by scalar local fields Xs, which are in one-to-one correspondence with the local integrals of motion; moreover, the scalars Xs are built from the components of the associated conserved currents in a universal way. The first of these scalars, X1, coincides with the composite field (TT¯ built from the components of the energy–momentum tensor. The deformations of quantum field theories generated by X1 are “solvable” in a certain sense, even if the original theory is not integrable. In a massive IQFT the deformations Xs are identified with the deformations of the corresponding factorizable S-matrix via the CDD factor. The situation is illustrated by explicit construction of the form factors of the operators Xs in sine-Gordon theory. We also make some remarks on the problem of UV completeness of such integrable deformations.
On space of integrable quantum field theories
Smirnov, F. A.; Zamolodchikov, A. B.
2017-02-01
We study deformations of 2D Integrable Quantum Field Theories (IQFT) which preserve integrability (the existence of infinitely many local integrals of motion). The IQFT are understood as "effective field theories", with finite ultraviolet cutoff. We show that for any such IQFT there are infinitely many integrable deformations generated by scalar local fields Xs, which are in one-to-one correspondence with the local integrals of motion; moreover, the scalars Xs are built from the components of the associated conserved currents in a universal way. The first of these scalars, X1, coincides with the composite field (T T bar) built from the components of the energy-momentum tensor. The deformations of quantum field theories generated by X1 are "solvable" in a certain sense, even if the original theory is not integrable. In a massive IQFT the deformations Xs are identified with the deformations of the corresponding factorizable S-matrix via the CDD factor. The situation is illustrated by explicit construction of the form factors of the operators Xs in sine-Gordon theory. We also make some remarks on the problem of UV completeness of such integrable deformations.
Wavelet analysis of the nuclear phase space
Energy Technology Data Exchange (ETDEWEB)
Jouault, B.; Sebille, F.; Mota, V. de la
1997-12-31
The description of transport phenomena in nuclear matter is addressed in a new approach based on the mathematical theory of wavelets and the projection methods of statistical physics. The advantage of this framework is to offer the opportunity to use information concepts common to both the formulation of physical properties and the mathematical description. This paper focuses on two features, the extraction of relevant informations using the geometrical properties of the underlying phase space and the optimization of the theoretical and numerical treatments based on convenient choices of the representation spaces. (author). 34 refs.
Quantum phases of dipolar soft-core bosons
Grimmer, D.; Safavi-Naini, A.; Capogrosso-Sansone, B.; Söyler, Ş. G.
2014-10-01
We study the phase diagram of a system of soft-core dipolar bosons confined to a two-dimensional optical lattice layer. We assume that dipoles are aligned perpendicular to the layer such that the dipolar interactions are purely repulsive and isotropic. We consider the full dipolar interaction and perform path-integral quantum Monte Carlo simulations using the worm algorithm. Besides a superfluid phase, we find various solid and supersolid phases. We show that, unlike what was found previously for the case of nearest-neighbor interaction, supersolid phases are stabilized by doping the solids not only with particles but with holes as well. We further study the stability of these quantum phases against thermal fluctuations. Finally, we discuss pair formation and the stability of the pair checkerboard phase formed in a bilayer geometry, and we suggest experimental conditions under which the pair checkerboard phase can be observed.
The Morse oscillator in position space, momentum space, and phase space
DEFF Research Database (Denmark)
Dahl, Jens Peder; Springborg, Michael
1988-01-01
functions are to be calculated. The wave and phase space functions are displayed in a series of curves and contour diagrams. An Appendix discusses the calculation of the modified Bessel functions of real, positive argument and complex order, which is required for calculating the phase space functions...
Tunneling of an energy eigenstate through a parabolic barrier viewed from Wigner phase space
DEFF Research Database (Denmark)
Heim, D.M.; Schleich, W.P.; Alsing, P.M.
2013-01-01
We analyze the tunneling of a particle through a repulsive potential resulting from an inverted harmonic oscillator in the quantum mechanical phase space described by the Wigner function. In particular, we solve the partial differential equations in phase space determining the Wigner function...... of an energy eigenstate of the inverted oscillator. The reflection or transmission coefficients R or T are then given by the total weight of all classical phase-space trajectories corresponding to energies below, or above the top of the barrier given by the Wigner function....
Quantum gravity effects in Myers-Perry space-times
Litim, Daniel F
2013-01-01
We study quantum gravity effects for Myers-Perry black holes assuming that the leading contributions arise from the renormalization group evolution of Newton's coupling. Provided that gravity weakens following the asymptotic safety conjecture, we find that quantum effects lift a degeneracy of higher-dimensional black holes, and dominate over kinematical ones induced by rotation, particularly for small black hole mass, large angular momentum, and higher space-time dimensionality. Quantum-corrected space-times display inner and outer horizons, and show the existence of a black hole of smallest mass in any dimension. Ultra-spinning solutions no longer persist. Thermodynamic properties including temperature, specific heat, the Komar integrals, and aspects of black hole mechanics are studied as well. Observing a softening of the ring singularity, we also discuss the validity of classical energy conditions.
Quantum gravity effects in Myers-Perry space-times
Energy Technology Data Exchange (ETDEWEB)
Litim, Daniel F.; Nikolakopoulos, Konstantinos [Department of Physics and Astronomy, University of Sussex,Falmer Campus, Brighton BN1 9QH (United Kingdom)
2014-04-03
We study quantum gravity effects for Myers-Perry black holes assuming that the leading contributions arise from the renormalization group evolution of Newton’s coupling. Provided that gravity weakens following the asymptotic safety conjecture, we find that quantum effects lift a degeneracy of higher-dimensional black holes, and dominate over kinematical ones induced by rotation, particularly for small black hole mass, large angular momentum, and higher space-time dimensionality. Quantum-corrected space-times display inner and outer horizons, and show the existence of a black hole of smallest mass in any dimension. Ultra-spinning solutions no longer persist. Thermodynamic properties including temperature, specific heat, the Komar integrals, and aspects of black hole mechanics are studied as well. Observing a softening of the ring singularity, we also discuss the validity of classical energy conditions.
Theoretical Proposals of Quantum Phase-slip Devices
Hriscu, A.M.
2012-01-01
This thesis describes a series of theoretical proposals of novel circuits that embed ultrathin superconducting nanowires with coherent quantum phase-slips (QPS). The motivation for our proposals is twofold: firstly, to facilitate unambiguous experimental verification of coherent phase-slips. Secondl
Quantum Monte Carlo simulation of topological phase transitions
Yamamoto, Arata; Kimura, Taro
2016-12-01
We study the electron-electron interaction effects on topological phase transitions by the ab initio quantum Monte Carlo simulation. We analyze two-dimensional class A topological insulators and three-dimensional Weyl semimetals with the long-range Coulomb interaction. The direct computation of the Chern number shows the electron-electron interaction modifies or extinguishes topological phase transitions.
Quantum Monte Carlo simulation of topological phase transitions
Yamamoto, Arata
2016-01-01
We study the electron-electron interaction effects on topological phase transitions by the ab-initio quantum Monte Carlo simulation. We analyze two-dimensional class A topological insulators and three-dimensional Weyl semimetals with the long-range Coulomb interaction. The direct computation of the Chern number shows the electron-electron interaction modifies or extinguishes topological phase transitions.
Strain-induced topological quantum phase transition in phosphorene oxide
Kang, Seoung-Hun; Park, Jejune; Woo, Sungjong; Kwon, Young-Kyun
Using ab initio density functional theory, we investigate the structural stability and electronic properties of phosphorene oxides (POx) with different oxygen compositions x. A variety of configurations are modeled and optimized geometrically to search for the equilibrium structure for each x value. Our electronic structure calculations on the equilibrium configuration obtained for each x reveal that the band gap tends to increase with the oxygen composition of x 0.5. We further explore the strain effect on the electronic structure of the fully oxidized phosphorene, PO, with x = 1. At a particular strain without spin-orbit coupling (SOC) is observed a band gap closure near the Γ point in the k space. We further find the strain in tandem with SOC induces an interesting band inversion with a reopened very small band gap (5 meV), and thus gives rise to a topological quantum phase transition from a normal insulator to a topological insulator. Such a topological phase transition is confirmed by the wave function analysis and the band topology identified by the Z2 invariant calculation.
Quantum phase transitions in Bose-Fermi systems
Petrellis, D; Iachello, F
2011-01-01
Quantum phase transitions in a system of N bosons with angular momentum L=0,2 (s,d) and a single fermion with angular momentum j are investigated both classically and quantum mechanically. It is shown that the presence of the odd fermion strongly influences the location and nature of the phase transition, especially the critical value of the control parameter at which the phase transition occurs. Experimental evidence for the U(5)-SU(3) (spherical to axially-deformed) transition in odd-even nuclei is presented.
Quantum Monte Carlo simulations of fidelity at magnetic quantum phase transitions.
