Motion analysis of optically trapped particles and cells using 2D Fourier analysis

DEFF Research Database (Denmark)

Kristensen, Martin Verner; Ahrendt, Peter; Lindballe, Thue Bjerring

2012-01-01

Motion analysis of optically trapped objects is demonstrated using a simple 2D Fourier transform technique. The displacements of trapped objects are determined directly from the phase shift between the Fourier transform of subsequent images. Using end-and side-view imaging, the stiffness...... of the trap is determined in three dimensions. The Fourier transform method is simple to implement and applicable in cases where the trapped object changes shape or where the lighting conditions change. This is illustrated by tracking a fluorescent particle and a myoblast cell, with subsequent determination...

Differentiating Fragmentation Pathways of Cholesterol by Two-Dimensional Fourier Transform Ion Cyclotron Resonance Mass Spectrometry.

Science.gov (United States)

van Agthoven, Maria A; Barrow, Mark P; Chiron, Lionel; Coutouly, Marie-Aude; Kilgour, David; Wootton, Christopher A; Wei, Juan; Soulby, Andrew; Delsuc, Marc-André; Rolando, Christian; O'Connor, Peter B

2015-12-01

Two-dimensional Fourier transform ion cyclotron resonance mass spectrometry is a data-independent analytical method that records the fragmentation patterns of all the compounds in a sample. This study shows the implementation of atmospheric pressure photoionization with two-dimensional (2D) Fourier transform ion cyclotron resonance mass spectrometry. In the resulting 2D mass spectrum, the fragmentation patterns of the radical and protonated species from cholesterol are differentiated. This study shows the use of fragment ion lines, precursor ion lines, and neutral loss lines in the 2D mass spectrum to determine fragmentation mechanisms of known compounds and to gain information on unknown ion species in the spectrum. In concert with high resolution mass spectrometry, 2D Fourier transform ion cyclotron resonance mass spectrometry can be a useful tool for the structural analysis of small molecules. Graphical Abstract ᅟ.

Fractional finite Fourier transform.

Science.gov (United States)

Khare, Kedar; George, Nicholas

2004-07-01

We show that a fractional version of the finite Fourier transform may be defined by using prolate spheroidal wave functions of order zero. The transform is linear and additive in its index and asymptotically goes over to Namias's definition of the fractional Fourier transform. As a special case of this definition, it is shown that the finite Fourier transform may be inverted by using information over a finite range of frequencies in Fourier space, the inversion being sensitive to noise. Numerical illustrations for both forward (fractional) and inverse finite transforms are provided.

Generalized prolate spheroidal wave functions for optical finite fractional Fourier and linear canonical transforms.

Science.gov (United States)

Pei, Soo-Chang; Ding, Jian-Jiun

2005-03-01

Prolate spheroidal wave functions (PSWFs) are known to be useful for analyzing the properties of the finite-extension Fourier transform (fi-FT). We extend the theory of PSWFs for the finite-extension fractional Fourier transform, the finite-extension linear canonical transform, and the finite-extension offset linear canonical transform. These finite transforms are more flexible than the fi-FT and can model much more generalized optical systems. We also illustrate how to use the generalized prolate spheroidal functions we derive to analyze the energy-preservation ratio, the self-imaging phenomenon, and the resonance phenomenon of the finite-sized one-stage or multiple-stage optical systems.

Determining Energies and Cross Sections of Individual Ions Using Higher-Order Harmonics in Fourier Transform Charge Detection Mass Spectrometry (FT-CDMS).

Science.gov (United States)

Harper, Conner C; Elliott, Andrew G; Lin, Haw-Wei; Williams, Evan R

2018-06-02

A general method for in situ measurements of the energy of individual ions trapped and weighed using charge detection mass spectrometry (CDMS) is described. Highly charged (> 300 e), individual polyethylene glycol (PEG) ions are trapped and oscillate within an electrostatic trap, producing a time domain signal. A segmented Fourier transform (FT) of this signal yields the temporal evolution of the fundamental and harmonic frequencies of ion motion throughout the 500-ms trap time. The ratio of the fundamental frequency and second harmonic (HAR) depends on the ion energy, which is an essential parameter for measuring ion mass in CDMS. This relationship is calibrated using simulated ion signals, and the calibration is compared to the HAR values measured for PEG ion signals where the ion energy was also determined using an independent method that requires that the ions be highly charged (> 300 e). The mean error of 0.6% between the two measurements indicates that the HAR method is an accurate means of ion energy determination that does not depend on ion size or charge. The HAR is determined dynamically over the entire trapping period, making it possible to observe the change in ion energy that takes place as solvent evaporates from the ion and collisions with background gas occur. This method makes it possible to measure mass changes, either from solvent evaporation or from molecular fragmentation (MS n ), as well as the cross sections of ions measured using CDMS. Graphical Abstract.

Sympathetic cooling and crystallization of ions in a linear Paul trap

International Nuclear Information System (INIS)

Drewsen, M.; Bowe, P.; Hornekaer, L.; Brodersen, C.; Schiffer, J.P.; Hangst, J.S.; Schiffer, J.P.

1999-01-01

Coulomb crystals, containing up to a few hundred ions of which more than 50% were cooled sympathetically by the Coulomb interaction with laser cooled Mg + ions, have been produced in a linear Paul trap. By controlling the balance of the radiation pressure from the two cooling lasers, the Coulomb crystals could be segregated according to ion species. Previous studies of ion crystals and molecular dynamics simulations suggest that the temperature may be around 10 mK or lower. The obtained results indicate that a wide range of atomic and molecular ions, which due to their internal structures are not amenable to direct laser cooling, can be effectively cooled and localized (crystallized) in linear Paul traps. For high resolution spectroscopy of such ions this may turn out to be very useful. copyright 1999 American Institute of Physics

Fourier Transform Mass Spectrometry.

Science.gov (United States)

Gross, Michael L.; Rempel, Don L.

1984-01-01

Discusses the nature of Fourier transform mass spectrometry and its unique combination of high mass resolution, high upper mass limit, and multichannel advantage. Examines its operation, capabilities and limitations, applications (ion storage, ion manipulation, ion chemistry), and future applications and developments. (JN)

Fourier Transform Ion Cyclotron Resonance Mass Spectrometry at the Cyclotron Frequency.

Science.gov (United States)

Nagornov, Konstantin O; Kozhinov, Anton N; Tsybin, Yury O

2017-04-01

The phenomenon of ion cyclotron resonance allows for determining mass-to-charge ratio, m/z, of an ensemble of ions by means of measurements of their cyclotron frequency, ω c . In Fourier transform ion cyclotron resonance mass spectrometry (FT-ICR MS), the ω c quantity is usually unavailable for direct measurements: the resonant state is located close to the reduced cyclotron frequency (ω + ), whereas the ω c and the corresponding m/z values may be calculated via theoretical derivation from an experimental estimate of the ω + quantity. Here, we describe an experimental observation of a new resonant state, which is located close to the ω c frequency and is established because of azimuthally-dependent trapping electric fields of the recently developed ICR cells with narrow aperture detection electrodes. We show that in mass spectra, peaks close to ω + frequencies can be reduced to negligible levels relative to peaks close to ω c frequencies. Due to reduced errors with which the ω c quantity is obtained, the new resonance provides a means of cyclotron frequency measurements with precision greater than that achieved when ω + frequency peaks are employed. The described phenomenon may be considered for a development into an FT-ICR MS technology with increased mass accuracy for applications in basic research, life, and environmental sciences. Graphical Abstract ᅟ.

A linear radiofrequency ion trap for accumulation, bunching, and emittance improvement of radioactive ion beams

International Nuclear Information System (INIS)

Herfurth, F.; Dilling, J.; Kellerbauer, A.

2000-05-01

An ion beam cooler and buncher has been developed for the manipulation of radioactive ion beams. The gas-filled linear radiofrequency ion trap system is installed at the Penning trap mass spectrometer ISOLTRAP at ISOLDE/CERN. Its purpose is to accumulate the 60-keV continuous ISOLDE ion beam with high efficiency and to convert it into low-energy low-emittance ion pulses. The efficiency was found to exceed 10% in agreement with simulations. A more than 10-fold reduction of the ISOLDE beam emittance can be achieved. The system has been used successfully for first on-line experiments. Its principle, setup and performance will be discussed. (orig.)

Studies of gas phase ion/molecule reactions by Fourier transform ion cyclotron resonance mass spectrometry

International Nuclear Information System (INIS)

Kleingeld, J.C.

1984-01-01

An important field in which Fourier-transform ion cyclotron resonance has useful applications is that of gas phase ion chemistry, the subject of this thesis. First, the general picture of ion-molecule reactions in the gas phase is discussed. Next, some positive ion-molecule reactions are described, whereas the remaining chapters deal with negative ion-molecule reactions. Most of these studies have been performed using the FT-ICR method. Reactions involving H 3 O - and NH 4 - ions are described whereas the other chapters deal with larger organic complexes. (Auth.)

Fourier Transform Mass Spectrometry

Science.gov (United States)

Scigelova, Michaela; Hornshaw, Martin; Giannakopulos, Anastassios; Makarov, Alexander

2011-01-01

This article provides an introduction to Fourier transform-based mass spectrometry. The key performance characteristics of Fourier transform-based mass spectrometry, mass accuracy and resolution, are presented in the view of how they impact the interpretation of measurements in proteomic applications. The theory and principles of operation of two types of mass analyzer, Fourier transform ion cyclotron resonance and Orbitrap, are described. Major benefits as well as limitations of Fourier transform-based mass spectrometry technology are discussed in the context of practical sample analysis, and illustrated with examples included as figures in this text and in the accompanying slide set. Comparisons highlighting the performance differences between the two mass analyzers are made where deemed useful in assisting the user with choosing the most appropriate technology for an application. Recent developments of these high-performing mass spectrometers are mentioned to provide a future outlook. PMID:21742802

Gas phase ion/molecule reactions as studied by Fourier Transform Ion Cyclotron Resonance mass spectrometry

International Nuclear Information System (INIS)

Joergensen, S.I.

1985-01-01

The subject of this thesis is gas phase ion/molecule reactions as studied by Fourier Transform Ion Cyclotron Resonance (FT-ICR) mass spectrometry (chapter 2 contains a short description of this method). Three chapters are mainly concerned with mechanistic aspects of gas phase ion/molecule reactions. An equally important aspect of the thesis is the stability and reactivity of α-thio carbanions, dipole stabilized carbanions and homoenolate anions, dealt with in the other four chapters. (Auth.)

Observation of String Ion Cloud in a Linear RF Trap

International Nuclear Information System (INIS)

Aramaki, M.; Kameyama, S.; Kono, A.; Sakawa, Y.; Shoji, T.

2009-01-01

We aim to study the effect of the long-range correlation among ions on their statistical characteristics using ion clouds confined in a linear rf ion trap. It is important to keep the ion cloud in one dimension, where the influence of the rf heating is negligible, for the detailed research on the effect of the Coulomb interaction on the statistical characteristics of the ion cloud. In this paper, the method of the generation of an ideal ion string is proposed. We also briefly report the performances of our experimental equipment and the preliminary results of generation of ideal 1D ion cloud.

A Linear Ion Trap with an Expanded Inscribed Diameter to Improve Optical Access for Fluorescence Spectroscopy

Science.gov (United States)

Rajagopal, Vaishnavi; Stokes, Chris; Ferzoco, Alessandra

2018-02-01

We report a custom-geometry linear ion trap designed for fluorescence spectroscopy of gas-phase ions at ambient to cryogenic temperatures. Laser-induced fluorescence from trapped ions is collected from between the trapping rods, orthogonal to the excitation laser that runs along the axis of the linear ion trap. To increase optical access to the ion cloud, the diameter of the round trapping rods is 80% of the inscribed diameter, rather than the roughly 110% used to approximate purely quadrupolar electric fields. To encompass as much of the ion cloud as possible, the first collection optic has a 25.4 mm diameter and a numerical aperture of 0.6. The choice of geometry and collection optics yields 107 detected photons/s from trapped rhodamine 6G ions. The trap is coupled to a closed-cycle helium refrigerator, which in combination with two 50 Ohm heaters enables temperature control to below 25 K on the rod electrodes. The purpose of the instrument is to broaden the applicability of fluorescence spectroscopy of gas-phase ions to cases where photon emission is a minority relaxation pathway. Such studies are important to understand how the microenvironment of a chromophore influences excited state charge transfer processes.

Applicability of hybrid linear ion trap-high resolution mass spectrometry and quadrupole-linear ion trap-mass spectrometry for mycotoxin analysis in baby food.