Schwandt, David; Alet, Fabien; Capponi, Sylvain
2009-10-23
When a system undergoes a quantum phase transition, the ground-state wave function shows a change of nature, which can be monitored using the fidelity concept. We introduce two quantum Monte Carlo schemes that allow the computation of fidelity and its susceptibility for large interacting many-body systems. These methods are illustrated on a two-dimensional Heisenberg model, where fidelity estimators show marked behavior at two successive quantum phase transitions. We also develop a scaling theory which relates the divergence of the fidelity susceptibility to the critical exponent of the correlation length. A good agreement is found with the numerical results.
Quantum space-times in the year 2002
Indian Academy of Sciences (India)
A P Balachandran
2002-08-01
We review certain emergent notions on the nature of space-time from noncommutative geometry and their radical implications. These ideas of space-time are suggested from developments in fuzzy physics, string theory, and deformation quantization. The review focuses on the ideas coming from fuzzy physics. We ﬁnd models of quantum space-time like fuzzy 4 on which states cannot be localized, but which ﬂuctuate into other manifolds like CP3. New uncertainty principles concerning such lack of localizability on quantum space-times are formulated. Such investigations show the possibility of formulating and answering questions like the probability of ﬁnding a point of a quantum manifold in a state localized on another one. Additional striking possibilities indicated by these developments is the (generic) failure of CPT theorem and the conventional spin-statistics connection. They even suggest that Planck’s `constant’ may not be a constant, but an operator which does not commute with all observables. All these novel possibilities arise within the rules of conventional quantum physics, and with no serious input from gravity physics.
Practical free-space quantum key distribution over 1 km
Buttler, W T; Kwiat, P G; Lamoreaux, S K; Luther, G G; Morgan, G L; Nordholt, J E; Peterson, C G; Simmons, C M
1998-01-01
A working free-space quantum key distribution (QKD) system has been developed and tested over an outdoor optical path of ~1 km at Los Alamos National Laboratory under nighttime conditions. Results show that QKD can provide secure real-time key distribution between parties who have a need to communicate secretly. Finally, we examine the feasibility of surface to satellite QKD.
Isochronous classical systems and quantum systems with equally spaced spectra
Energy Technology Data Exchange (ETDEWEB)
Carinena, J F; Perelomov, A M; Ranada, M F [Departamento de Fisica Teorica, Facultad de Ciencias, Universidad de Zaragoza, 50009 Zaragoza (Spain)
2007-11-15
We study isoperiodic classical systems, what allows us to find the classical isochronous systems, i.e. having a period independent of the energy. The corresponding quantum analog, systems with an equally spaced spectrum are analysed by looking for possible creation-like differential operators. The harmonic oscillator and the isotonic oscillator are the two main essentially unique examples of such situation.
Quantum phase transition of the transverse-field quantum Ising model on scale-free networks.
Yi, Hangmo
2015-01-01
I investigate the quantum phase transition of the transverse-field quantum Ising model in which nearest neighbors are defined according to the connectivity of scale-free networks. Using a continuous-time quantum Monte Carlo simulation method and the finite-size scaling analysis, I identify the quantum critical point and study its scaling characteristics. For the degree exponent λ=6, I obtain results that are consistent with the mean-field theory. For λ=4.5 and 4, however, the results suggest that the quantum critical point belongs to a non-mean-field universality class. Further simulations indicate that the quantum critical point remains mean-field-like if λ>5, but it continuously deviates from the mean-field theory as λ becomes smaller.
Quantum phase transition of the transverse-field quantum Ising model on scale-free networks
Yi, Hangmo
2015-01-01
I investigate the quantum phase transition of the transverse-field quantum Ising model in which nearest neighbors are defined according to the connectivity of scale-free networks. Using a continuous-time quantum Monte Carlo simulation method and the finite-size scaling analysis, I identify the quantum critical point and study its scaling characteristics. For the degree exponent λ =6 , I obtain results that are consistent with the mean-field theory. For λ =4.5 and 4, however, the results suggest that the quantum critical point belongs to a non-mean-field universality class. Further simulations indicate that the quantum critical point remains mean-field-like if λ >5 , but it continuously deviates from the mean-field theory as λ becomes smaller.
Institute of Scientific and Technical Information of China (English)
Lu Jun
2004-01-01
The stationary-state nonlinear Schr(o)dinger equation, which models the dilute-gas Bose-Einstein condensate, is introduced within the framework of the quantum phase-space representation established by Torres-Vega and Frederick.The exact solutions of equation are obtained in the phase space, by means of the wave-mechanics method. The the phase space eigenfunctions. The eigenfunction with a hypersecant part is discussed as an example.
Quantum Chemistry via Walks in Determinant Space
Energy Technology Data Exchange (ETDEWEB)
Umrigar, Cyrus J. [Cornell Univ., Ithaca, NY (United States)
2016-01-05
There are many chemical questions of practical interest to the DOE that could be answered if there were an electronic structure method that provided consistently accurate results for all systems at an affordable computational cost. The coupled cluster method with single, double and perturbative triple excitations (CCSD(T)) is the most frequently used high-order method, but it has known deficiencies, e.g., in the description of stretched bonds. The full configuration interaction (FCI) method is the most robust method for treating electronic correlations, but it is little used because its computational cost scales exponentially in the size of the system. The largest calculation that has been done to date employed 10 billion determinants. In this regard, there was a major advance in 2010. The Alavi group at Cambridge University developed a stochastic approach to FCI --- combining it with ideas from quantum Monte Carlo (QMC) --- called FCIQMC, that allows one to go to a far larger number of determinants in certain circumstances. The computational cost is exponential in the system and basis size but with a much reduced exponent compared to conventional FCI. In this project Umrigar's group made several major improvements to the FCIQMC method that increased its efficiency by many orders of magnitude. In addition this project resulted in a cross-fertilization of ideas between the FCIQMC method, the older phaseless auxilliary-field quantum Monte Carlo (AFQMC) method developed by Zhang and Krakauer (two of the PI's of this project), and symmetry-restored wavefunctions developed by Scuseria (also a PI of this project).
Computed Tomography of Transverse Phase Space
Energy Technology Data Exchange (ETDEWEB)
Watts, A. [Fermilab; Johnstone, C. [Fermilab; Johnstone, J. [Fermilab
2016-09-19
Two computed tomography techniques are explored to reconstruct beam transverse phase space using both simulated beam and multi-wire profile data in the Fermilab Muon Test Area ("MTA") beamline. Both Filtered Back-Projection ("FBP") and Simultaneous Algebraic Reconstruction Technique ("SART") algorithms [2] are considered and compared. Errors and artifacts are compared as a function of each algorithm’s free parameters, and it is shown through simulation and MTA beamline profiles that SART is advantageous for reconstructions with limited profile data.
Noncanonical Phase-Space Noncommutative Black Holes
Bastos, Catarina; Dias, Nuno; Prata, João
2012-01-01
In this contribution we present a noncanonical phase-space noncommutative (NC) extension of a Kantowski Sachs (KS) cosmological model to describe the interior of a Schwarzschild black hole (BH). We evaluate the thermodynamical quantities inside this NC Schwarzschild BH and compare with the well known quantities. We find that for a NCBH the temperature and entropy have the same mass dependence as the Hawking quantities for a Schwarzschild BH.
Modulated phases of graphene quantum Hall polariton fluids
Pellegrino, Francesco M. D.; Giovannetti, Vittorio; MacDonald, Allan H.; Polini, Marco
2016-11-01
There is a growing experimental interest in coupling cavity photons to the cyclotron resonance excitations of electron liquids in high-mobility semiconductor quantum wells or graphene sheets. These media offer unique platforms to carry out fundamental studies of exciton-polariton condensation and cavity quantum electrodynamics in a regime, in which electron-electron interactions are expected to play a pivotal role. Here, focusing on graphene, we present a theoretical study of the impact of electron-electron interactions on a quantum Hall polariton fluid, that is a fluid of magneto-excitons resonantly coupled to cavity photons. We show that electron-electron interactions are responsible for an instability of graphene integer quantum Hall polariton fluids towards a modulated phase. We demonstrate that this phase can be detected by measuring the collective excitation spectra, which is often at a characteristic wave vector of the order of the inverse magnetic length.
Spin dynamics and spin freezing at ferromagnetic quantum phase transitions
Schmakat, P.; Wagner, M.; Ritz, R.; Bauer, A.; Brando, M.; Deppe, M.; Duncan, W.; Duvinage, C.; Franz, C.; Geibel, C.; Grosche, F. M.; Hirschberger, M.; Hradil, K.; Meven, M.; Neubauer, A.; Schulz, M.; Senyshyn, A.; Süllow, S.; Pedersen, B.; Böni, P.; Pfleiderer, C.