Science.gov (United States)

Rubert, Josep; James, Kevin J; Mañes, Jordi; Soler, Carla

2012-02-03

Recent developments in mass spectrometers have created a paradoxical situation; different mass spectrometers are available, each of them with their specific strengths and drawbacks. Hybrid instruments try to unify several advantages in one instrument. In this study two of wide-used hybrid instruments were compared: hybrid quadrupole-linear ion trap-mass spectrometry (QTRAP®) and the hybrid linear ion trap-high resolution mass spectrometry (LTQ-Orbitrap®). Both instruments were applied to detect the presence of 18 selected mycotoxins in baby food. Analytical parameters were validated according to 2002/657/CE. Limits of quantification (LOQs) obtained by QTRAP® instrument ranged from 0.45 to 45 μg kg⁻¹ while lower limits of quantification (LLOQs) values were obtained by LTQ-Orbitrap®: 7-70 μg kg⁻¹. The correlation coefficients (r) in both cases were upper than 0.989. These values highlighted that both instruments were complementary for the analysis of mycotoxin in baby food; while QTRAP® reached best sensitivity and selectivity, LTQ-Orbitrap® allowed the identification of non-target and unknowns compounds. Copyright © 2011 Elsevier B.V. All rights reserved.

Mass measurement errors of Fourier-transform mass spectrometry (FTMS): distribution, recalibration, and application.

Science.gov (United States)

Zhang, Jiyang; Ma, Jie; Dou, Lei; Wu, Songfeng; Qian, Xiaohong; Xie, Hongwei; Zhu, Yunping; He, Fuchu

2009-02-01

The hybrid linear trap quadrupole Fourier-transform (LTQ-FT) ion cyclotron resonance mass spectrometer, an instrument with high accuracy and resolution, is widely used in the identification and quantification of peptides and proteins. However, time-dependent errors in the system may lead to deterioration of the accuracy of these instruments, negatively influencing the determination of the mass error tolerance (MET) in database searches. Here, a comprehensive discussion of LTQ/FT precursor ion mass error is provided. On the basis of an investigation of the mass error distribution, we propose an improved recalibration formula and introduce a new tool, FTDR (Fourier-transform data recalibration), that employs a graphic user interface (GUI) for automatic calibration. It was found that the calibration could adjust the mass error distribution to more closely approximate a normal distribution and reduce the standard deviation (SD). Consequently, we present a new strategy, LDSF (Large MET database search and small MET filtration), for database search MET specification and validation of database search results. As the name implies, a large-MET database search is conducted and the search results are then filtered using the statistical MET estimated from high-confidence results. By applying this strategy to a standard protein data set and a complex data set, we demonstrate the LDSF can significantly improve the sensitivity of the result validation procedure.

The fractional Fourier transform and applications

Science.gov (United States)

Bailey, David H.; Swarztrauber, Paul N.

1991-01-01

This paper describes the 'fractional Fourier transform', which admits computation by an algorithm that has complexity proportional to the fast Fourier transform algorithm. Whereas the discrete Fourier transform (DFT) is based on integral roots of unity e exp -2(pi)i/n, the fractional Fourier transform is based on fractional roots of unity e exp -2(pi)i(alpha), where alpha is arbitrary. The fractional Fourier transform and the corresponding fast algorithm are useful for such applications as computing DFTs of sequences with prime lengths, computing DFTs of sparse sequences, analyzing sequences with noninteger periodicities, performing high-resolution trigonometric interpolation, detecting lines in noisy images, and detecting signals with linearly drifting frequencies. In many cases, the resulting algorithms are faster by arbitrarily large factors than conventional techniques.

Performance of the linear ion trap Orbitrap mass analyzer for qualitative and quantitative analysis of drugs of abuse and relevant metabolites in sewage water.

Science.gov (United States)

Bijlsma, Lubertus; Emke, Erik; Hernández, Félix; de Voogt, Pim

2013-03-20

This work illustrates the potential of liquid chromatography coupled to a hybrid linear ion trap Fourier Transform Orbitrap mass spectrometer for the simultaneous identification and quantification of 24 drugs of abuse and relevant metabolites in sewage water. The developed methodology consisted of automatic solid-phase extraction using Oasis HLB cartridges, chromatographic separation of the targeted drugs, full-scan accurate mass data acquisition under positive electrospray ionization mode over an m/z range of 50-600Da at a resolution of 30,000 FWHM and simultaneous MS(n) measurements to obtain information of fragment ions generated in the linear ion trap. Accurate mass of the protonated molecule, together with at least one nominal mass product ion and retention time allowed the confident identification of the compounds detected in these complex matrices. In addition to the highly reliable qualitative analysis, Orbitrap analyzer also proved to have satisfactory potential for quantification at sub-ppb analyte levels, a possibility that has been very little explored in the literature until now. The limits of quantification ranged from 4 to 68ngL(-1) in influent sewage water, and from 2 to 35ngL(-1) in effluent, with the exception of MDA, morphine and THC that presented higher values as a consequence of the high ionization suppression in this type of samples. Satisfactory recoveries (70-120%) and precision (abuse could be identified and quantified, mainly MDMA, benzoylecgonine, codeine, oxazepam and temazepam. Orbitrap also showed potential for retrospective investigation of ketamine metabolites in the samples without the need of additional analysis. Copyright © 2013 Elsevier B.V. All rights reserved.

Design and Application of a High-Temperature Linear Ion Trap Reactor

Science.gov (United States)

Jiang, Li-Xue; Liu, Qing-Yu; Li, Xiao-Na; He, Sheng-Gui

2018-01-01

A high-temperature linear ion trap reactor with hexapole design was homemade to study ion-molecule reactions at variable temperatures. The highest temperature for the trapped ions is up to 773 K, which is much higher than those in available reports. The reaction between V2O6 - cluster anions and CO at different temperatures was investigated to evaluate the performance of this reactor. The apparent activation energy was determined to be 0.10 ± 0.02 eV, which is consistent with the barrier of 0.12 eV calculated by density functional theory. This indicates that the current experimental apparatus is prospective to study ion-molecule reactions at variable temperatures, and more kinetic details can be obtained to have a better understanding of chemical reactions that have overall barriers. [Figure not available: see fulltext.

Mini ion trap mass spectrometer

Science.gov (United States)

Dietrich, D.D.; Keville, R.F.

1995-09-19

An ion trap is described which operates in the regime between research ion traps which can detect ions with a mass resolution of better than 1:10{sup 9} and commercial mass spectrometers requiring 10{sup 4} ions with resolutions of a few hundred. The power consumption is kept to a minimum by the use of permanent magnets and a novel electron gun design. By Fourier analyzing the ion cyclotron resonance signals induced in the trap electrodes, a complete mass spectra in a single combined structure can be detected. An attribute of the ion trap mass spectrometer is that overall system size is drastically reduced due to combining a unique electron source and mass analyzer/detector in a single device. This enables portable low power mass spectrometers for the detection of environmental pollutants or illicit substances, as well as sensors for on board diagnostics to monitor engine performance or for active feedback in any process involving exhausting waste products. 10 figs.

Internal calibration on adjacent samples (InCAS) with Fourier transform mass spectrometry.

Science.gov (United States)

O'Connor, P B; Costello, C E

2000-12-15

Using matrix-assisted laser desorption/ionization (MAL DI) on a trapped ion mass spectrometer such as a Fourier transform mass spectrometer (FTMS) allows accumulation of ions in the cell from multiple laser shots prior to detection. If ions from separate MALDI samples are accumulated simultaneously in the cell, ions from one sample can be used to calibrate ions from the other sample. Since the ions are detected simultaneously in the cell, this is, in effect, internal calibration, but there are no selective desorption effects in the MALDI source. This method of internal calibration with adjacent samples is demonstrated here on cesium iodide clusters, peptides, oligosaccharides, poly(propylene glycol), and fullerenes and provides typical FTMS internal calibration mass accuracy of < 1 ppm.

Discrete Fourier and wavelet transforms an introduction through linear algebra with applications to signal processing

CERN Document Server

Goodman, Roe W

2016-01-01

This textbook for undergraduate mathematics, science, and engineering students introduces the theory and applications of discrete Fourier and wavelet transforms using elementary linear algebra, without assuming prior knowledge of signal processing or advanced analysis.It explains how to use the Fourier matrix to extract frequency information from a digital signal and how to use circulant matrices to emphasize selected frequency ranges. It introduces discrete wavelet transforms for digital signals through the lifting method and illustrates through examples and computer explorations how these transforms are used in signal and image processing. Then the general theory of discrete wavelet transforms is developed via the matrix algebra of two-channel filter banks. Finally, wavelet transforms for analog signals are constructed based on filter bank results already presented, and the mathematical framework of multiresolution analysis is examined.

Atmospheric pressure chemical ionization Fourier transform ion cyclotron resonance mass spectrometry for complex thiophenic mixture analysis

KAUST Repository

Hourani, Nadim; Andersson, Jan T.; Mö ller, Isabelle; Amad, Maan H.; Witt, Matthí as; Sarathy, Mani

2013-01-01

oil (VGO) and injected using the same method. The samples were analyzed using Fourier transform ion cyclotron resonance mass spectrometry (FTICR MS). RESULTS PASH model analytes were successfully ionized and mainly [M + H]+ ions were produced. The same

RPLC-lon-trap-FTMS method for lipid profiling of plasma: Method validation And application to p53 mutant mouse model

NARCIS (Netherlands)

Hu, C.; Dommelen, J. van; Heijden, R. van der; Spijksma, G.; Reijmers, T.H.; Wang, M.; Slee, E.; Lu, X.; Xu, G.; Greef, J. van der; Hankemeier, T.

2008-01-01

A reversed-phase liquid chromatography-linear ion trap-Fourier transform ion cyclotron resonance-mass spectrometry method was developed for the profiling of lipids in human and mouse plasma. With the use of a fused-core C₈ column and a binary gradient, more than 160 lipids belonging to

Automatic Fourier transform and self-Fourier beams due to parabolic potential

Energy Technology Data Exchange (ETDEWEB)

Zhang, Yiqi, E-mail: zhangyiqi@mail.xjtu.edu.cn [Key Laboratory for Physical Electronics and Devices of the Ministry of Education & Shaanxi Key Lab of Information Photonic Technique, Xi’an Jiaotong University, Xi’an 710049 (China); Liu, Xing [Key Laboratory for Physical Electronics and Devices of the Ministry of Education & Shaanxi Key Lab of Information Photonic Technique, Xi’an Jiaotong University, Xi’an 710049 (China); Belić, Milivoj R., E-mail: milivoj.belic@qatar.tamu.edu [Science Program, Texas A& M University at Qatar, P.O. Box 23874 Doha (Qatar); Zhong, Weiping [Department of Electronic and Information Engineering, Shunde Polytechnic, Shunde 528300 (China); Petrović, Milan S. [Institute of Physics, P.O. Box 68, 11001 Belgrade (Serbia); Zhang, Yanpeng, E-mail: ypzhang@mail.xjtu.edu.cn [Key Laboratory for Physical Electronics and Devices of the Ministry of Education & Shaanxi Key Lab of Information Photonic Technique, Xi’an Jiaotong University, Xi’an 710049 (China)

2015-12-15

We investigate the propagation of light beams including Hermite–Gauss, Bessel–Gauss and finite energy Airy beams in a linear medium with parabolic potential. Expectedly, the beams undergo oscillation during propagation, but quite unexpectedly they also perform automatic Fourier transform, that is, periodic change from the beam to its Fourier transform and back. In addition to oscillation, the finite-energy Airy beams exhibit periodic inversion during propagation. The oscillating period of parity-asymmetric beams is twice that of the parity-symmetric beams. Based on the propagation in parabolic potential, we introduce a class of optically-interesting beams that are self-Fourier beams—that is, the beams whose Fourier transforms are the beams themselves.

The morphing of geographical features by Fourier transformation.

Science.gov (United States)

Li, Jingzhong; Liu, Pengcheng; Yu, Wenhao; Cheng, Xiaoqiang

2018-01-01

This paper presents a morphing model of vector geographical data based on Fourier transformation. This model involves three main steps. They are conversion from vector data to Fourier series, generation of intermediate function by combination of the two Fourier series concerning a large scale and a small scale, and reverse conversion from combination function to vector data. By mirror processing, the model can also be used for morphing of linear features. Experimental results show that this method is sensitive to scale variations and it can be used for vector map features' continuous scale transformation. The efficiency of this model is linearly related to the point number of shape boundary and the interceptive value n of Fourier expansion. The effect of morphing by Fourier transformation is plausible and the efficiency of the algorithm is acceptable.

Fluorescence profiles and cooling dynamics of laser-cooled Mg+ ions in a linear rf ion trap

International Nuclear Information System (INIS)

Zhao Xianzhen; Ryjkov, Vladimir L.; Schuessler, Hans A.

2006-01-01

Fluorescence line profiles and their implications on the cooling dynamics of the Mg + ions stored in a linear rf trap are studied. The line profile is dictated by the temperature of the ion cloud at different laser detunings. The upper bound of the lowest temperature was estimated for different values of the rf trapping potential amplitude and the buffer gas pressure. A general trend of this ultimate temperature to increase with the rf trapping voltage and buffer gas pressure is expected, with an abrupt change at some critical value corresponding to the transition to and from a strongly correlated liquid or crystal state. While on the one hand this expectation was confirmed when the buffer gas pressure was varied; on the other hand the influence of the amplitude of the trapping voltage on the ultimate temperature shows an interesting new feature of first dipping down before the sharp increase occurs

Two-dimensional analysis of trapped-ion eigenmodes

International Nuclear Information System (INIS)

Marchand, R.; Tang, W.M.; Rewoldt, G.

1979-11-01

A fully two-dimensional eigenmode analysis of the trapped-ion instability in axisymmetric toroidal geometry is presented. The calculations also takes into account the basic dynamics associated with other low frequency modes such as the trapped-electron instability and the ion-temperature-gradient instability. The poloidal structure of the mode is taken into account by Fourier expanding the perturbed electrostatic potential, PHI, in theta

Representation of the quantum Fourier transform on multilevel basic elements by a sequence of selective rotation operators

Science.gov (United States)

Ermilov, A. S.; Zobov, V. E.

2007-12-01

To experimentally realize quantum computations on d-level basic elements (qudits) at d > 2, it is necessary to develop schemes for the technical realization of elementary logical operators. We have found sequences of selective rotation operators that represent the operators of the quantum Fourier transform (Walsh-Hadamard matrices) for d = 3-10. For the prime numbers 3, 5, and 7, the well-known method of linear algebra is applied, whereas, for the factorable numbers 6, 9, and 10, the representation of virtual spins is used (which we previously applied for d = 4, 8). Selective rotations can be realized, for example, by means of pulses of an RF magnetic field for systems of quadrupole nuclei or laser pulses for atoms and ions in traps.

Investigation on H-containing shallow trap of hydrogenated TiO2 with in situ Fourier transform infrared diffuse reflection spectroscopy.

Science.gov (United States)

Han, Bing; Hang Hu, Yun

2017-07-28

A novel technique, high temperature high pressure in situ Fourier transform infrared diffuse reflection spectroscopy, was successfully used to investigate the formation and stability of shallow trap states in P25 TiO 2 nanoparticles. Two types of shallow traps (with and without H atoms) were identified. The H-containing shallow trap can be easily generated by heating in H 2 atmosphere. However, the trap is unstable in vacuum at 600 °C. In contrast, the H-free shallow trap, which can be formed by heating in vacuum, is stable even at 600 °C. The energy gaps between shallow trap states and the conduction band are 0.09 eV for H-containing shallow trap and 0.13 eV for H-free shallow trap, indicating that the H-containing shallow trap state is closer to the conduction band than that without H.

Approximating the Analytic Fourier Transform with the Discrete Fourier Transform

OpenAIRE

Axelrod, Jeremy

2015-01-01

The Fourier transform is approximated over a finite domain using a Riemann sum. This Riemann sum is then expressed in terms of the discrete Fourier transform, which allows the sum to be computed with a fast Fourier transform algorithm more rapidly than via a direct matrix multiplication. Advantages and limitations of using this method to approximate the Fourier transform are discussed, and prototypical MATLAB codes implementing the method are presented.

Optical Trapping of Ion Coulomb Crystals

Science.gov (United States)

Schmidt, Julian; Lambrecht, Alexander; Weckesser, Pascal; Debatin, Markus; Karpa, Leon; Schaetz, Tobias

2018-04-01

The electronic and motional degrees of freedom of trapped ions can be controlled and coherently coupled on the level of individual quanta. Assembling complex quantum systems ion by ion while keeping this unique level of control remains a challenging task. For many applications, linear chains of ions in conventional traps are ideally suited to address this problem. However, driven motion due to the magnetic or radio-frequency electric trapping fields sometimes limits the performance in one dimension and severely affects the extension to higher-dimensional systems. Here, we report on the trapping of multiple barium ions in a single-beam optical dipole trap without radio-frequency or additional magnetic fields. We study the persistence of order in ensembles of up to six ions within the optical trap, measure their temperature, and conclude that the ions form a linear chain, commonly called a one-dimensional Coulomb crystal. As a proof-of-concept demonstration, we access the collective motion and perform spectrometry of the normal modes in the optical trap. Our system provides a platform that is free of driven motion and combines advantages of optical trapping, such as state-dependent confinement and nanoscale potentials, with the desirable properties of crystals of trapped ions, such as long-range interactions featuring collective motion. Starting with small numbers of ions, it has been proposed that these properties would allow the experimental study of many-body physics and the onset of structural quantum phase transitions between one- and two-dimensional crystals.

Matrix-assisted laser desorption fourier transform mass spectrometry for biological compounds

Energy Technology Data Exchange (ETDEWEB)

Hettich, R.; Buchanan, M.

1990-01-01

The recent development of matrix-assisted UV laser desorption (LD) mass spectrometry has made possible the ionization and detection of extremely large molecules (with molecular weights exceeding 100,000 Daltons). This technique has generated enormous interest in the biological community for the direct examination of large peptides and oligonucleotides. Although this matrix-assisted ionization method has been developed and used almost exclusively with time-of-flight (TOF) mass spectrometers, research is currently in progress to demonstrate this technique with trapped ion mass spectrometers, such as Fourier transform ion cyclotron resonance mass spectrometry (FTMS). The potential capabilities of FTMS for wide mass range, high resolution measurement, and ion trapping experiments suggest that this instrumental technique should be useful for the detailed structural characterization of large ions generated by the matrix-assisted technique. We have recently demonstrated that matrix-assisted ultraviolet laser desorption can be successfully used with FTMS for the ionization of small peptides. The objective of this report is to summarize the application and current limitations of matrix-assisted laser desorption FTMS for the characterization of peptides and oligonucleotides at the isomeric level. 4 refs., 3 figs., 2 tabs.

Optical Trapping of Ion Coulomb Crystals

Directory of Open Access Journals (Sweden)

Julian Schmidt

2018-05-01

Full Text Available The electronic and motional degrees of freedom of trapped ions can be controlled and coherently coupled on the level of individual quanta. Assembling complex quantum systems ion by ion while keeping this unique level of control remains a challenging task. For many applications, linear chains of ions in conventional traps are ideally suited to address this problem. However, driven motion due to the magnetic or radio-frequency electric trapping fields sometimes limits the performance in one dimension and severely affects the extension to higher-dimensional systems. Here, we report on the trapping of multiple barium ions in a single-beam optical dipole trap without radio-frequency or additional magnetic fields. We study the persistence of order in ensembles of up to six ions within the optical trap, measure their temperature, and conclude that the ions form a linear chain, commonly called a one-dimensional Coulomb crystal. As a proof-of-concept demonstration, we access the collective motion and perform spectrometry of the normal modes in the optical trap. Our system provides a platform that is free of driven motion and combines advantages of optical trapping, such as state-dependent confinement and nanoscale potentials, with the desirable properties of crystals of trapped ions, such as long-range interactions featuring collective motion. Starting with small numbers of ions, it has been proposed that these properties would allow the experimental study of many-body physics and the onset of structural quantum phase transitions between one- and two-dimensional crystals.

An Automated High Performance Capillary Liquid Chromatography Fourier Transform Ion Cyclotron Resonance Mass Spectrometer for High-Throughput Proteomics

International Nuclear Information System (INIS)

Belov, Mikhail E.; Anderson, Gordon A.; Wingerd, Mark A.; Udseth, Harold R.; Tang, Keqi; Prior, David C.; Swanson, Kenneth R.; Buschbach, Michael A.; Strittmatter, Eric F.; Moore, Ronald J.; Smith, Richard D.

2004-01-01

We report on a fully automated 9.4 tesla Fourier transform ion resonance cyclotron (FTICR) mass spectrometer coupled to reverse-phase chromatography for high-throughput proteomic studies. Modifications made to the front-end of a commercial FTICR instrument--a dual-ESI-emitter ion source; dual-channel electrodynamic ion funnel; and collisional-cooling, selection and accumulation quadrupoles--significantly improved the sensitivity, dynamic range and mass measurement accuracy of the mass spectrometer. A high-pressure capillary liquid chromatography (LC) system was incorporated with an autosampler that enabled 24 h/day operation. A novel method for accumulating ions in the ICR cell was also developed. Unattended operation of the instrument revealed the exceptional reproducibility (1-5% deviation in elution times for peptides from a bacterial proteome), repeatability (10-20% deviation in detected abundances for peptides from the same aliquot analyzed a few weeks apart) and robustness (high-throughput operation for 5 months without downtime) of the LC/FTICR system. When combined with modulated-ion-energy gated trapping, the internal calibration of FTICR mass spectra decreased dispersion of mass measurement errors for peptide identifications in conjunction with high resolution capillary LC separations to < 5 ppm over a dynamic range for each spectrum of 10 3

The linear canonical transformation : definition and properties

NARCIS (Netherlands)

Bastiaans, Martin J.; Alieva, Tatiana; Healy, J.J.; Kutay, M.A.; Ozaktas, H.M.; Sheridan, J.T.

2016-01-01

In this chapter we introduce the class of linear canonical transformations, which includes as particular cases the Fourier transformation (and its generalization: the fractional Fourier transformation), the Fresnel transformation, and magnifier, rotation and shearing operations. The basic properties

The JPL Hg(sup +) Extended Linear Ion Trap Frequency Standard: Status, Stability, and Accuracy Prospects

Science.gov (United States)

Tjoelker, R. L.; Prestage, J. D.; Maleki, L.

1996-01-01

Microwave frequency standards based on room temperature (sup 199)Hg(sup +) ions in a Linear Ion Trap (LITS) presently achieve a Signal to Noise and line Q inferred short frequency stability. Long term stability has been measured for averaging intervals up to 5 months with apparent sensitivity to variations in ion number/temperature limiting the flicker floor.

Structure and dynamics of ion clusters in linear octupole traps: Phase diagrams, chirality, and melting mechanisms

International Nuclear Information System (INIS)

Yurtsever, E.; Onal, E. D.; Calvo, F.

2011-01-01

The stable structures and melting dynamics of clusters of identical ions bound by linear octupole radiofrequency traps are theoretically investigated by global optimization methods and molecular dynamics simulations. By varying the cluster sizes in the range of 10-1000 ions and the extent of trap anisotropy by more than one order of magnitude, we find a broad variety of stable structures based on multiple rings at small sizes evolving into tubular geometries at large sizes. The binding energy of these clusters is well represented by two contributions arising from isotropic linear and octupolar traps. The structures generally exhibit strong size effects, and chiral arrangements spontaneously emerge in many crystals. Sufficiently large clusters form nested, coaxial tubes with different thermal stabilities. As in isotropic octupolar clusters, the inner tubes melt at temperatures that are lower than the overall melting point.

Characterization of ion Coulomb crystals in a linear Paul trap

International Nuclear Information System (INIS)

Okada, K.; Takayanagi, T.; Wada, M.; Ohtani, S.; Schuessler, H. A.

2010-01-01

We describe a simple and fast method for simulating observed images of ion Coulomb crystals. In doing so, cold elastic collisions between Coulomb crystals and virtual very light atoms are implemented in a molecular dynamics (MD) simulation code. Such an approach reproduces the observed images of Coulomb crystals by obtaining density plots of the statistics of existence of each ion. The simple method has the advantage of short computing time in comparison with previous calculation methods. As a demonstration of the simulation, the formation of a planar Coulomb crystal with a small number of ions has been investigated in detail in a linear ion trap both experimentally and by simulation. However, also large Coulomb crystals including up to 1400 ions have been photographed and simulated to extract the secular temperature and the number of ions. For medium-sized crystals, a comparison between experiments and calculations has been performed. Moreover, an MD simulation of the sympathetic cooling of small molecular ions was performed in order to test the possibility of extracting the temperature and the number of refrigerated molecular ions from crystal images of laser-cooled ions. Such information is basic to studying ultracold ion-molecule reactions using ion Coulomb crystals including sympathetically cooled molecular ions.

App. 1. Fourier series and Fourier transform

International Nuclear Information System (INIS)

Anon.

1977-01-01

Definitions, formulas and practical properties in quantum mechanics are presented: Fourier series (development of periodic function, Bessel-Parseval equality); Fourier transform (Parseval-Plancherel formula, Fourier transform in three-dimensional space) [fr

Ion Trap Quantum Computing

Science.gov (United States)

2011-12-01

variations of ion traps, including (1) the cylindrically symmetric 3D ring trap; (2) the linear trap with a combination of cavity QED; (#) the symmetric...concepts of quantum information. The major demonstration has been the test of a Bell inequality as demonstrated by Rowe et al. [50] and a decoherence...famous physics experiment [62]. Wolfgang Paul demonstrated a similar apparatus during his Nobel Prize speech [63]. This device is hyperbolic- parabolic

Fast numerical algorithm for the linear canonical transform.