2015-07-01
We report selected experimental results on the spin dynamics and spin freezing at ferromagnetic quantum phase transitions to illustrate some of the most prominent escape routes by which ferromagnetic quantum criticality is avoided in real materials. In the transition metal Heusler compound Fe2TiSn we observe evidence for incipient ferromagnetic quantum criticality. High pressure studies in MnSi reveal empirical evidence for a topological non-Fermi liquid state without quantum criticality. Single crystals of the hexagonal Laves phase compound Nb1- y Fe2+ y provide evidence of a ferromagnetic to spin density wave transition as a function of slight compositional changes. Last but not least, neutron depolarisation imaging in CePd1- x Rh x underscore evidence taken from the bulk properties of the formation of a Kondo cluster glass.
Berry phase jumps and giant nonreciprocity in Dirac quantum dots
Rodriguez-Nieva, Joaquin F.; Levitov, Leonid S.
2016-12-01
We predict that a strong nonreciprocity in the resonance spectra of Dirac quantum dots can be induced by the Berry phase. The nonreciprocity arises in relatively weak magnetic fields and is manifest in anomalously large field-induced splittings of quantum dot resonances which are degenerate at B =0 due to time-reversal symmetry. This exotic behavior, which is governed by field-induced jumps in the Berry phase of confined electronic states, is unique to quantum dots in Dirac materials and is absent in conventional quantum dots. The effect is strong for gapless Dirac particles and can overwhelm the B -induced orbital and Zeeman splittings. A finite Dirac mass suppresses the effect. The nonreciprocity, predicted for generic two-dimensional Dirac materials, is accessible through Faraday and Kerr optical rotation measurements and scanning tunneling spectroscopy.
Chirp-driven giant phase space vortices
Trivedi, Pallavi; Ganesh, Rajaraman
2016-06-01
In a collisionless, unbounded, one-dimensional plasma, modelled using periodic boundary conditions, formation of steady state phase space coherent structures or phase space vortices (PSV) is investigated. Using a high resolution one-dimensional Vlasov-Poisson solver based on piecewise-parabolic advection scheme, the formation of giant PSV is addressed numerically. For an infinitesimal external drive amplitude and wavenumber k, we demonstrate the existence of a window of chirped external drive frequency that leads to the formation of giant PSV. The linear, small amplitude, external drive, when chirped, is shown to couple effectively to the plasma and increase both streaming of "untrapped" and "trapped" particle fraction. The steady state attained after the external drive is turned off and is shown to lead to a giant PSV with multiple extrema and phase velocities, with excess density fraction, defined as the deviation from the Maxwellian background, Δ n / n 0 ≃ 20 % - 25 % . It is shown that the process depends on the chirp time duration Δt. The excess density fraction Δn/n0, which contains both trapped and untrapped particle contribution, is also seen to scale with Δt, only inhibited by the gradient of the distribution in velocity space. Both single step drive and multistep chirp processes are shown to lead to steady state giant PSV, with multiple extrema due to embedded holes and clumps, long after the external drive is turned off.
The Geometry of Quantum Lens Spaces: Real Spectral Triples and Bundle Structure
Energy Technology Data Exchange (ETDEWEB)
Sitarz, Andrzej, E-mail: andrzej.sitarz@uj.edu.pl [Jagiellonian University, Institute of Physics (Poland); Venselaar, Jan Jitse, E-mail: jvensel1@gwdg.de [Georg-August Universität Göttingen, Mathematisches Institut (Germany)
2015-12-15
We study almost real spectral triples on quantum lens spaces, as orbit spaces of free actions of cyclic groups on the spectral geometry on the quantum group SU{sub q}(2). These spectral triples are given by weakening some of the conditions of a real spectral triple. We classify the irreducible almost real spectral triples on quantum lens spaces and we study unitary equivalences of such quantum lens spaces. Applying a useful characterization of principal U(1)-fibrations in noncommutative geometry, we show that all such quantum lens spaces are principal U(1)-fibrations over quantum teardrops.
A New Perspective on Path Integral Quantum Mechanics in Curved Space-Time
Directory of Open Access Journals (Sweden)
Singh Dinesh
2013-09-01
Full Text Available Abstract. A new approach to path integral quantum mechanics in curved space-time is presented for scalar particle propagation, expressed in terms of Lie transport and Fermi or Riemann normal co-ordinates to describe local curvature. While the presence of local curvature results in a strictly non-unitary representation of local time translation, the formalism nevertheless correctly recovers the free-particle Lagrangian in curved space-time, along with new terms that predict a simultaneous breakdown of time-reversal symmetry and a quantum violation of the weak equivalence principle at the particle’s Compton wavelength scale. Furthermore, the formalism reveals the prediction of a gauge-invariant phase factor interpreted as the gravitational Aharonov-Bohm effect and Berry’s phase.
The area quantum and Snyder space
Energy Technology Data Exchange (ETDEWEB)
Romero, Juan M. [Instituto de Ciencias Nucleares, Universidad Nacional Autonoma de Mexico, Apartado Postal 70-543, Mexico 04510 DF (Mexico)], E-mail: sanpedro@nucleares.unam.mx; Zamora, Adolfo [Departamento de Matematicas Aplicadas y Sistemas, Universidad Autonoma Metropolitana-Cuajimalpa, Mexico 01120 DF (Mexico)], E-mail: zamora@correo.cua.uam.mx
2008-03-13
We show that in the Snyder space the area of the disc and of the sphere can be quantized. It is also shown that the area spectrum of the sphere can be related to the Bekenstein conjecture for the area spectrum of a black hole horizon.
Mott glass phase in a diluted bilayer Heisenberg quantum antiferromagnet
Ma, Nv-Sen; Sandvik, Anders W.; Yao, Dao-Xin
2015-09-01
We use quantum Monte Carlo simulations to study a dimer-diluted S = 1/2 Heisenberg model on a bilayer square lattice with intralayer interaction J1 and interlayer interaction J2. Below the classical percolation threshold pc, the system has three phases reachable by tuning the interaction ratio g = J2/J1: a Néel ordered phase, a gapless quantum glass phase, and a gapped quantum paramagnetic phase. We present the ground-state phase diagram in the plane of dilution p and interaction ratio g. The quantum glass phase is certified to be of the gapless Mott glass type, having a uniform susceptibility vanishing at zero temperature T and following a stretched exponential form at T > 0; χu exp(-b/Tα) with α < 1. At the phase transition point from Neel ordered to Mott glass, we find that the critical exponents are different from those of the clean system described by the standard O(3) universality class in 2+1 dimensions.
Measurement of Phase Coherence in Space Turbulence
Belmont, G.; Panis, J.; Rezeau, L.; Sahraoui, F.
2008-12-01
In many space plasmas such as Magnetosheath, intense magnetic fluctuations are permanently observed, with power law spectra. Assuming these fluctuations belong to some kind of turbulence, which can legitimately be suspected, spectra are clearly not sufficient to characterize it. Is this turbulence made of non linear "phase-coherent" structures, like in the classical Kolmogorov image, or is it made of incoherent waves as in weak turbulence? Is it homogeneous in space and scales or is it intermittent? " Many methods allow analyzing the statistical properties of turbulence, and the results obtained by tools such as structure functions or wavelets are of course influenced by all these properties, such providing indirect information about them. But few of them are specifically dedicated to the study of phase coherence so that the consequences that can be inferred from them are generally not univocal for this point of view. We will review those few tools existing in the literature that allow measuring more directly the phase coherence and present a new method, called "phase gradient analysis", which we are presently developing for this analysis. Preliminary results of this new tool will be presented.
Realizing quantum controlled phase flip through cavity QED
Xiao, Yun-Feng; Lin, Xiu-Min; Gao, Jie; Yang, Yong; Han, Zheng-Fu; Guo, Guang-Can
2004-10-01
We propose a scheme to realize quantum controlled phase flip (CPF) between two rare-earth ions embedded in the respective microsphere cavity via interacting with a single-photon pulse in sequence. The numerical simulations illuminate that the CPF gate between ions is robust and scalable with extremely high fidelity and low error rate. Our scheme is more applicable than other schemes presented before based on current laboratory cavity-QED technology, and it is possible to be used as an applied unit gate in future quantum computation and quantum communication.
Realizing Quantum Controlled Phase Flip through Cavity-QED
Xiao, Y F; Gao, J; Yang, Y; Han, Z F; Guo, G C; Xiao, Yun-Feng; Lin, Xiu-Min; Gao, Jie; Yang, Yong; Han, Zheng-Fu; Guo, Guang-Can
2004-01-01
We propose a scheme to realize quantum controlled phase flip (CPF) between two rare earth ions embedded in respective microsphere cavity via interacting with a single-photon pulse in sequence. The numerical simulations illuminate that the CPF gate between ions is robust and scalable with extremely high fidelity and low error rate. Our scheme is more applicable than other schemes presented before based on current laboratory cavity-QED technology, and it is possible to be used as an applied unit gate in future quantum computation and quantum communication.