Science.gov (United States)

Hennelly, Bryan M; Sheridan, John T

2005-05-01

The linear canonical transform (LCT) describes the effect of any quadratic phase system (QPS) on an input optical wave field. Special cases of the LCT include the fractional Fourier transform (FRT), the Fourier transform (FT), and the Fresnel transform (FST) describing free-space propagation. Currently there are numerous efficient algorithms used (for purposes of numerical simulation in the area of optical signal processing) to calculate the discrete FT, FRT, and FST. All of these algorithms are based on the use of the fast Fourier transform (FFT). In this paper we develop theory for the discrete linear canonical transform (DLCT), which is to the LCT what the discrete Fourier transform (DFT) is to the FT. We then derive the fast linear canonical transform (FLCT), an N log N algorithm for its numerical implementation by an approach similar to that used in deriving the FFT from the DFT. Our algorithm is significantly different from the FFT, is based purely on the properties of the LCT, and can be used for FFT, FRT, and FST calculations and, in the most general case, for the rapid calculation of the effect of any QPS.

Fourier Transfrom Ion Cyclotron Resonance Mass Spectrometry at High Magnetic Field

Science.gov (United States)

Marshall, Alan G.

1998-03-01

At high magnetic field (9.4 tesla at NHMFL), Fourier transform ion cyclotron resonance mass spectrometry performance improves dramatically: mass resolving power, axialization efficiency, and scan speed (each proportional to B), maximum ion mass, dynamic range, ion trapping period, kinetic energy, and electron self-cooling rate for sympathetic cooling (each proportional to B^2), and ion coalescence tendency (proportional 1/B^2). These advantages may apply singly (e.g., unit mass resolution for proteins of >100,000 Da), or compound (e.g., 10-fold improvement in S/N ratio for 9.4 T vs. 6 T at the same resolving power). Examples range from direct determination of molecular formulas of diesel fuel components by accurate mass measurement (=B10.1 ppm) to protein structure and dynamics probed by H/D exchange. This work was supported by N.S.F. (CHE-93-22824; CHE-94-13008), N.I.H. (GM-31683), Florida State University, and the National High Magnetic Field Laboratory in Tallahassee, FL.

Ions generated from uranyl nitrate solutions by electrospray ionization (ESI) and detected with Fourier transform ion-cyclotron resonance (FT-ICR) mass spectrometry.

Science.gov (United States)

Pasilis, Sofie; Somogyi, Arpád; Herrmann, Kristin; Pemberton, Jeanne E

2006-02-01

Electrospray ionization (ESI) of uranyl nitrate solutions generates a wide variety of positively and negatively charged ions, including complex adducts of uranyl ions with methoxy, hydroxy, and nitrate ligands. In the positive ion mode, ions detected by Fourier transform ion cyclotron resonance (FT-ICR) mass spectrometry are sensitive to instrumental tuning parameters such as quadrupole operating frequency and trapping time. Positive ions correspond to oligomeric uranyl nitrate species that can be characterized as having a general formula of [(UO(2))(n)(A)(m)(CH(3)OH)(s)](+) or [(UO(2))(n)(O)(A)(m)(CH(3)OH)(s)](+) with n = 1-4, m = 1-7, s = 0 or 1, and A = OH, NO(3), CH(3)O or a combination of these, although the formation of NO(3)-containing species is preferred. In the negative ion mode, complexes of the form [(UO(2))(NO(3))(m)](-) (m = 1-3) are detected, although the formation of the oxo-containing ions [(UO(2))(O)(n)(NO(3))(m)](-) (n = 1-2, m = 1-2) and the hydroxy-containing ions [(UO(2))(OH)(n)(NO(3))(m)](-) (n = 1-2, m = 0-1) are also observed. The extent of coordinative unsaturation of both positive and negative ions can be determined by ligand association/exchange and H/D exchange experiments using D(2)O and CD(3)OD as neutral reaction partners in the gas-phase. Positive ions are of varying stability and reactivity and may fragment extensively upon collision with D(2)O, CD(3)OD and N(2) in sustained off-resonance irradiation/collision-induced dissociation (SORI-CID) experiments. Electron-transfer reactions, presumably occurring during electrospray ionization but also in SORI-CID, can result in reduction of U(VI) to U(V) and perhaps even U(IV).

Precursor and Neutral Loss Scans in an RF Scanning Linear Quadrupole Ion Trap

Science.gov (United States)

Snyder, Dalton T.; Szalwinski, Lucas J.; Schrader, Robert L.; Pirro, Valentina; Hilger, Ryan; Cooks, R. Graham

2018-03-01

Methodology for performing precursor and neutral loss scans in an RF scanning linear quadrupole ion trap is described and compared to the unconventional ac frequency scan technique. In the RF scanning variant, precursor ions are mass selectively excited by a fixed frequency resonance excitation signal at low Mathieu q while the RF amplitude is ramped linearly to pass ions through the point of excitation such that the excited ion's m/z varies linearly with time. Ironically, a nonlinear ac frequency scan is still required for ejection of the product ions since their frequencies vary nonlinearly with the linearly varying RF amplitude. In the case of the precursor scan, the ejection frequency must be scanned so that it is fixed on a product ion m/z throughout the RF scan, whereas in the neutral loss scan, it must be scanned to maintain a constant mass offset from the excited precursor ions. Both simultaneous and sequential permutation scans are possible; only the former are demonstrated here. The scans described are performed on a variety of samples using different ionization sources: protonated amphetamine ions generated by nanoelectrospray ionization (nESI), explosives ionized by low-temperature plasma (LTP), and chemical warfare agent simulants sampled from a surface and analyzed with swab touch spray (TS). We lastly conclude that the ac frequency scan variant of these MS/MS scans is preferred due to electronic simplicity. In an accompanying manuscript, we thus describe the implementation of orthogonal double resonance precursor and neutral loss scans on the Mini 12 using constant RF voltage. [Figure not available: see fulltext.

Simulating the performance of a distance-3 surface code in a linear ion trap

Science.gov (United States)

Trout, Colin J.; Li, Muyuan; Gutiérrez, Mauricio; Wu, Yukai; Wang, Sheng-Tao; Duan, Luming; Brown, Kenneth R.

2018-04-01

We explore the feasibility of implementing a small surface code with 9 data qubits and 8 ancilla qubits, commonly referred to as surface-17, using a linear chain of 171Yb+ ions. Two-qubit gates can be performed between any two ions in the chain with gate time increasing linearly with ion distance. Measurement of the ion state by fluorescence requires that the ancilla qubits be physically separated from the data qubits to avoid errors on the data due to scattered photons. We minimize the time required to measure one round of stabilizers by optimizing the mapping of the two-dimensional surface code to the linear chain of ions. We develop a physically motivated Pauli error model that allows for fast simulation and captures the key sources of noise in an ion trap quantum computer including gate imperfections and ion heating. Our simulations showed a consistent requirement of a two-qubit gate fidelity of ≥99.9% for the logical memory to have a better fidelity than physical two-qubit operations. Finally, we perform an analysis of the error subsets from the importance sampling method used to bound the logical error rates to gain insight into which error sources are particularly detrimental to error correction.

Generalized Fourier transforms classes

DEFF Research Database (Denmark)

Berntsen, Svend; Møller, Steen

2002-01-01

The Fourier class of integral transforms with kernels $B(\\omega r)$ has by definition inverse transforms with kernel $B(-\\omega r)$. The space of such transforms is explicitly constructed. A slightly more general class of generalized Fourier transforms are introduced. From the general theory...

Fourier transforms principles and applications

CERN Document Server

Hansen, Eric W

2014-01-01

Fourier Transforms: Principles and Applications explains transform methods and their applications to electrical systems from circuits, antennas, and signal processors-ably guiding readers from vector space concepts through the Discrete Fourier Transform (DFT), Fourier series, and Fourier transform to other related transform methods.  Featuring chapter end summaries of key results, over two hundred examples and four hundred homework problems, and a Solutions Manual this book is perfect for graduate students in signal processing and communications as well as practicing engineers.

Ultra High-Mass Resolution Paper Spray by Fourier Transform Ion Cyclotron Resonance Mass Spectrometry

Directory of Open Access Journals (Sweden)

Kevin D. Quinn

2012-01-01

Full Text Available Paper Spray Ionization is an atmospheric pressure ionization technique that utilizes an offline electro-osmotic flow to generate ions off a paper medium. This technique can be performed on a Bruker SolariX Fourier transform ion cyclotron resonance mass spectrometer by modifying the existing nanospray source. High-resolution paper spray spectra were obtained for both organic and biological samples to demonstrate the benefit of linking the technique with a high-resolution mass analyzer. Error values in the range 0.23 to 2.14 ppm were obtained for calf lung surfactant extract with broadband mass resolving power (m/Δm50% above 60,000 utilizing an external calibration standard.

Quantized motion of trapped ions

International Nuclear Information System (INIS)

Steinbach, J.

1999-01-01

This thesis is concerned with a theoretical and numerical study of the preparation and coherent manipulation of quantum states in the external and internal degrees of freedom of trapped ions. In its first part, this thesis proposes and investigates schemes for generating several nonclassical states for the quantized vibrational motion of a trapped ion. Based on dark state preparation specific laser excitation configurations are presented which, given appropriately chosen initial states, realize the desired motional states in the steady-state, indicated by the cessation of the fluorescence emitted by the ion. The focus is on the SU(1,1) intelligent states in both their single- and two-mode realization, corresponding to one- and two-dimensional motion of the ion. The presented schemes are also studied numerically using a Monte-Carlo state-vector method. The second part of the thesis describes how two vibrational degrees of freedom of a single trapped ion can be coupled through the action of suitably chosen laser excitation. Concentrating on a two-dimensional ion trap with dissimilar vibrational frequencies a variety of quantized two-mode couplings are derived. The focus is on a linear coupling that takes excitations from one mode to another. It is demonstrated how this can result in a state rotation, in which it is possible to coherently transfer the motional state of the ion between orthogonal directions without prior knowledge of that motional state. The third part of this thesis presents a new efficient method for generating maximally entangled internal states of a collection of trapped ions. The method is deterministic and independent of the number of ions in the trap. As the essential element of the scheme a mechanism for the realization of a controlled NOT operation that can operate on multiple ions is proposed. The potential application of the scheme for high-precision frequency standards is explored. (author)

Determination of vanillin, ethyl vanillin, and coumarin in infant formula by liquid chromatography-quadrupole linear ion trap mass spectrometry.

Science.gov (United States)

Shen, Yan; Han, Chao; Liu, Bin; Lin, Zhengfeng; Zhou, Xiujin; Wang, Chengjun; Zhu, Zhenou

2014-02-01

A simple, precise, accurate, and validated liquid chromatography-quadrupole linear ion trap mass spectrometry method was developed for the determination of vanillin, ethyl vanillin, and coumarin in infant formula samples. Following ultrasonic extraction with methanol/water (1:1, vol/vol), and clean-up on an HLB solid-phase extraction cartridge (Waters Corp., Milford, MA), samples were separated on a Waters XSelect HSS T3 column (150 × 2.1-mm i.d., 5-μm film thickness; Waters Corp.), with 0.1% formic acid solution-acetonitrile as mobile phase at a flow rate of 0.25 mL/min. Quantification of the target was performed by the internal standard approach, using isotopically labeled compounds for each chemical group, to correct matrix effects. Data acquisition was carried out in multiple reaction monitoring transitions mode, monitoring 2 multiple reaction monitoring transitions to ensure an accurate identification of target compounds in the samples. Additional identification and confirmation of target compounds were performed using the enhanced product ion modus of the linear ion trap. The novel liquid chromatography-quadrupole linear ion trap mass spectrometry platform offers the best sensitivity and specificity for characterization and quantitative determination of vanillin, ethyl vanillin, and coumarin in infant formula and fulfills the quality criteria for routine laboratory application. Copyright © 2014 American Dairy Science Association. Published by Elsevier Inc. All rights reserved.

Theory of peak coalescence in Fourier transform ion cyclotron resonance mass spectrometry.

Science.gov (United States)

Boldin, Ivan A; Nikolaev, Eugene N

2009-10-01

Peak coalescence, i.e. the merging of two close peaks in a Fourier transform ion cyclotron resonance (FTICR) mass spectrum at a high number of ions, plays an important role in various FTICR experiments. In order to describe the coalescence phenomenon we would like to propose a new theory of motion for ion clouds with close mass-to-charge ratios, driven by a uniform magnetic field and Coulomb interactions between the clouds. We describe the motion of the ion clouds in terms of their averaged drift motion in crossed magnetic and electric fields. The ion clouds are considered to be of constant size and their motion is studied in two dimensions. The theory deals with the first-order approximation of the equations of motion in relation to dm/m, where dm is the mass difference and m is the mass of a single ion. The analysis was done for an arbitrary inter-cloud interaction potential, which makes it possible to analyze finite-size ion clouds of any shape. The final analytical expression for the condition of the onset of coalescence is found for the case of uniformly charged spheres. An algorithm for finding this condition for an arbitrary interaction potential is proposed. The critical number of ions for the peak coalescence to take place is shown to depend quadratically on the magnetic field strength and to be proportional to the cyclotron radius and inversely proportional to the ion masses. Copyright (c) 2009 John Wiley & Sons, Ltd.

Mats and LaSpec: High-precision experiments using ion traps and lasers at Fair

Energy Technology Data Exchange (ETDEWEB)

Rodriguez, D.; Lallena, A.M.; Blaum, K.; Bohm, C.; Cakirli, R.B.; Crespo Lopez-Urrutia, J.R.; Eliseev, S.; Ketelaer, J.; Kreim, M.S.; Kowalska, M.; Litvinov, Y.A.; Nagy, S.; Neidherr, D.; Repp, J.; Roux, C.; Schabinger, B.; Ullrich, J.; Nortershauser, W.; Eberhardt, K.; Geppert, C.; Kramer, J.; Krieger, A.; Sanchez, R.; Ahammed, M.; Das, P.; Ray, A.; Algora, A.; Rubio, B.; Tain, J.L.; Audi, G.; Lunney, D.; Naimi, S.; Aysto, J.; Jokinen, A.; Kolhinen, V.; Moore, I.; Beck, D.; Block, M.; Geissel, H.; Heinz, S.; Herfurth, F.; Litvinov, Y.A.; Minaya-Ramirez, E.; Plab, W.R.; Quint, W.; Scheidenberger, C.; Winkler, M.; Bender, M.; Billowes, J.; Campbell, P.; Flanagan, K.T.; Schwarz, S.; Bollen, G.; Ferrer, R.; George, S.; Kester, O.; Brodeur, M.; Brunner, T.; Delheij, P.; Dilling, J.; Ettenauer, S.; Lapierre, A.; Bushaw, B.A.; Cano-Ott, D.; Martinez, T.; Cortes, G.; Gomez-Hornillos, M.B.; Dax, A.; Herlert, A.; Yordanov, D.; De, A.; Dickel, T.; Geissel, H.; Jesch, C.; Kuhl, T.; Petrick, M.; PlaB, W.R.; Scheidenberger, C.; Garcia-Ramos, J.E.; Gartzke, E.; Habs, D.; Szerypo, J.; Thirolf, P.G.; Weber, C.; Gusev, Y.; Nesterenko, D.; Novikov, Y.N.; Popov, A.; Seliverstov, M.; Vasiliev, A.; Vorobjev, G.; Heenen, P.H.; Marx, G.; Schweikhard, L.; Ziegler, F.; Hobein, M.; Schuch, R.; Solders, A.; Suhonen, M.; Huber, G.; Wendt, K.; Huyse, M.; Koudriavtsev, I.; Neyens, G.; Van Duppen, P.; Le Blanc, F.; Matos, M.; Reinhard, P.G.; Schneider, D.

2010-05-15

Nuclear ground state properties including mass, charge radii, spins and moments can be determined by applying atomic physics techniques such as Penning-trap based mass spectrometry and laser spectroscopy. The MATS and LaSpec setups at the low-energy beamline at FAIR will allow us to extend the knowledge of these properties further into the region far from stability. With MATS (Precision Measurements of very short-lived nuclei using an Advanced Trapping System for highly-charged ions) at FAIR we aim to apply several techniques to very short-lived radionuclides: High-accuracy mass measurements, in-trap conversion electron and alpha spectroscopy, and trap-assisted spectroscopy. The experimental setup of MATS is a unique combination of an electron beam ion trap for charge breeding, ion traps for beam preparation, and a high-precision Penning trap system for mass measurements and decay studies. For the mass measurements, MATS offers both a high accuracy and a high sensitivity. A relative mass uncertainty of 10{sup -9} can be reached by employing highly-charged ions and a non-destructive Fourier-Transform Ion-Cyclotron-Resonance (FT-ICR) detection technique on single stored ions. Decay studies in ion traps will become possible with MATS. Laser spectroscopy of radioactive isotopes and isomers is an efficient and model-independent approach for the determination of nuclear ground and isomeric state properties. Hyperfine structures and isotope shifts in electronic transitions exhibit readily accessible information on the nuclear spin, magnetic dipole and electric quadrupole moments as well as root-mean-square charge radii. The accuracy of laser-spectroscopic-determined nuclear properties is very high while requirements concerning production rates are moderate. This Technical Design Report describes a new Penning trap mass spectrometry setup as well as a number of complementary experimental devices for laser spectroscopy. Since MATS and LaSpec require high-quality low

Mats and LaSpec: High-precision experiments using ion traps and lasers at Fair

International Nuclear Information System (INIS)

Rodriguez, D.; Lallena, A.M.; Blaum, K.; Bohm, C.; Cakirli, R.B.; Crespo Lopez-Urrutia, J.R.; Eliseev, S.; Ketelaer, J.; Kreim, M.S.; Kowalska, M.; Litvinov, Y.A.; Nagy, S.; Neidherr, D.; Repp, J.; Roux, C.; Schabinger, B.; Ullrich, J.; Nortershauser, W.; Eberhardt, K.; Geppert, C.; Kramer, J.; Krieger, A.; Sanchez, R.; Ahammed, M.; Das, P.; Ray, A.; Algora, A.; Rubio, B.; Tain, J.L.; Audi, G.; Lunney, D.; Naimi, S.; Aysto, J.; Jokinen, A.; Kolhinen, V.; Moore, I.; Beck, D.; Block, M.; Geissel, H.; Heinz, S.; Herfurth, F.; Litvinov, Y.A.; Minaya-Ramirez, E.; Plab, W.R.; Quint, W.; Scheidenberger, C.; Winkler, M.; Bender, M.; Billowes, J.; Campbell, P.; Flanagan, K.T.; Schwarz, S.; Bollen, G.; Ferrer, R.; George, S.; Kester, O.; Brodeur, M.; Brunner, T.; Delheij, P.; Dilling, J.; Ettenauer, S.; Lapierre, A.; Bushaw, B.A.; Cano-Ott, D.; Martinez, T.; Cortes, G.; Gomez-Hornillos, M.B.; Dax, A.; Herlert, A.; Yordanov, D.; De, A.; Dickel, T.; Geissel, H.; Jesch, C.; Kuhl, T.; Petrick, M.; PlaB, W.R.; Scheidenberger, C.; Garcia-Ramos, J.E.; Gartzke, E.; Habs, D.; Szerypo, J.; Thirolf, P.G.; Weber, C.; Gusev, Y.; Nesterenko, D.; Novikov, Y.N.; Popov, A.; Seliverstov, M.; Vasiliev, A.; Vorobjev, G.; Heenen, P.H.; Marx, G.; Schweikhard, L.; Ziegler, F.; Hobein, M.; Schuch, R.; Solders, A.; Suhonen, M.; Huber, G.; Wendt, K.; Huyse, M.; Koudriavtsev, I.; Neyens, G.; Van Duppen, P.; Le Blanc, F.; Matos, M.; Reinhard, P.G.; Schneider, D.

2010-01-01

Nuclear ground state properties including mass, charge radii, spins and moments can be determined by applying atomic physics techniques such as Penning-trap based mass spectrometry and laser spectroscopy. The MATS and LaSpec setups at the low-energy beamline at FAIR will allow us to extend the knowledge of these properties further into the region far from stability. With MATS (Precision Measurements of very short-lived nuclei using an Advanced Trapping System for highly-charged ions) at FAIR we aim to apply several techniques to very short-lived radionuclides: High-accuracy mass measurements, in-trap conversion electron and alpha spectroscopy, and trap-assisted spectroscopy. The experimental setup of MATS is a unique combination of an electron beam ion trap for charge breeding, ion traps for beam preparation, and a high-precision Penning trap system for mass measurements and decay studies. For the mass measurements, MATS offers both a high accuracy and a high sensitivity. A relative mass uncertainty of 10 -9 can be reached by employing highly-charged ions and a non-destructive Fourier-Transform Ion-Cyclotron-Resonance (FT-ICR) detection technique on single stored ions. Decay studies in ion traps will become possible with MATS. Laser spectroscopy of radioactive isotopes and isomers is an efficient and model-independent approach for the determination of nuclear ground and isomeric state properties. Hyperfine structures and isotope shifts in electronic transitions exhibit readily accessible information on the nuclear spin, magnetic dipole and electric quadrupole moments as well as root-mean-square charge radii. The accuracy of laser-spectroscopic-determined nuclear properties is very high while requirements concerning production rates are moderate. This Technical Design Report describes a new Penning trap mass spectrometry setup as well as a number of complementary experimental devices for laser spectroscopy. Since MATS and LaSpec require high-quality low-energy beams

Signals and transforms in linear systems analysis

CERN Document Server

Wasylkiwskyj, Wasyl

2013-01-01

Signals and Transforms in Linear Systems Analysis covers the subject of signals and transforms, particularly in the context of linear systems theory. Chapter 2 provides the theoretical background for the remainder of the text. Chapter 3 treats Fourier series and integrals. Particular attention is paid to convergence properties at step discontinuities. This includes the Gibbs phenomenon and its amelioration via the Fejer summation techniques. Special topics include modulation and analytic signal representation, Fourier transforms and analytic function theory, time-frequency analysis and frequency dispersion. Fundamentals of linear system theory for LTI analogue systems, with a brief account of time-varying systems, are covered in Chapter 4 . Discrete systems are covered in Chapters 6 and 7.  The Laplace transform treatment in Chapter 5 relies heavily on analytic function theory as does Chapter 8 on Z -transforms. The necessary background on complex variables is provided in Appendix A. This book is intended to...

Generalized Fourier transforms classes

DEFF Research Database (Denmark)

Berntsen, Svend; Møller, Steen

2002-01-01

The Fourier class of integral transforms with kernels $B(\\omega r)$ has by definition inverse transforms with kernel $B(-\\omega r)$. The space of such transforms is explicitly constructed. A slightly more general class of generalized Fourier transforms are introduced. From the general theory foll...... follows that integral transform with kernels which are products of a Bessel and a Hankel function or which is of a certain general hypergeometric type have inverse transforms of the same structure....

Determination of Oxidized Phosphatidylcholines by Hydrophilic Interaction Liquid Chromatography Coupled to Fourier Transform Mass Spectrometry

Directory of Open Access Journals (Sweden)

Pia Sala

2015-04-01

Full Text Available A novel liquid chromatography-mass spectrometry (LC-MS approach for analysis of oxidized phosphatidylcholines by an Orbitrap Fourier Transform mass spectrometer in positive electrospray ionization (ESI coupled to hydrophilic interaction liquid chromatography (HILIC was developed. This method depends on three selectivity criteria for separation and identification: retention time, exact mass at a resolution of 100,000 and collision induced dissociation (CID fragment spectra in a linear ion trap. The process of chromatography development showed the best separation properties with a silica-based Kinetex column. This type of chromatography was able to separate all major lipid classes expected in mammalian samples, yielding increased sensitivity of oxidized phosphatidylcholines over reversed phase chromatography. Identification of molecular species was achieved by exact mass on intact molecular ions and CID tandem mass spectra containing characteristic fragments. Due to a lack of commercially available standards, method development was performed with copper induced oxidation products of palmitoyl-arachidonoyl-phosphatidylcholine, which resulted in a plethora of lipid species oxidized at the arachidonoyl moiety. Validation of the method was done with copper oxidized human low-density lipoprotein (LDL prepared by ultracentrifugation. In these LDL samples we could identify 46 oxidized molecular phosphatidylcholine species out of 99 possible candidates.

Ion Motion Stability in Asymmetric Surface Electrode Ion Traps

Science.gov (United States)

Shaikh, Fayaz; Ozakin, Arkadas

2010-03-01

Many recently developed designs of the surface electrode ion traps for quantum information processing have asymmetry built into their geometries. The asymmetry helps rotate the trap axes to angles with respect to electrode surface that facilitate laser cooling of ions but introduces a relative angle between the RF and DC fields and invalidates the classical stability analysis of the symmetric case for which the equations of motion are decoupled. For asymmetric case the classical motion of a single ion is given by a coupled, multi-dimensional version of Mathieu's equation. In this poster we discuss the stability diagram of asymmetric surface traps by performing an approximate multiple scale perturbation analysis of the coupled Mathieu equations, and validate the results with numerical simulations. After obtaining the stability diagram for the linear fields, we simulate the motion of an ion in a given asymmetric surface trap, utilizing a method-of-moments calculation of the electrode fields. We obtain the stability diagram and compare it with the ideal case to find the region of validity. Finally, we compare the results of our stability analysis to experiments conducted on a microfabricated asymmetric surface trap.