Topological Effects on Quantum Phase Slips in Superfluid Spin Transport
Kim, Se Kwon; Tserkovnyak, Yaroslav
2016-03-01
We theoretically investigate effects of quantum fluctuations on superfluid spin transport through easy-plane quantum antiferromagnetic spin chains in the large-spin limit. Quantum fluctuations result in the decaying spin supercurrent by unwinding the magnetic order parameter within the easy plane, which is referred to as phase slips. We show that the topological term in the nonlinear sigma model for the spin chains qualitatively differentiates the decaying rate of the spin supercurrent between the integer versus half-odd-integer spin chains. An experimental setup for a magnetoelectric circuit is proposed, in which the dependence of the decaying rate on constituent spins can be verified by measuring the nonlocal magnetoresistance.
Real-space imaging of fractional quantum Hall liquids.
Hayakawa, Junichiro; Muraki, Koji; Yusa, Go
2013-01-01
Electrons in semiconductors usually behave like a gas--as independent particles. However, when confined to two dimensions under a perpendicular magnetic field at low temperatures, they condense into an incompressible quantum liquid. This phenomenon, known as the fractional quantum Hall (FQH) effect, is a quantum-mechanical manifestation of the macroscopic behaviour of correlated electrons that arises when the Landau-level filling factor is a rational fraction. However, the diverse microscopic interactions responsible for its emergence have been hidden by its universality and macroscopic nature. Here, we report real-space imaging of FQH liquids, achieved with polarization-sensitive scanning optical microscopy using trions (charged excitons) as a local probe for electron spin polarization. When the FQH ground state is spin-polarized, the triplet/singlet intensity map exhibits a spatial pattern that mirrors the intrinsic disorder potential, which is interpreted as a mapping of compressible and incompressible electron liquids. In contrast, when FQH ground states with different spin polarization coexist, domain structures with spontaneous quasi-long-range order emerge, which can be reproduced remarkably well from the disorder patterns using a two-dimensional random-field Ising model. Our results constitute the first reported real-space observation of quantum liquids in a class of broken symmetry state known as the quantum Hall ferromagnet.
Quantum kinematics on q-deformed quantum spaces I, Mathematical Framework
Wachter, H
2006-01-01
The aim of these two papers (I and II) is to try to give fundamental concepts of quantum kinematics to q-deformed quantum spaces. Paper I introduces the relevant mathematical concepts. A short review of the basic ideas of q-deformed analysis is given. These considerations are continued by introducing q-deformed analogs of Fourier transformations and delta functions. Their properties are discussed in detail. Furthermore, q-deformed versions of sesquilinear forms are defined, their basic properties are derived, and q-analogs of the Fourier-Plancherel identity are proved. In paper II these reasonings are applied to wave functions on position and momentum space.
Characterization of optical quantum circuits using resonant phase shifts
Poot, Menno
2016-01-01
We demonstrate that important information about linear optical circuits can be obtained through the phase shift induced by integrated optical resonators. As a proof of principle, the phase of an unbalanced Mach-Zehnder interferometer is determined. Then the method is applied to a complex optical circuit designed for linear optical quantum computation. In this controlled-NOT gate with qubit initialization and tomography stages, the relative phases are determined as well as the coupling ratios of its directional couplers.
Hexatic and Microemulsion Phases in the 2d Quantum Plasma
Clark, Bryan; Casula, Michele; Ceperley, David
2009-03-01
It has been long known that the two-dimensional one component plasma supports both a Wigner-crystal and liquid phase. Classically [1,2], it is known that a hexatic phase exists but it is not known how this hexatic phase extends into the quantum regime. Moreover, at low temperature, phenomenological arguments [3] from Jamei, et. al. suggest the existence of microemulsion phases including stripes and bubbles. We use diffusion and path integral Monte Carlo to map out this phase diagram. We are able to extend the hexatic phase into the quantum regime as well as quantify the nature of the defects and exponents in the long range quantum system. We also specify the the nature, extent and existence (or lack thereof) of the expected low-T microemulsion phases. [0pt] [1] Muto, S. & Aoki, H. Crystallization of a classical two-dimensional electron system: Positional and orientational orders. Phys. Rev. B 59, 14911(1999).[0pt] [2] He, W.J. et al. Phase transition in a classical two-dimensional electron system. Phys. Rev. B 68, 195104(2003).[0pt] [3] Jamei, R., Kivelson, S. & Spivak, B. Universal Aspects of Coulomb-Frustrated Phase Separation. Phys. Rev. Lett. 94, 056805-4(2005).
Dissipation-driven quantum phase transitions in collective spin systems
Energy Technology Data Exchange (ETDEWEB)
Morrison, S [Institute for Theoretical Physics, University of Innsbruck, A-6020 Innsbruck (Austria); Parkins, A S [Department of Physics, University of Auckland, Private Bag 92019, Auckland (New Zealand)], E-mail: smor161@aucklanduni.ac.nz
2008-10-14
We consider two different collective spin systems subjected to strong dissipation-on the same scale as interaction strengths and external fields-and show that either continuous or discontinuous dissipative quantum phase transitions can occur as the dissipation strength is varied. First, we consider a well-known model of cooperative resonance fluorescence that can exhibit a second-order quantum phase transition, and analyse the entanglement properties near the critical point. Next, we examine a dissipative version of the Lipkin-Meshkov-Glick interacting collective spin model, where we find that either first- or second-order quantum phase transitions can occur, depending only on the ratio of the interaction and external field parameters. We give detailed results and interpretation for the steady-state entanglement in the vicinity of the critical point, where it reaches a maximum. For the first-order transition we find that the semiclassical steady states exhibit a region of bistability. (fast track communication)
Quantum turing machine and brain model represented by Fock space
Iriyama, Satoshi; Ohya, Masanori
2016-05-01
The adaptive dynamics is known as a new mathematics to treat with a complex phenomena, for example, chaos, quantum algorithm and psychological phenomena. In this paper, we briefly review the notion of the adaptive dynamics, and explain the definition of the generalized Turing machine (GTM) and recognition process represented by the Fock space. Moreover, we show that there exists the quantum channel which is described by the GKSL master equation to achieve the Chaos Amplifier used in [M. Ohya and I. V. Volovich, J. Opt. B 5(6) (2003) 639., M. Ohya and I. V. Volovich, Rep. Math. Phys. 52(1) (2003) 25.
Unified Description of Quantum Mechanics on a Curved Space
Nakamura, M
2014-01-01
Starting with the first-order singular Lagrangian, the problem of the quantization of a dynamical system constrained to a submanifold embedded in the higher-dimensional Euclidean space is investigated within the framework of operatorial quantization formalism. Through the projection operator method (POM) with the constraint star-products, it is shown that both of the constraint quantum system with the usual constraint and that with the derivative-type constraint are naturally constructed from one Lagarangian. It is proved that the system with the usual constraint is the sub-system of that with the derivative-type one. Furthermore, the quantum corrections in the resultant Hamiltonians are discussed.
Aspects of quantum field theory in curved space-time
Energy Technology Data Exchange (ETDEWEB)
Fulling, S.A. (Texas A and M Univ., College Station, TX (USA). Dept. of Mathematics)
1989-01-01
The theory of quantum fields on curved spacetimes has attracted great attention since the discovery, by Stephen Hawking, of black-hole evaporation. It remains an important subject for the understanding of such contemporary topics as inflationary cosmology, quantum gravity and superstring theory. The topics covered include normal-mode expansions for a general elliptic operator, Fock space, the Casimir effect, the Klein 'paradox', particle definition and particle creation in expanding universes, asymptotic expansion of Green's functions and heat kernels, and renormalization of the stress tensor. (author).
Number-Phase Wigner Representation for Scalable Stochastic Simulations of Controlled Quantum Systems
Hush, M R; Hope, J J
2011-01-01
Simulation of conditional master equations is important to describe systems under continuous measurement and for the design of control strategies in quantum systems. For large bosonic systems, such as BEC and atom lasers, full quantum field simulations must rely on scalable stochastic methods whose convergence time is restricted by the use of representations based on coherent states. Here we show that typical measurements on atom-optical systems have a common form that allows for an efficient simulation using the number-phase Wigner (NPW) phase-space representation. We demonstrate that a stochastic method based on the NPW can converge over an order of magnitude longer and more precisely than its coherent equivalent. This opens the possibility of realistic simulations of controlled multi-mode quantum systems.
Regular and chaotic classical dynamics in the U(5)-SU(3) quantum phase transition of the IBM
Macek, M
2012-01-01
We study the classical dynamics in a generic first-order quantum phase transition between the U(5) and SU(3) limits of the interacting boson model. The dynamics is chaotic, of H\\'enon-Heiles type, in the spherical phase and is regular, yet sensitive to local degeneracies, in the deformed phase. Both types of dynamics persist in the coexistence region resulting in a divided phase space.