Tunable fractional-order Fourier transformer

International Nuclear Information System (INIS)

Malyutin, A A

2006-01-01

A fractional two-dimensional Fourier transformer whose orders are tuned by means of optical quadrupoles is described. It is shown that in the optical scheme considered, the Fourier-transform order a element of [0,1] in one of the mutually orthogonal planes corresponds to the transform order (2-a) in another plane, i.e., to inversion and inverse Fourier transform of the order a. (laser modes and beams)

Integrated fiber-mirror ion trap for strong ion-cavity coupling

International Nuclear Information System (INIS)

Brandstätter, B.; Schüppert, K.; Casabone, B.; Friebe, K.; Stute, A.; Northup, T. E.; McClung, A.; Schmidt, P. O.; Deutsch, C.; Reichel, J.; Blatt, R.

2013-01-01

We present and characterize fiber mirrors and a miniaturized ion-trap design developed to integrate a fiber-based Fabry-Perot cavity (FFPC) with a linear Paul trap for use in cavity-QED experiments with trapped ions. Our fiber-mirror fabrication process not only enables the construction of FFPCs with small mode volumes, but also allows us to minimize the influence of the dielectric fiber mirrors on the trapped-ion pseudopotential. We discuss the effect of clipping losses for long FFPCs and the effect of angular and lateral displacements on the coupling efficiencies between cavity and fiber. Optical profilometry allows us to determine the radii of curvature and ellipticities of the fiber mirrors. From finesse measurements, we infer a single-atom cooperativity of up to 12 for FFPCs longer than 200 μm in length; comparison to cavities constructed with reference substrate mirrors produced in the same coating run indicates that our FFPCs have similar scattering losses. We characterize the birefringence of our fiber mirrors, finding that careful fiber-mirror selection enables us to construct FFPCs with degenerate polarization modes. As FFPCs are novel devices, we describe procedures developed for handling, aligning, and cleaning them. We discuss experiments to anneal fiber mirrors and explore the influence of the atmosphere under which annealing occurs on coating losses, finding that annealing under vacuum increases the losses for our reference substrate mirrors. X-ray photoelectron spectroscopy measurements indicate that these losses may be attributable to oxygen depletion in the mirror coating. Special design considerations enable us to introduce a FFPC into a trapped ion setup. Our unique linear Paul trap design provides clearance for such a cavity and is miniaturized to shield trapped ions from the dielectric fiber mirrors. We numerically calculate the trap potential in the absence of fibers. In the experiment additional electrodes can be used to compensate

Optical surfacing via linear ion source

International Nuclear Information System (INIS)

Wu, Lixiang; Wei, Chaoyang; Shao, Jianda

2017-01-01

We present a concept of surface decomposition extended from double Fourier series to nonnegative sinusoidal wave surfaces, on the basis of which linear ion sources apply to the ultra-precision fabrication of complex surfaces and diffractive optics. The modified Fourier series, or sinusoidal wave surfaces, build a relationship between the fabrication process of optical surfaces and the surface characterization based on power spectral density (PSD) analysis. Also, we demonstrate that the one-dimensional scanning of linear ion source is applicable to the removal of mid-spatial frequency (MSF) errors caused by small-tool polishing in raster scan mode as well as the fabrication of beam sampling grating of high diffractive uniformity without a post-processing procedure. The simulation results show that optical fabrication with linear ion source is feasible and even of higher output efficiency compared with the conventional approach.

Optical surfacing via linear ion source

Energy Technology Data Exchange (ETDEWEB)

Wu, Lixiang, E-mail: wulx@hdu.edu.cn [Key Lab of RF Circuits and Systems of Ministry of Education, Zhejiang Provincial Key Lab of LSI Design, Microelectronics CAD Center, College of Electronics and Information, Hangzhou Dianzi University, Hangzhou (China); Wei, Chaoyang, E-mail: siomwei@siom.ac.cn [Key Laboratory of Materials for High Power Laser, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai 201800 (China); Shao, Jianda, E-mail: jdshao@siom.ac.cn [Key Laboratory of Materials for High Power Laser, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai 201800 (China)

2017-04-15

We present a concept of surface decomposition extended from double Fourier series to nonnegative sinusoidal wave surfaces, on the basis of which linear ion sources apply to the ultra-precision fabrication of complex surfaces and diffractive optics. The modified Fourier series, or sinusoidal wave surfaces, build a relationship between the fabrication process of optical surfaces and the surface characterization based on power spectral density (PSD) analysis. Also, we demonstrate that the one-dimensional scanning of linear ion source is applicable to the removal of mid-spatial frequency (MSF) errors caused by small-tool polishing in raster scan mode as well as the fabrication of beam sampling grating of high diffractive uniformity without a post-processing procedure. The simulation results show that optical fabrication with linear ion source is feasible and even of higher output efficiency compared with the conventional approach.

Ion bunch stacking in a Penning trap after purification in an electrostatic mirror trap

CERN Document Server

Rosenbusch, M; Blaum, K; Borgmann, Ch; Kreim, S; Lunney, D; Manea, V; Schweikhard, L; Wienholtz, F; Wolf, R N

2014-01-01

The success of many measurements in analytical mass spectrometry as well as in precision mass determinations for atomic and nuclear physics is handicapped when the ion sources deliver ``contaminations'', i.e., unwanted ions of masses similar to those of the ions of interest. In particular, in ion-trapping devices, large amounts of contaminant ions result in significant systematic errors-if the measurements are possible at all. We present a solution for such cases: The ions from a quasi-continuous source are bunched in a linear radio-frequency-quadrupole ion trap, separated by a multi-reflection time-of-flight section followed by a Bradbury-Nielsen gate, and then captured in a Penning trap. Buffer-gas cooling is used to damp the ion motion in the latter, which allows a repeated opening of the Penning trap for a stacking of mass-selected ion bunches. Proof-of-principle demonstrations have been performed with the ISOLTRAP setup at ISOLDE/CERN, both with Cs-133(+) ions from an off-line ion source and by applicati...

Quantum information processing with trapped ions

International Nuclear Information System (INIS)

Haeffner, H.; Haensel, W.; Rapol, U.; Koerber, T.; Benhelm, J.; Riebe, M.; Chek-al-Kar, D.; Schmidt-Kaler, F.; Becher, C.; Roos, C.; Blatt, R.

2005-01-01

Single Ca + ions and crystals of Ca + ions are confined in a linear Paul trap and are investigated for quantum information processing. Here we report on recent experimental advancements towards a quantum computer with such a system. Laser-cooled trapped ions are ideally suited systems for the investigation and implementation of quantum information processing as one can gain almost complete control over their internal and external degrees of freedom. The combination of a Paul type ion trap with laser cooling leads to unique properties of trapped cold ions, such as control of the motional state down to the zero-point of the trapping potential, a high degree of isolation from the environment and thus a very long time available for manipulations and interactions at the quantum level. The very same properties make single trapped atoms and ions well suited for storing quantum information in long lived internal states, e.g. by encoding a quantum bit (qubit) of information within the coherent superposition of the S 1/2 ground state and the metastable D 5/2 excited state of Ca + . Recently we have achieved the implementation of simple algorithms with up to 3 qubits on an ion-trap quantum computer. We will report on methods to implement single qubit rotations, the realization of a two-qubit universal quantum gate (Cirac-Zoller CNOT-gate), the deterministic generation of multi-particle entangled states (GHZ- and W-states), their full tomographic reconstruction, the realization of deterministic quantum teleportation, its quantum process tomography and the encoding of quantum information in decoherence-free subspaces with coherence times exceeding 20 seconds. (author)

Scalable error correction in distributed ion trap computers

International Nuclear Information System (INIS)

Oi, Daniel K. L.; Devitt, Simon J.; Hollenberg, Lloyd C. L.

2006-01-01

A major challenge for quantum computation in ion trap systems is scalable integration of error correction and fault tolerance. We analyze a distributed architecture with rapid high-fidelity local control within nodes and entangled links between nodes alleviating long-distance transport. We demonstrate fault-tolerant operator measurements which are used for error correction and nonlocal gates. This scheme is readily applied to linear ion traps which cannot be scaled up beyond a few ions per individual trap but which have access to a probabilistic entanglement mechanism. A proof-of-concept system is presented which is within the reach of current experiment

Simultaneous and Sequential MS/MS Scan Combinations and Permutations in a Linear Quadrupole Ion Trap.

Science.gov (United States)

Snyder, Dalton T; Szalwinski, Lucas J; Cooks, R Graham

2017-10-17

Methods of performing precursor ion scans as well as neutral loss scans in a single linear quadrupole ion trap have recently been described. In this paper we report methodology for performing permutations of MS/MS scan modes, that is, ordered combinations of precursor, product, and neutral loss scans following a single ion injection event. Only particular permutations are allowed; the sequences demonstrated here are (1) multiple precursor ion scans, (2) precursor ion scans followed by a single neutral loss scan, (3) precursor ion scans followed by product ion scans, and (4) segmented neutral loss scans. (5) The common product ion scan can be performed earlier in these sequences, under certain conditions. Simultaneous scans can also be performed. These include multiple precursor ion scans, precursor ion scans with an accompanying neutral loss scan, and multiple neutral loss scans. We argue that the new capability to perform complex simultaneous and sequential MS n operations on single ion populations represents a significant step in increasing the selectivity of mass spectrometry.

Intrinsic anharmonic effects on the phonon frequencies and effective spin-spin interactions in a quantum simulator made from trapped ions in a linear Paul trap

Science.gov (United States)

McAneny, M.; Freericks, J. K.

2014-11-01

The Coulomb repulsion between ions in a linear Paul trap gives rise to anharmonic terms in the potential energy when expanded about the equilibrium positions. We examine the effect of these anharmonic terms on the accuracy of a quantum simulator made from trapped ions. To be concrete, we consider a linear chain of Yb171+ ions stabilized close to the zigzag transition. We find that for typical experimental temperatures, frequencies change by no more than a factor of 0.01 % due to the anharmonic couplings. Furthermore, shifts in the effective spin-spin interactions (driven by a spin-dependent optical dipole force) are also, in general, less than 0.01 % for detunings to the blue of the transverse center-of-mass frequency. However, detuning the spin interactions near other frequencies can lead to non-negligible anharmonic contributions to the effective spin-spin interactions. We also examine an odd behavior exhibited by the harmonic spin-spin interactions for a range of intermediate detunings, where nearest-neighbor spins with a larger spatial separation on the ion chain interact more strongly than nearest neighbors with a smaller spatial separation.

General Correlation Theorem for Trinion Fourier Transform

OpenAIRE

Bahri, Mawardi

2017-01-01

- The trinion Fourier transform is an extension of the Fourier transform in the trinion numbers setting. In this work we derive the correlation theorem for the trinion Fourier transform by using the relation between trinion convolution and correlation definitions in the trinion Fourier transform domains.

Note: Ion source design for ion trap systems

Science.gov (United States)

Noriega, J. R.; Quevedo, M.; Gnade, B.; Vasselli, J.

2013-06-01

A small plasma (glow discharge) based ion source and circuit are described in this work. The ion source works by producing a high voltage pulsed discharge between two electrodes in a pressure range of 50-100 mTorr. A third mesh electrode is used for ion extraction. The electrodes are small stainless steel screws mounted in a MACOR ionization chamber in a linear arrangement. The electrode arrangement is driven by a circuit, design for low power operation. This design is a proof of concept intended for applications on small cylindrical ion traps.