General Quantum Modeling of Combining Concepts: A Quantum Field Model in Fock Space
Aerts, Diederik
2007-01-01
We extend a quantum model in Hilbert space developed in Aerts (2007a) into a quantum field theoric model in Fock space for the modeling of the combination of concepts. Items and concepts are represented by vectors in Fock space and membership weights of items are modeled by quantum probabilities. We apply this theory to model the disjunction of concepts and show that the predictions of our theory for the membership weights of items regarding the disjunction of concepts match with great accuracy the complete set of results of an experiment conducted by Hampton (1988b). It are the quantum effects of interference and superposition of that are at the origin of the effects of overextension and underextension observed by Hampton as deviations from a classical use of the disjunction. It is essential for the perfect matches we obtain between the predictions of the quantum field model and Hampton's experimental data that items can be in superpositions of `different numbers states' which proves that the genuine structu...
Quantum Phase Analysis of Field-Free Molecular Alignment
Yun, Sang Jae; Lee, Jongmin; Nam, Chang Hee
2015-01-01
We present quantum mechanical explanations for unresolved phenomena observed in field-free molecular alignment by a femtosecond laser pulse. Quantum phase analysis of molecular rotational states reveals the physical origin of the following phenomena: strong alignment peaks appear periodically, and the temporal shape of each alignment peak changes in an orderly fashion depending on molecular species; the strongest alignment is not achieved at the first peak; the transition between aligned and anti-aligned states is very fast compared to the time scale of rotational dynamics. These features are understood in a unified way analogous to that describing a carrier-envelope-phase-stabilized mode-locked laser.
Anomalous phase shift in a twisted quantum loop
Energy Technology Data Exchange (ETDEWEB)
Taira, Hisao [Division of Applied Physics, Graduate School of Engineering, Hokkaido University, Sapporo, Hokkaido 060-8628 (Japan); Shima, Hiroyuki, E-mail: taira@eng.hokudai.ac.j [Department of Applied Mathematics 3, LaCaN, Universitat Politecnica de Catalunya (UPC), Barcelona 08034 (Spain)
2010-09-03
The coherent motion of electrons in a twisted quantum ring is considered to explore the effect of torsion inherent to the ring. Internal torsion of the ring composed of helical atomic configuration yields a non-trivial quantum phase shift in the electrons' eigenstates. This torsion-induced phase shift causes novel kinds of persistent current flow and an Aharonov-Bohm-like conductance oscillation. The two phenomena can occur even when no magnetic flux penetrates inside the twisted ring, thus being in complete contrast with the counterparts observed in untwisted rings.
nLukac, Maarti; Kameyama, Michitaka
2011-01-01
It has been experimentally proven that realizing universal quantum gates using higher-radices logic is practically and technologically possible. We developed a Parallel Genetic Algorithm that synthesizes Boolean reversible circuits realized with a variety of quantum gates on qudits with various radices. In order to allow synthesizing circuits of medium sizes in the higher radix quantum space we performed the experiments using a GPU accelerated Genetic Algorithm. Using the accelerated GA we compare heuristic improvements to the mutation process based on cost minimization, on the adaptive cost of the primitives and improvements due to Baldwinian vs. Lamarckian GA. We also describe various fitness function formulations that allowed for various realizations of well known universal Boolean reversible or quantum-probabilistic circuits.
Effects of quantum space time foam in the neutrino sector
Klapdor-Kleingrothaus, H V; Sarkar, U
2000-01-01
We discuss violations of CPT and quantum mechanics due to interactions of neutrinos with space-time quantum foam. Neutrinoless double beta decay and oscillations of neutrinos from astrophysical sources (supernovae, active galactic nuclei) are analysed. It is found that the propagation distance is the crucial quantity entering any bounds on EHNS parameters. Thus, while the bounds from neutrinoless double beta decay are not significant, the data of the supernova 1987a imply a bound being several orders of magnitude more stringent than the ones known from the literature. Even more stringent limits may be obtained from the investigation of neutrino oscillations from active galactic nuclei sources, which have an impressive potential for the search of quantum foam interactions in the neutrino sector.
A Quantum Probability Explanation in Fock Space for Borderline Contradictions
Sozzo, Sandro
2013-01-01
The construction of a consistent theory for structuring and representing how concepts combine and interact is one of the main challenges for the scholars involved in cognitive studies. All traditional approaches are still facing serious hindrances when dealing with combinations of concepts and concept vagueness. One of the main consequences of these difficulties is the existence of borderline cases which is hardly explainable from the point of view of classical (fuzzy set) logic and probability theory. Resting on a quantum-theoretic approach which successfully models conjunctions and disjuncions of two concepts, we propound a quantum probability model in Fock space which faithfully reproduces the experimental data collected by Alxatib and Pelletier (2011) on borderline contradictions. Our model allows one to explain the occurrence of the latter contradictions in terms of genuine quantum effects, such as contextuality, superposition, interference and emergence. In particular, we claim that it is the specific m...
New Dynamical Scaling Universality for Quantum Networks Across Adiabatic Quantum Phase Transitions
Acevedo, Oscar L.; Rodriguez, Ferney J.; Quiroga, Luis; Johnson, Neil F.; Rey, Ana M.
2014-05-01
We reveal universal dynamical scaling behavior across adiabatic quantum phase transitions in networks ranging from traditional spatial systems (Ising model) to fully connected ones (Dicke and Lipkin-Meshkov-Glick models). Our findings, which lie beyond traditional critical exponent analysis and adiabatic perturbation approximations, are applicable even where excitations have not yet stabilized and, hence, provide a time-resolved understanding of quantum phase transitions encompassing a wide range of adiabatic regimes. We show explicitly that even though two systems may traditionally belong to the same universality class, they can have very different adiabatic evolutions. This implies that more stringent conditions need to be imposed than at present, both for quantum simulations where one system is used to simulate the other and for adiabatic quantum computing schemes.
Space-based research in fundamental physics and quantum technologies
Turyshev, S G; Shao, M; Yu, N; Kusenko, A; Wright, E L; Everitt, C W F; Kasevich, M A; Lipa, J A; Mester, J C; Reasenberg, R D; Walsworth, R L; Ashby, N; Gould, H; Paik, H -J
2007-01-01
Space-based experiments today can uniquely address important questions related to the fundamental laws of Nature. In particular, high-accuracy physics experiments in space can test relativistic gravity and probe the physics beyond the Standard Model; they can perform direct detection of gravitational waves and are naturally suited for precision investigations in cosmology and astroparticle physics. In addition, atomic physics has recently shown substantial progress in the development of optical clocks and atom interferometers. If placed in space, these instruments could turn into powerful high-resolution quantum sensors greatly benefiting fundamental physics. We discuss the current status of space-based research in fundamental physics, its discovery potential, and its importance for modern science. We offer a set of recommendations to be considered by the upcoming National Academy of Sciences' Decadal Survey in Astronomy and Astrophysics. In our opinion, the Decadal Survey should include space-based research ...
Non Hermitian quantum mechanics in non commutative space
Giri, Pulak Ranjan
2008-01-01
We study non Hermitian quantum systems in noncommutative space as well as a \\cal{PT} symmetric deformation of this space. Specifically, a \\mathcal{PT}-symmetric harmonic oscillator together with iC(x_1+x_2) interaction is discussed in this space and solutions are obtained. It is shown that in the \\cal{PT} deformed noncommutative space the Hamiltonian may or may not possess real eigenvalues depending on the choice of the noncommutative parameters. However, it is shown that in standard noncommutative space, the iC(x_1+x_2) interaction generates only real eigenvalues despite the fact that the Hamiltonian is not \\mathcal{PT}-symmetric. A complex interacting anisotropic oscillator system has also been discussed.
Quantum-optical states in finite-dimensional Hilbert space; 1, General formalism
Miranowicz, A; Imoto, N; Miranowicz, Adam; Leonski, Wieslaw; Imoto, Nobuyuki
2001-01-01
The interest in quantum-optical states confined in finite-dimensional Hilbert spaces has recently been stimulated by the progress in quantum computing, quantum-optical state preparation and measurement techniques, in particular, by the development of the discrete quantum-state tomography. In the first part of our review we present two essentially different approaches to define harmonic oscillator states in the finite-dimensional Hilbert spaces. One of them is related to the truncation scheme of Pegg, Phillips and Barnett [Phys. Rev. Lett. 81, 1604 (1998)] -- the so-called quantum scissors device. The second method corresponds to the truncation scheme of Leo\\'nski and Tana\\'s [Phys. Rev. A 49, R20 (1994)]. We propose some new definitions of the states related to these truncation schemes and find their explicit forms in the Fock representation. We discuss finite-dimensional generalizations of coherent states, phase coherent states, displaced number states, Schr\\"odinger cats, and squeezed vacuum. We show some i...
Phase transition of light on complex quantum networks.
Halu, Arda; Garnerone, Silvano; Vezzani, Alessandro; Bianconi, Ginestra
2013-02-01
Recent advances in quantum optics and atomic physics allow for an unprecedented level of control over light-matter interactions, which can be exploited to investigate new physical phenomena. In this work we are interested in the role played by the topology of quantum networks describing coupled optical cavities and local atomic degrees of freedom. In particular, using a mean-field approximation, we study the phase diagram of the Jaynes-Cummings-Hubbard model on complex networks topologies, and we characterize the transition between a Mott-like phase of localized polaritons and a superfluid phase. We found that, for complex topologies, the phase diagram is nontrivial and well defined in the thermodynamic limit only if the hopping coefficient scales like the inverse of the maximal eigenvalue of the adjacency matrix of the network. Furthermore we provide numerical evidences that, for some complex network topologies, this scaling implies an asymptotically vanishing hopping coefficient in the limit of large network sizes. The latter result suggests the interesting possibility of observing quantum phase transitions of light on complex quantum networks even with very small couplings between the optical cavities.
The symplectic camel and phase space quantization
Energy Technology Data Exchange (ETDEWEB)
Gosson, Maurice de [Blekinge Institute of Technology, Karlskrona (Sweden)
2001-11-30
We show that a result of symplectic topology, Gromov's non-squeezing theorem, also known as the 'principle of the symplectic camel', can be used to quantize phase space in cells. That quantization scheme leads to the correct energy levels for integrable systems and to Maslov quantization of Lagrangian manifolds by purely topological arguments. We finally show that the argument leading to the proof of the non-squeezing theorem leads to a classical form of Heisenberg's inequalities. (author)
Dissipative fragmentation in a phase space approach
Energy Technology Data Exchange (ETDEWEB)
Adorno, A.; Di Toro, M.; Bonasera, A.; Gregoire, C.; Gulminelli, F.
Semi-classical approaches have evidenced the role of one and two-body dissipation in nucleus-nucleus collisions. On the other hand, a substantial energy dissipation and some angular momentum transfer have been observed at moderate energy where a fragmentation process is the dominant reaction mechanism. In order to analyse main features of these reactions, we developed a phenomenological model taking into account phase space constraints. The transition between deep inelastic collisions and abrasion-like fragmentation is described and a general agreement with available data is found.
Experimental Observations of Ion Phase-Space Vortices
DEFF Research Database (Denmark)
Pécseli, Hans; Armstrong, R. J.; Trulsen, J.
1981-01-01
Experimental observations of ion phase-space vortices are reported. The ion phase-space vortices form in the region of heated ions behind electrostatic ion acoustic shocks. The results are in qualitative agreement with numerical and analytic studies....
Phase-controlled entanglement in a quantum-beat laser: application to quantum lithography
Sete, Eyob A.; Dorfman, Konstantin E.; Dowling, Jonathan P.
2011-11-01
We study entanglement generation and control in a quantum-beat laser coupled to a two-mode squeezed vacuum reservoir. We show that the generated entanglement is robust against cavity losses and environmental decoherence and can be controlled by tuning the phases of the microwave and the squeezed input fields. Moreover, we discuss two-photon correlations, absorption and implementations in quantum optical lithography.
Absorbing State Phase Transition with Competing Quantum and Classical Fluctuations
Marcuzzi, Matteo; Buchhold, Michael; Diehl, Sebastian; Lesanovsky, Igor
2016-06-01
Stochastic processes with absorbing states feature examples of nonequilibrium universal phenomena. While the classical regime has been thoroughly investigated in the past, relatively little is known about the behavior of these nonequilibrium systems in the presence of quantum fluctuations. Here, we theoretically address such a scenario in an open quantum spin model which, in its classical limit, undergoes a directed percolation phase transition. By mapping the problem to a nonequilibrium field theory, we show that the introduction of quantum fluctuations stemming from coherent, rather than statistical, spin flips alters the nature of the transition such that it becomes first order. In the intermediate regime, where classical and quantum dynamics compete on equal terms, we highlight the presence of a bicritical point with universal features different from the directed percolation class in a low dimension. We finally propose how this physics could be explored within gases of interacting atoms excited to Rydberg states.
Black holes as critical point of quantum phase transition.
Dvali, Gia; Gomez, Cesar
We reformulate the quantum black hole portrait in the language of modern condensed matter physics. We show that black holes can be understood as a graviton Bose-Einstein condensate at the critical point of a quantum phase transition, identical to what has been observed in systems of cold atoms. The Bogoliubov modes that become degenerate and nearly gapless at this point are the holographic quantum degrees of freedom responsible for the black hole entropy and the information storage. They have no (semi)classical counterparts and become inaccessible in this limit. These findings indicate a deep connection between the seemingly remote systems and suggest a new quantum foundation of holography. They also open an intriguing possibility of simulating black hole information processing in table-top labs.
Black holes as critical point of quantum phase transition
Energy Technology Data Exchange (ETDEWEB)
Dvali, Gia [Arnold Sommerfeld Center for Theoretical Physics, Department fuer Physik, Ludwig-Maximilians-Universitaet Muenchen, Muenchen (Germany); Max-Planck-Institut fuer Physik, Muenchen (Germany); CERN, Theory Department, Geneva 23 (Switzerland); New York University, Department of Physics, Center for Cosmology and Particle Physics, New York, NY (United States); Gomez, Cesar [Arnold Sommerfeld Center for Theoretical Physics, Department fuer Physik, Ludwig-Maximilians-Universitaet Muenchen, Muenchen (Germany); Universidad Autonoma de Madrid, Instituto de Fisica Teorica UAM-CSIC, C-XVI, Madrid (Spain)
2014-02-15
We reformulate the quantum black hole portrait in the language of modern condensed matter physics. We show that black holes can be understood as a graviton Bose-Einstein condensate at the critical point of a quantum phase transition, identical to what has been observed in systems of cold atoms. The Bogoliubov modes that become degenerate and nearly gapless at this point are the holographic quantum degrees of freedom responsible for the black hole entropy and the information storage. They have no (semi)classical counterparts and become inaccessible in this limit. These findings indicate a deep connection between the seemingly remote systems and suggest a new quantum foundation of holography. They also open an intriguing possibility of simulating black hole information processing in table-top labs. (orig.)
Characterizing quantum phase transitions by single qubit operations
Giampaolo, S M; De Siena, S
2006-01-01
We introduce observable quantities, borrowing from concepts of quantum information theory, for the characterization of quantum phase transitions in spin systems. These observables are uniquely defined in terms of single spin unitary operations. We define the energy gap between the ground state and the state produced by the action of a single-qubit local gate. We show that this static quantity involves only single-site expectations and two-point correlation functions on the ground state. We then discuss a dynamical local observable defined as the acceleration of quantum state evolution after performing an instaneous single-qubit perturbation on the ground state. This quantity involves three-point correlations as well. We show that both the static and the dynamical observables detect and characterize completely quantum critical points in a class of spin systems.
Black Holes as Critical Point of Quantum Phase Transition
Dvali, Gia
2014-01-01
We reformulate the quantum black hole portrait in the language of modern condensed matter physics. We show that black holes can be understood as a graviton Bose-Einstein condensate at the critical point of a quantum phase transition, identical to what has been observed in systems of cold atoms. The Bogoliubov modes that become degenerate and nearly gapless at this point are the holographic quantum degrees of freedom responsible for the black hole entropy and the information storage. They have no (semi)classical counterparts and become inaccessible in this limit. These findings indicate a deep connection between the seemingly remote systems and suggest a new quantum foundation of holography. They also open an intriguing possibility of simulating black hole information processing in table-top labs.
Black holes as critical point of quantum phase transition
Dvali, Gia; Gomez, Cesar
2014-02-01
We reformulate the quantum black hole portrait in the language of modern condensed matter physics. We show that black holes can be understood as a graviton Bose-Einstein condensate at the critical point of a quantum phase transition, identical to what has been observed in systems of cold atoms. The Bogoliubov modes that become degenerate and nearly gapless at this point are the holographic quantum degrees of freedom responsible for the black hole entropy and the information storage. They have no (semi)classical counterparts and become inaccessible in this limit. These findings indicate a deep connection between the seemingly remote systems and suggest a new quantum foundation of holography. They also open an intriguing possibility of simulating black hole information processing in table-top labs.
Space Transportation Engine Program (STEP), phase B
1990-10-01
The Space Transportation Engine Program (STEP) Phase 2 effort includes preliminary design and activities plan preparation that will allow smooth and time transition into a Prototype Phase and then into Phases 3, 4, and 5. A Concurrent Engineering approach using Total Quality Management (TQM) techniques, is being applied to define an oxygen-hydrogen engine. The baseline from Phase 1/1' studies was used as a point of departure for trade studies and analyses. Existing STME system models are being enhanced as more detailed module/component characteristics are determined. Preliminary designs for the open expander, closed expander, and gas generator cycles were prepared, and recommendations for cycle selection made at the Design Concept Review (DCR). As a result of July '90 DCR, and information subsequently supplied to the Technical Review Team, a gas generator cycle was selected. Results of the various Advanced Development Programs (ADP's) for the Advanced Launch Systems (ALS) were contributive to this effort. An active vehicle integration effort is supplying the NASA, Air Force, and vehicle contractors with engine parameters and data, and flowing down appropriate vehicle requirements. Engine design and analysis trade studies are being documented in a data base that was developed and is being used to organize information. To date, seventy four trade studies were input to the data base.