Sideband cooling and coherent dynamics in a microchip multi-segmented ion trap

Energy Technology Data Exchange (ETDEWEB)

Schulz, Stephan A; Poschinger, Ulrich; Ziesel, Frank; Schmidt-Kaler, Ferdinand [Universitaet Ulm, Institut fuer Quanteninformationsverarbeitung, Albert-Einstein-Allee 11, D-89069 Ulm (Germany)], E-mail: stephan.schulz@uni-ulm.de

2008-04-15

Miniaturized ion trap arrays with many trap segments present a promising architecture for scalable quantum information processing. The miniaturization of segmented linear Paul traps allows partitioning the microtrap into different storage and processing zones. The individual position control of many ions-each of them carrying qubit information in its long-lived electronic levels-by the external trap control voltages is important for the implementation of next generation large-scale quantum algorithms. We present a novel scalable microchip multi-segmented ion trap with two different adjacent zones, one for the storage and another dedicated to the processing of quantum information using single ions and linear ion crystals. A pair of radio-frequency-driven electrodes and 62 independently controlled dc electrodes allows shuttling of single ions or linear ion crystals with numerically designed axial potentials at axial and radial trap frequencies of a few megahertz. We characterize and optimize the microtrap using sideband spectroscopy on the narrow S{sub 1/2}{r_reversible}D{sub 5/2} qubit transition of the {sup 40}Ca{sup +} ion, and demonstrate coherent single-qubit Rabi rotations and optical cooling methods. We determine the heating rate using sideband cooling measurements to the vibrational ground state, which is necessary for subsequent two-qubit quantum logic operations. The applicability for scalable quantum information processing is proved.

Electrodynamically trapped Yb+ ions for quantum information processing

International Nuclear Information System (INIS)

Balzer, Chr.; Braun, A.; Hannemann, T.; Wunderlich, Chr.; Paape, Chr.; Ettler, M.; Neuhauser, W.

2006-01-01

Highly efficient, nearly deterministic, and isotope selective generation of Yb + ions by one- and two-color photoionization is demonstrated. State preparation and state selective detection of hyperfine states in 171 Yb + is investigated in order to optimize the purity of the prepared state and to time-optimize the detection process. Linear laser-cooled Yb + ion crystals confined in a Paul trap are demonstrated. Advantageous features of different previous ion trap experiments are combined, while at the same time the number of possible error sources is reduced by using a comparatively simple experimental apparatus. This opens a new path toward quantum state manipulation of individual trapped ions, and in particular, to scalable quantum computing

A Short Biography of Joseph Fourier and Historical Development of Fourier Series and Fourier Transforms

Science.gov (United States)

Debnath, Lokenath

2012-01-01

This article deals with a brief biographical sketch of Joseph Fourier, his first celebrated work on analytical theory of heat, his first great discovery of Fourier series and Fourier transforms. Included is a historical development of Fourier series and Fourier transforms with their properties, importance and applications. Special emphasis is made…

Demonstration of Cold 40Ca+ Ions Confined in a Microscopic Surface-Electrode Ion Trap

International Nuclear Information System (INIS)

Chen Liang; Wan Wei; Xie Yi; Wu Hao-Yu; Zhou Fei; Feng Mang

2013-01-01

40 Ca + ions are successfully confined, under the cooling of a red-detuned laser, in a home-built microscopic surface-electrode (MSE) trap. With all electrodes deposited on a low-rf-loss substrate, our 500-μm-scale MSE trap is designed involving three potential wells and manufactured by the standard technique of the printed circuit board. Both linear and two-dimensional crystals of 40 Ca + are observed in the trap after preliminary micromotion compensation is carried out. The development of the MSE trap aims at large-scale trapped-ion quantum information processing

Cold highly charged ions in a cryogenic Paul trap

Energy Technology Data Exchange (ETDEWEB)

Versolato, O. O., E-mail: oscar.versolato@mpi-hd.mpg.de; Schwarz, M.; Windberger, A.; Ullrich, J. [Max-Planck-Institut fuer Kernphysik (Germany); Schmidt, P. O. [Physikalisch-Technische Bundesanstalt (Germany); Drewsen, M. [University of Aarhus, Department of Physics and Astronomy (Denmark); Crespo Lopez-Urrutia, J. R. [Max-Planck-Institut fuer Kernphysik (Germany)

2013-03-15

Narrow optical transitions in highly charged ions (HCIs) are of particular interest for metrology and fundamental physics, exploiting the high sensitivity of HCIs to new physics. The highest sensitivity for a changing fine structure constant ever predicted for a stable atomic system is found in Ir{sup 17 + }. However, laser spectroscopy of HCIs is hindered by the large ({approx} 10{sup 6} K) temperatures at which they are produced and trapped. An unprecedented improvement in such laser spectroscopy can be obtained when HCIs are cooled down to the mK range in a linear Paul trap. We have developed a cryogenic linear Paul trap in which HCIs will be sympathetically cooled by {sup 9}Be{sup + } ions. Optimized optical access for laser light is provided while maintaining excellent UHV conditions. The Paul trap will be connected to an electron beam ion trap (EBIT) which is able to produce a wide range of HCIs. This EBIT will also provide the first experimental input needed for the determination of the transition energies in Ir{sup 17 + }, enabling further laser-spectroscopic investigations of this promising HCI.

Fourier transform resampling: Theory and application

International Nuclear Information System (INIS)

Hawkins, W.G.

1996-01-01

One of the most challenging problems in medical imaging is the development of reconstruction algorithms for nonstandard geometries. This work focuses on the application of Fourier analysis to the problem of resampling or rebinning. Conventional resampling methods utilizing some form of interpolation almost always result in a loss of resolution in the tomographic image. Fourier Transform Resampling (FTRS) offers potential improvement because the Modulation Transfer Function (MTF) of the process behaves like an ideal low pass filter. The MTF, however, is nonstationary if the coordinate transformation is nonlinear. FTRS may be viewed as a generalization of the linear coordinate transformations of standard Fourier analysis. Simulated MTF's were obtained by projecting point sources at different transverse positions in the flat fan beam detector geometry. These MTF's were compared to the closed form expression for FIRS. Excellent agreement was obtained for frequencies at or below the estimated cutoff frequency. The resulting FTRS algorithm is applied to simulations with symmetric fan beam geometry, an elliptical orbit and uniform attenuation, with a normalized root mean square error (NRME) of 0.036. Also, a Tc-99m point source study (1 cm dia., placed in air 10 cm from the COR) for a circular fan beam acquisition was reconstructed with a hybrid resampling method. The FWHM of the hybrid resampling method was 11.28 mm and compares favorably with a direct reconstruction (FWHM: 11.03 mm)

Control of the conformations of ion Coulomb crystals in a Penning trap

Science.gov (United States)

Mavadia, Sandeep; Goodwin, Joseph F.; Stutter, Graham; Bharadia, Shailen; Crick, Daniel R.; Segal, Daniel M.; Thompson, Richard C.

2013-01-01

Laser-cooled atomic ions form ordered structures in radiofrequency ion traps and in Penning traps. Here we demonstrate in a Penning trap the creation and manipulation of a wide variety of ion Coulomb crystals formed from small numbers of ions. The configuration can be changed from a linear string, through intermediate geometries, to a planar structure. The transition from a linear string to a zigzag geometry is observed for the first time in a Penning trap. The conformations of the crystals are set by the applied trap potential and the laser parameters, and agree with simulations. These simulations indicate that the rotation frequency of a small crystal is mainly determined by the laser parameters, independent of the number of ions and the axial confinement strength. This system has potential applications for quantum simulation, quantum information processing and tests of fundamental physics models from quantum field theory to cosmology. PMID:24096901

Generalizing, optimizing, and inventing numerical algorithms for the fractional Fourier, Fresnel, and linear canonical transforms

Science.gov (United States)

Hennelly, Bryan M.; Sheridan, John T.

2005-05-01

By use of matrix-based techniques it is shown how the space-bandwidth product (SBP) of a signal, as indicated by the location of the signal energy in the Wigner distribution function, can be tracked through any quadratic-phase optical system whose operation is described by the linear canonical transform. Then, applying the regular uniform sampling criteria imposed by the SBP and linking the criteria explicitly to a decomposition of the optical matrix of the system, it is shown how numerical algorithms (employing interpolation and decimation), which exhibit both invertibility and additivity, can be implemented. Algorithms appearing in the literature for a variety of transforms (Fresnel, fractional Fourier) are shown to be special cases of our general approach. The method is shown to allow the existing algorithms to be optimized and is also shown to permit the invention of many new algorithms.

Cryogenic surface ion traps

International Nuclear Information System (INIS)

Niedermayr, M.

2015-01-01

Microfabricated surface traps are a promising architecture to realize a scalable quantum computer based on trapped ions. In principle, hundreds or thousands of surface traps can be located on a single substrate in order to provide large arrays of interacting ions. To this end, trap designs and fabrication methods are required that provide scalable, stable and reproducible ion traps. This work presents a novel surface-trap design developed for cryogenic applications. Intrinsic silicon is used as the substrate material of the traps. The well-developed microfabrication and structuring methods of silicon are utilized to create simple and reproducible traps. The traps were tested and characterized in a cryogenic setup. Ions could be trapped and their life time and motional heating were investigated. Long ion lifetimes of several hours were observed and the measured heating rates were reproducibly low at around 1 phonon per second at a trap frequency of 1 MHz. (author) [de

Fourier transformation for engineering and natural science

International Nuclear Information System (INIS)

Klingen, B.

2001-01-01

The following topics are covered: functions, Dirac delta function, Fourier operators, Fourier integrals, Fourier transformation and periodic functions, discrete Fourier transformations and discrete filters, applications. (WL)

Multi-Beam Radio Frequency (RF) Aperture Arrays Using Multiplierless Approximate Fast Fourier Transform (FFT)

Science.gov (United States)

2017-08-01

Fourier transform, discrete Fourier transform, digital array processing , antenna beamformers 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF...125 3.7 Simulation of 2-D Beams Cross Sections .................................................................... 125 3.7.1 8...unlimited. List of Figures Figure Page Figure 1: N-beam Array Processing System using a Linear Array

Cluster observations of trapped ions interacting with magnetosheath mirror modes

Directory of Open Access Journals (Sweden)

J. Soucek

2011-06-01

Full Text Available Mirror modes are among the most intense low frequency plasma wave phenomena observed in the magnetosheaths of magnetized planets. They appear as large amplitude non-propagating fluctuations in the magnetic field magnitude and plasma density. These structures are widely accepted to represent a non-linear stage of the mirror instability, dominant in plasmas with large ion beta and a significant ion temperature anisotropy T⊥/T∥>1. It has long been recognized that the mirror instability both in the linear and non-linear stage is a kinetic process and that the behavior of resonant particles at small parallel velocities is crucial for its development and saturation. While the dynamics of the instability and the effect of trapped particles have been studied extensively in theoretical models and numerical simulations, only spurious observations of the trapped ions were published to date. In this work we used data from the Cluster spacecraft to perform the first detailed experimental study of ion velocity distribution associated with mirror mode oscillations. We show a conclusive evidence for the predicted cooling of resonant ions at small parallel velocities and heating of trapped ions at intermediate pitch angles.

Controlling trapping potentials and stray electric fields in a microfabricated ion trap through design and compensation

International Nuclear Information System (INIS)

Charles Doret, S; Amini, Jason M; Wright, Kenneth; Volin, Curtis; Killian, Tyler; Ozakin, Arkadas; Denison, Douglas; Hayden, Harley; Pai, C-S; Slusher, Richart E; Harter, Alexa W

2012-01-01

Recent advances in quantum information processing with trapped ions have demonstrated the need for new ion trap architectures capable of holding and manipulating chains of many (>10) ions. Here we present the design and detailed characterization of a new linear trap, microfabricated with scalable complementary metal-oxide-semiconductor (CMOS) techniques, that is well-suited to this challenge. Forty-four individually controlled dc electrodes provide the many degrees of freedom required to construct anharmonic potential wells, shuttle ions, merge and split ion chains, precisely tune secular mode frequencies, and adjust the orientation of trap axes. Microfabricated capacitors on dc electrodes suppress radio-frequency pickup and excess micromotion, while a top-level ground layer simplifies modeling of electric fields and protects trap structures underneath. A localized aperture in the substrate provides access to the trapping region from an oven below, permitting deterministic loading of particular isotopic/elemental sequences via species-selective photoionization. The shapes of the aperture and radio-frequency electrodes are optimized to minimize perturbation of the trapping pseudopotential. Laboratory experiments verify simulated potentials and characterize trapping lifetimes, stray electric fields, and ion heating rates, while measurement and cancellation of spatially-varying stray electric fields permits the formation of nearly-equally spaced ion chains. (paper)

Trapping radioactive ions

CERN Document Server

Kluge, Heinz-Jürgen

2004-01-01

Trapping devices for atomic and nuclear physics experiments with radioactive ions are becoming more and more important at accelerator facilities. While about ten years ago only one online Penning trap experiment existed, namely ISOLTRAP at ISOLDE/CERN, meanwhile almost every radioactive beam facility has installed or plans an ion trap setup. This article gives an overview on ion traps in the operation, construction or planing phase which will be used for fundamental studies with short-lived radioactive nuclides such as mass spectrometry, laser spectroscopy and nuclear decay spectroscopy. In addition, this article summarizes the use of gas cells and radiofrequency quadrupole (Paul) traps at different facilities as a versatile tool for ion beam manipulation like retardation, cooling, bunching, and cleaning.