Renyi-Wehrl entropies as measures of localization in phase space
Gnutzmann, S; Gnutzmann, Sven; Zyczkowski, Karol
2001-01-01
We generalize the concept of the Wehrl entropy of quantum states which gives a basis-independent measure of their localization in phase space. We discuss the minimal values and the typical values of these R{enyi-Wehrl entropies for pure states for spin systems. According to Lieb's conjecture the minimal values are provided by the spin coherent states. Though Lieb's conjecture remains unproven, we give new proofs of partial results that may be generalized for other systems. We also investigate random pure states and calculate the mean Renyi-Wehrl entropies averaged over the natural measure in the space of pure quantum states.
Renyi-Wehrl entropies as measures of localization in phase space
Energy Technology Data Exchange (ETDEWEB)
Gnutzmann, Sven [Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot (Israel)]. E-mail: sven@gnutzmann.net; Zyczkowski, Karol [Centrum Fizyki Teoretycznej, Polska Akademia Nauk, Warszawa (Poland)]. E-mail: karol@theta1.cft.edu.pl
2001-11-30
We generalize the concept of the Wehrl entropy of quantum states which gives a basis-independent measure of their localization in phase space. We discuss the minimal values and the typical values of these Renyi-Wehrl entropies for pure states for spin systems. According to Lieb's conjecture the minimal values are provided by the spin coherent states. Though Lieb's conjecture remains unproven, we give new proofs of partial results that may be generalized for other systems. We also investigate random pure states and calculate the mean Renyi-Wehrl entropies averaged over the natural measure in the space of pure quantum states. (author)
Quantum phase transition in a common metal.
Yeh, A; Soh, Yeong-Ah; Brooke, J; Aeppli, G; Rosenbaum, T F; Hayden, S M
2002-10-03
The classical theory of solids, based on the quantum mechanics of single electrons moving in periodic potentials, provides an excellent description of substances ranging from semiconducting silicon to superconducting aluminium. Over the last fifteen years, it has become increasingly clear that there are substances for which the conventional approach fails. Among these are certain rare earth compounds and transition metal oxides, including high-temperature superconductors. A common feature of these materials is complexity, in the sense that they have relatively large unit cells containing heterogeneous mixtures of atoms. Although many explanations have been put forward for their anomalous properties, it is still possible that the classical theory might suffice. Here we show that a very common chromium alloy has some of the same peculiarities as the more exotic materials, including a quantum critical point, a strongly temperature-dependent Hall resistance and evidence for a 'pseudogap'. This implies that complexity is not a prerequisite for unconventional behaviour. Moreover, it should simplify the general task of explaining anomalous properties because chromium is a relatively simple system in which to work out in quantitative detail the consequences of the conventional theory of solids.
Quantum cryptography for secure free-space communications
Energy Technology Data Exchange (ETDEWEB)
Hughes, R.J.; Buttler, W.T.; Kwiat, P.G.; Lamoreaux, S.K.; Luther, G.G.; Morgan, G.L.; Nordholt, J.E.; Peterson, C.G.
1999-03-01
The secure distribution of the secret random bit sequences known as key material, is an essential precursor to their use for the encryption and decryption of confidential communications. Quantum cryptography is a new technique for secure key distribution with single-photon transmissions: Heisenberg`s uncertainty principle ensures that an adversary can neither successfully tap the key transmissions, nor evade detection (eavesdropping raises the key error rate above a threshold value). The authors have developed experimental quantum cryptography systems based on the transmission of non-orthogonal photon polarization states to generate shared key material over line-of-sight optical links. Key material is built up using the transmission of a single-photon per bit of an initial secret random sequence. A quantum-mechanically random subset of this sequence is identified, becoming the key material after a data reconciliation stage with the sender. The authors have developed and tested a free-space quantum key distribution (QKD) system over an outdoor optical path of {approximately}1 km at Los Alamos National Laboratory under nighttime conditions. Results show that free-space QKD can provide secure real-time key distribution between parties who have a need to communicate secretly. Finally, they examine the feasibility of surface to satellite QKD.
Free-Space Quantum Signatures Using Heterodyne Measurements
Croal, Callum; Peuntinger, Christian; Heim, Bettina; Khan, Imran; Marquardt, Christoph; Leuchs, Gerd; Wallden, Petros; Andersson, Erika; Korolkova, Natalia
2016-09-01
Digital signatures guarantee the authorship of electronic communications. Currently used "classical" signature schemes rely on unproven computational assumptions for security, while quantum signatures rely only on the laws of quantum mechanics to sign a classical message. Previous quantum signature schemes have used unambiguous quantum measurements. Such measurements, however, sometimes give no result, reducing the efficiency of the protocol. Here, we instead use heterodyne detection, which always gives a result, although there is always some uncertainty. We experimentally demonstrate feasibility in a real environment by distributing signature states through a noisy 1.6 km free-space channel. Our results show that continuous-variable heterodyne detection improves the signature rate for this type of scheme and therefore represents an interesting direction in the search for practical quantum signature schemes. For transmission values ranging from 100% to 10%, but otherwise assuming an ideal implementation with no other imperfections, the signature length is shorter by a factor of 2 to 10. As compared with previous relevant experimental realizations, the signature length in this implementation is several orders of magnitude shorter.
Free-Space Quantum Signatures Using Heterodyne Measurements.
Croal, Callum; Peuntinger, Christian; Heim, Bettina; Khan, Imran; Marquardt, Christoph; Leuchs, Gerd; Wallden, Petros; Andersson, Erika; Korolkova, Natalia
2016-09-02
Digital signatures guarantee the authorship of electronic communications. Currently used "classical" signature schemes rely on unproven computational assumptions for security, while quantum signatures rely only on the laws of quantum mechanics to sign a classical message. Previous quantum signature schemes have used unambiguous quantum measurements. Such measurements, however, sometimes give no result, reducing the efficiency of the protocol. Here, we instead use heterodyne detection, which always gives a result, although there is always some uncertainty. We experimentally demonstrate feasibility in a real environment by distributing signature states through a noisy 1.6 km free-space channel. Our results show that continuous-variable heterodyne detection improves the signature rate for this type of scheme and therefore represents an interesting direction in the search for practical quantum signature schemes. For transmission values ranging from 100% to 10%, but otherwise assuming an ideal implementation with no other imperfections, the signature length is shorter by a factor of 2 to 10. As compared with previous relevant experimental realizations, the signature length in this implementation is several orders of magnitude shorter.
Dynamic phase response and amplitude-phase coupling of self-assembled semiconductor quantum dots
Lingnau, Benjamin; Herzog, Bastian; Kolarczik, Mirco; Woggon, Ulrike; Lüdge, Kathy; Owschimikow, Nina
2017-06-01
The optical excitation of semiconductor gain media introduces both gain and refractive index changes, commonly referred to as amplitude-phase coupling. Quantum-confined structures with an energetically well separated carrier reservoir usually exhibit a decreased amplitude-phase coupling compared to bulk materials. However, its magnitude and definition is still controversially discussed. We investigate the fundamental processes influencing the amplitude-phase coupling in semiconductor quantum-dot media using a coupled-carrier rate-equation model. We are able to analyze the dependence on the electronic structure and suggest routes towards an optimization of the dynamic phase response of the gain material.
Emission energy control of semiconductor quantum dots using phase change material
Kanazawa, Shohei; Sato, Yu; Yamamura, Ariyoshi; Saiki, Toshiharu
2015-03-01
Semiconductor quantum dots have paid much attention as it is a promising candidate for quantum, optical devices, such as quantum computer and quantum dot laser. We propose a local emission energy control method of semiconductor quantum dots using applying strain by volume expansion of phase change material. Phase change material can change its phase crystalline to amorphous, and the volume expand by its phase change. This method can control energy shift direction and amount by amorphous religion and depth. Using this method, we matched emission energy of two InAs/InP quantum dots. This achievement can connect to observing superradiance phenomenon and quantum dot coupling effect.
Quantum Phase Transitions and Dimerized Phases in Frustrated Spin Ladder
Institute of Scientific and Technical Information of China (English)
WEN Rui; LIU Guang-Hua; TIAN Guang-Shan
2011-01-01
In this paper, we study the phase diagram of a frustrated spin ladder model by applying the bosonization technique and the density-matrix renormalization-group (DMRG) algorithm. Effect of the intra-chain next-nearestneighbor (NNN) super-exchange interaction is investigated in detail and the order parameters are calculated to detect the emergence of the dimerized phases. We find that the intra-chain NNN interaction plays a key role in inducing dimerized phases.
Falomir, H.; Pisani, P. A. G.; Vega, F.; Cárcamo, D.; Méndez, F.; Loewe, M.
2016-02-01
We study two-dimensional Hamiltonians in phase space with noncommutativity both in coordinates and momenta. We consider the generator of rotations on the noncommutative plane and the Lie algebra generated by Hermitian rotationally invariant quadratic forms of noncommutative dynamical variables. We show that two quantum phases are possible, characterized by the Lie algebras {sl}(2,{{R}}) or su(2) according to the relation between the noncommutativity parameters, with the rotation generator related with the Casimir operator. From this algebraic perspective, we analyze the spectrum of some simple models with nonrelativistic rotationally invariant Hamiltonians in this noncommutative phase space, such as the isotropic harmonic oscillator, the Landau problem and the cylindrical well potential.
Falomir, H; Vega, F; Cárcamo, D; Méndez, F; Loewe, M
2015-01-01
We study two-dimensional Hamiltonians in phase space with noncommutativity both in coordinates and momenta. We consider the generator of rotations on the noncommutative plane and the Lie algebra generated by Hermitian rotationally invariant quadratic forms of noncommutative dynamical variables. We show that two quantum phases are possible, characterized by the Lie algebras $sl(2,\\mathbb{R})$ or $su(2)$ according to the relation between the noncommutativity parameters. From this perspective, we analyze the spectrum of some simple models with nonrelativistic rotationally invariant Hamiltonians in this noncommutative phase space, as the isotropic harmonic oscillator, the Landau problem and the cylindrical well potential.
Measurement of the velocity of a quantum object: A role of phase and group velocities
Lapinski, Mikaila; Rostovtsev, Yuri V.
2017-08-01
We consider the motion of a quantum particle in a free space. Introducing an explicit measurement procedure for velocity, we demonstrate that the measured velocity is related to the group and phase velocities of the corresponding matter waves. We show that for long distances the measured velocity coincides with the matter wave group velocity. We discuss the possibilities to demonstrate these effects for the optical pulses in coherently driven media or for radiation propagating in waveguides.
Auto-compensating differential phase shift quantum key distribution
Han, X; Zhou, C; Zeng, H; Han, Xiaohong; Wu, Guang; Zhou, Chunyuan; Zeng, Heping
2005-01-01
We propose an auto-compensating differential phase shift scheme for quantum key distribution with a high key-creation efficiency, which skillfully makes use of automatic alignment of the photon polarization states in optical fiber with modified Michelson interferometers composed of unequal arms with Faraday mirrors at the ends. The Faraday-mirrors-based Michelson interferometers not only function as pulse splitters, but also enable inherent compensation of polarization mode dispersion in the optic-fiber paths at both Alice's and Bob's sites. The sequential pulses encoded by differential phase shifts pass through the quantum channel with the same polarization states, resulting in a stable key distribution immune to the polarization mode dispersion in the quantum channel. Such a system features perfect stability and higher key creation efficiency over traditional schemes.
Emergence of coherence and the dynamics of quantum phase transitions
Braun, Simon; Friesdorf, Mathis; Hodgman, Sean S.; Schreiber, Michael; Ronzheimer, Jens Philipp; Riera, Arnau; del Rey, Marco; Bloch, Immanuel; Eisert, Jens
2015-01-01
The dynamics of quantum phase transitions pose one of the most challenging problems in modern many-body physics. Here, we study a prototypical example in a clean and well-controlled ultracold atom setup by observing the emergence of coherence when crossing the Mott insulator to superfluid quantum phase transition. In the 1D Bose–Hubbard model, we find perfect agreement between experimental observations and numerical simulations for the resulting coherence length. We, thereby, perform a largely certified analog quantum simulation of this strongly correlated system reaching beyond the regime of free quasiparticles. Experimentally, we additionally explore the emergence of coherence in higher dimensions, where no classical simulations are available, as well as for negative temperatures. For intermediate quench velocities, we observe a power-law behavior of the coherence length, reminiscent of the Kibble–Zurek mechanism. However, we find nonuniversal exponents that cannot be captured by this mechanism or any other known model. PMID:25775515
Benford's Law: Detection of Quantum Phase Transitions similarly as Earthquakes
De, Aditi Sen
2011-01-01
More than a century earlier, it was predicted that the first significant digit appearing in a data, be it from natural sciences or from some mathematical series, will be nonuniformly distributed, with the number one appearing with the highest frequency. This law goes by the name of Benford's law. It has been observed to hold for data from a huge variety of sources, ranging from earthquakes to infectious disease cases. Quantum phase transitions are cooperative phenomena where qualitative changes occur in physical quantities of a many-body system at zero temperature. We find that Benford's law can be applied to detect quantum phase transitions in a way that is very similar to how it can distinguish earthquakes from background noise. Being certainly of very different physical origins, seismic activity and quantum cooperative phenomena may therefore be detected by similar methods. The result may provide methods to overcome the limitations associated with precise measurements in experiments.
Quantum Phase Transitions in Anti-ferromagnetic Planar Cubic Lattices
Wellard, C J; Wellard, Cameron; Orus, Roman
2004-01-01
Motivated by its relation to an NP-hard problem we analyze the ground state properties of anti-ferromagnetic Ising-spin networks in planar cubic lattices under the action of homogeneous transverse and longitudinal magnetic fields. We consider different instances of the cubic geometry and find a set of quantum phase transitions for each one of the systems, which we characterize by means of entanglement behavior and majorization theory. Entanglement scaling at the critical region is in agreement with results arising from conformal symmetry, therefore even the simplest planar systems can display very large amounts of quantum correlation. No conclusion can be made as to the scaling behavior of the minimum energy gap, with the data allowing equally good fits to exponential and power law decays. Analysis of entanglement and especially of majorization instead of the energy spectrum proves to be a good way of detecting quantum phase transitions in highly frustrated configurations.
Quantum product and parabolic orbits in homogeneous spaces
Pech, Clélia
2012-01-01
Chaput, Manivel and Perrin proved a formula describing the quantum product by Schubert classes associated to cominuscule weights in a rational projective homogeneous space X. In the case where X has Picard rank one, we link this formula to the stratification of X by P-orbits, where P is the parabolic subgroup associated to the cominuscule weight. We deduce a decomposition of the Hasse diagram of X, i.e the diagram describing the cup-product with the hyperplane class.
Quantum-dot Semiconductor Optical Amplifiers in State Space Model
Institute of Scientific and Technical Information of China (English)
Hussein Taleb; Kambiz Abedi; Saeed Golmohammadi
2013-01-01
A state space model (SSM) is derived for quantum-dot semiconductor optical amplifiers (QD-SOAs).Rate equations of QD-SOA are formulated in the form of state update equations,where average occupation probabilities along QD-SOA cavity are considered as state variables of the system.Simulations show that SSM calculates QD-SOA's static and dynamic characteristics with high accuracy.
Free-space quantum key distribution with entangled photons
Marcikic, I; Kurtsiefer, C; Marcikic, Ivan; Lamas-Linares, Antia; Kurtsiefer, Christian
2006-01-01
We report on a complete experimental implementation of a quantum key distribution protocol through a free space link using polarization-entangled photon pairs from a compact parametric down-conversion source. Over 10 hours of uninterrupted communication between sites 1.5 km apart, we observe average key generation rates of 630 per second after error correction and privacy amplification. Our scheme requires no specific hardware channel for synchronization apart from a classical wireless link, and no explicit random number generator.
Cavity-assisted dynamical quantum phase transition in superconducting quantum simulators
Tian, Lin
Coupling a quantum many-body system to a cavity can create bifurcation points in the phase diagram, where the many-body system switches between different phases. Here I will discuss the dynamical quantum phase transitions at the bifurcation points of a one-dimensional transverse field Ising model coupled to a cavity. The Ising model can be emulated with various types of superconducting qubits connected in a chain. With a time-dependent Bogoliubov method, we show that an infinitesimal quench of the driving field can cause gradual evolution of the transverse field on the Ising spins to pass through the quantum critical point. Our calculation shows that the cavity-induced nonlinearity plays an important role in the dynamics of this system. Quasiparticles can be excited in the Ising chain during this process, which results in the deviation of the system from its adiabatic ground state. This work is supported by the National Science Foundation under Award Number 0956064.
Symmetries of nonrelativistic phase space and the structure of quark-lepton generation
Źenczykowski, Piotr
2009-06-01
According to the Hamiltonian formalism, nonrelativistic phase space may be considered as an arena of physics, with momentum and position treated as independent variables. Invariance of x2 + p2 constitutes then a natural generalization of ordinary rotational invariance. We consider Dirac-like linearization of this form, with position and momentum satisfying standard commutation relations. This leads to the identification of a quantum-level structure from which some phase space properties might emerge. Genuine rotations and reflections in phase space are tied to the existence of new quantum numbers, unrelated to ordinary 3D space. Their properties allow their identification with the internal quantum numbers characterising the structure of a single quark-lepton generation in the Standard Model. In particular, the algebraic structure of the Harari-Shupe preon model of fundamental particles is reproduced exactly and without invoking any subparticles. Analysis of the Clifford algebra of nonrelativistic phase space singles out an element which might be associated with the concept of lepton mass. This element is transformed into a corresponding element for a single coloured quark, leading to a generalization of the concept of mass and a different starting point for the discussion of quark unobservability.