Trapping radioactive ions

International Nuclear Information System (INIS)

Kluge, H.-J.; Blaum, K.

2004-01-01

Trapping devices for atomic and nuclear physics experiments with radioactive ions are becoming more and more important at accelerator facilities. While about ten years ago only one online Penning trap experiment existed, namely ISOLTRAP at ISOLDE/CERN, meanwhile almost every radioactive beam facility has installed or plans an ion trap setup. This article gives an overview on ion traps in the operation, construction or planing phase which will be used for fundamental studies with short-lived radioactive nuclides such as mass spectrometry, laser spectroscopy and nuclear decay spectroscopy. In addition, this article summarizes the use of gas cells and radiofrequency quadrupole (Paul) traps at different facilities as a versatile tool for ion beam manipulation like retardation, cooling, bunching, and cleaning

A Unified Method of Finding Laplace Transforms, Fourier Transforms, and Fourier Series. [and] An Inversion Method for Laplace Transforms, Fourier Transforms, and Fourier Series. Integral Transforms and Series Expansions. Modules and Monographs in Undergraduate Mathematics and Its Applications Project. UMAP Units 324 and 325.

Science.gov (United States)

Grimm, C. A.

This document contains two units that examine integral transforms and series expansions. In the first module, the user is expected to learn how to use the unified method presented to obtain Laplace transforms, Fourier transforms, complex Fourier series, real Fourier series, and half-range sine series for given piecewise continuous functions. In…

On fractional Fourier transform moments

NARCIS (Netherlands)

Alieva, T.; Bastiaans, M.J.

2000-01-01

Based on the relation between the ambiguity function represented in a quasi-polar coordinate system and the fractional power spectra, the fractional Fourier transform moments are introduced. Important equalities for the global second-order fractional Fourier transform moments are derived and their

Digital quantum simulation, Schrödinger cat state spectroscopy and setting up a linear ion trap

International Nuclear Information System (INIS)

Hempel, C.

2014-01-01

This PhD thesis reports on two experiments in the field of quantum information processing using trapped calcium ions. In addition, the text covers the setup and characterization of a new linear Paul trap accompanied by a novel implementation of single-ion addressing using an acousto-optic deflector. The first of the two experiments is concerned with the proof-of-principle implementation of digital quantum simulations using up to 6 ions and 100 gate operations. It investigates the scaling behavior of simulations of elementary models of magnetism in terms of the number of involved spins and the complexity of their mutual interactions. The second experiment introduces the application of a Schroedinger cat state in the indirect detection of photon scattering events on a broad electronic transition. The method is shown to have a sensitivity down to the single photon level in a proof-of-principle demonstration using a mixed-isotope crystal of 40Ca+ and 44Ca+. A brief outlook towards future experiments and extensions of the experimental setup concludes the manuscript.(author) [de

Development of a radiofrequency linear ion trap for {beta} decay study

Energy Technology Data Exchange (ETDEWEB)

Li, G. [McGill Univ., Montreal, Quebec (Canada); Argonne National Laboratory, Argonne, Illinois (United States); Scielzo, N.D. [Lawrence Livermore National Laboratory, Livermore, California (United States); Segel, R.E. [Northwestern Univ., Illinois (United States); and others

2010-07-01

A Beta decay Paul Trap (BPT) has been constructed at Argonne National Laboratory for the precise measurement of beta decay. We have demonstrated the capability of producing and transferring a low-energy, bunched, and isotopically pure ions beam. In BPT the ions are cooled to sub-eV energies, and confined in a volume of less than 1 mm{sup 3}. The trap has an open geometry which allows four sets of radiation detectors covering a substantial potion of solid angle. In combination with versatile detectors, BPT is able to precisely determine the entire decay kinematics of many isotopes. (author)

An introduction to Laplace transforms and Fourier series

CERN Document Server

Dyke, Phil

2014-01-01

Laplace transforms continue to be a very important tool for the engineer, physicist and applied mathematician. They are also now useful to financial, economic and biological modellers as these disciplines become more quantitative. Any problem that has underlying linearity and with solution based on initial values can be expressed as an appropriate differential equation and hence be solved using Laplace transforms. In this book, there is a strong emphasis on application with the necessary mathematical grounding. There are plenty of worked examples with all solutions provided. This enlarged new edition includes generalised Fourier series and a completely new chapter on wavelets. Only knowledge of elementary trigonometry and calculus are required as prerequisites. An Introduction to Laplace Transforms and Fourier Series will be useful for second and third year undergraduate students in engineering, physics or mathematics, as well as for graduates in any discipline such as financial mathematics, econometrics and ...

Electro-Optical Imaging Fourier-Transform Spectrometer

Science.gov (United States)

Chao, Tien-Hsin; Zhou, Hanying

2006-01-01

An electro-optical (E-O) imaging Fourier-transform spectrometer (IFTS), now under development, is a prototype of improved imaging spectrometers to be used for hyperspectral imaging, especially in the infrared spectral region. Unlike both imaging and non-imaging traditional Fourier-transform spectrometers, the E-O IFTS does not contain any moving parts. Elimination of the moving parts and the associated actuator mechanisms and supporting structures would increase reliability while enabling reductions in size and mass, relative to traditional Fourier-transform spectrometers that offer equivalent capabilities. Elimination of moving parts would also eliminate the vibrations caused by the motions of those parts. Figure 1 schematically depicts a traditional Fourier-transform spectrometer, wherein a critical time delay is varied by translating one the mirrors of a Michelson interferometer. The time-dependent optical output is a periodic representation of the input spectrum. Data characterizing the input spectrum are generated through fast-Fourier-transform (FFT) post-processing of the output in conjunction with the varying time delay.

The β-decay Paul trap: A radiofrequency-quadrupole ion trap for precision β-decay studies

International Nuclear Information System (INIS)

Scielzo, N.D.; Li, G.; Sternberg, M.G.; Savard, G.; Bertone, P.F.; Buchinger, F.; Caldwell, S.; Clark, J.A.; Crawford, J.; Deibel, C.M.; Fallis, J.; Greene, J.P.

2012-01-01

The β-decay Paul trap is a linear radiofrequency-quadrupole ion trap that has been developed for precision β-decay studies. The design of the trap electrodes allows a variety of radiation detectors to surround the cloud of trapped ions. The momentum of the low-energy recoiling daughter nuclei following β decay is negligibly perturbed by scattering and is available for study. This advantageous property of traps allows the kinematics of particles that are difficult or even impossible to directly detect to be precisely reconstructed using conservation of energy and momentum. An ion-trap system offers several advantages over atom traps, such as higher trapping efficiencies and element-independent capabilities. The first precision experiment using this system is a measurement of β-decay angular correlations in the decay of 8 Li performed by inferring the momentum of the neutrino from the kinematic shifts imparted to the breakup α particles. Many other β-decay studies that would benefit from a determination of the nuclear recoil can be performed with this system.

The {beta}-decay Paul trap: A radiofrequency-quadrupole ion trap for precision {beta}-decay studies

Energy Technology Data Exchange (ETDEWEB)

Scielzo, N.D., E-mail: scielzo1@llnl.gov [Physics Division, Argonne National Laboratory, Argonne, Illinois 60439 (United States); Physical and Life Sciences Directorate, Lawrence Livermore National Laboratory, Livermore, California 94550 (United States); Li, G. [Physics Division, Argonne National Laboratory, Argonne, Illinois 60439 (United States); Department of Physics, McGill University, Montreal, Quebec, Canada H3A 2T8 (Canada); Sternberg, M.G.; Savard, G. [Physics Division, Argonne National Laboratory, Argonne, Illinois 60439 (United States); Department of Physics, University of Chicago, Chicago, Illinois 60637 (United States); Bertone, P.F. [Physics Division, Argonne National Laboratory, Argonne, Illinois 60439 (United States); Buchinger, F. [Department of Physics, McGill University, Montreal, Quebec, Canada H3A 2T8 (Canada); Caldwell, S. [Physics Division, Argonne National Laboratory, Argonne, Illinois 60439 (United States); Department of Physics, University of Chicago, Chicago, Illinois 60637 (United States); Clark, J.A. [Physics Division, Argonne National Laboratory, Argonne, Illinois 60439 (United States); Crawford, J. [Department of Physics, McGill University, Montreal, Quebec, Canada H3A 2T8 (Canada); Deibel, C.M. [Physics Division, Argonne National Laboratory, Argonne, Illinois 60439 (United States); Joint Institute for Nuclear Astrophysics, Michigan State University, East Lansing, Michigan 48824 (United States); Fallis, J. [Physics Division, Argonne National Laboratory, Argonne, Illinois 60439 (United States); Department of Physics and Astronomy, University of Manitoba, Winnipeg, Manitoba, Canada R3T 2N2 (Canada); Greene, J.P. [Physics Division, Argonne National Laboratory, Argonne, Illinois 60439 (United States); and others

2012-07-21

The {beta}-decay Paul trap is a linear radiofrequency-quadrupole ion trap that has been developed for precision {beta}-decay studies. The design of the trap electrodes allows a variety of radiation detectors to surround the cloud of trapped ions. The momentum of the low-energy recoiling daughter nuclei following {beta} decay is negligibly perturbed by scattering and is available for study. This advantageous property of traps allows the kinematics of particles that are difficult or even impossible to directly detect to be precisely reconstructed using conservation of energy and momentum. An ion-trap system offers several advantages over atom traps, such as higher trapping efficiencies and element-independent capabilities. The first precision experiment using this system is a measurement of {beta}-decay angular correlations in the decay of {sup 8}Li performed by inferring the momentum of the neutrino from the kinematic shifts imparted to the breakup {alpha} particles. Many other {beta}-decay studies that would benefit from a determination of the nuclear recoil can be performed with this system.

A new twist to fourier transforms

CERN Document Server

Meikle, Hamish D

2004-01-01

Making use of the inherent helix in the Fourier transform expression, this book illustrates both Fourier transforms and their properties in the round. The author draws on elementary complex algebra to manipulate the transforms, presenting the ideas in such a way as to avoid pages of complicated mathematics. Similarly, abbreviations are not used throughout and the language is kept deliberately clear so that the result is a text that is accessible to a much wider readership.The treatment is extended with the use of sampled data to finite and discrete transforms, the fast Fourier transform, or FFT, being a special case of a discrete transform. The application of Fourier transforms in statistics is illustrated for the first time using the examples operational research and later radar detection. In addition, a whole chapter on tapering or weighting functions is added for reference. The whole is rounded off by a glossary and examples of diagrams in three dimensions made possible by today's mathematics programs

Fourier transform of momentum distribution in vanadium

International Nuclear Information System (INIS)

Singh, A.K.; Manuel, A.A.; Peter, M.; Singru, R.M.

1985-01-01

Experimental Compton profile and 2D-angular correlation of positron annihilation radiation data from vanadium are analyzed by the mean of their Fourier transform. They are compared with the functions calculated with the help of both the linear muffin-tin orbital and the Hubbard-Mijnarends band structure methods. The results show that the functions are influenced by the positron wave function, by the e + -e - many-body correlations and by the differences in the electron wave functions used for the band structure calculations. It is concluded that Fourier analysis is a sensitive approach to investigate the momentum distributions in transition metals and to understnad the effects of the positron. (Auth.)

An optical Fourier transform coprocessor with direct phase determination.

Science.gov (United States)

Macfaden, Alexander J; Gordon, George S D; Wilkinson, Timothy D

2017-10-20

The Fourier transform is a ubiquitous mathematical operation which arises naturally in optics. We propose and demonstrate a practical method to optically evaluate a complex-to-complex discrete Fourier transform. By implementing the Fourier transform optically we can overcome the limiting O(nlogn) complexity of fast Fourier transform algorithms. Efficiently extracting the phase from the well-known optical Fourier transform is challenging. By appropriately decomposing the input and exploiting symmetries of the Fourier transform we are able to determine the phase directly from straightforward intensity measurements, creating an optical Fourier transform with O(n) apparent complexity. Performing larger optical Fourier transforms requires higher resolution spatial light modulators, but the execution time remains unchanged. This method could unlock the potential of the optical Fourier transform to permit 2D complex-to-complex discrete Fourier transforms with a performance that is currently untenable, with applications across information processing and computational physics.

Method of local pointed function reduction of original shape in Fourier transformation

International Nuclear Information System (INIS)

Dosch, H.; Slavyanov, S.Yu.

2002-01-01

The method for analytical reduction of the original shape in the one-dimensional Fourier transformation by the fourier image modulus is proposed. The basic concept of the method consists in the presentation of the model shape in the form of the local peak functions sum. The eigenfunctions, generated by the linear differential equations with the polynomial coefficients, are selected as the latter ones. This provides for the possibility of managing the Fourier transformation without numerical integration. This reduces the reverse task to the nonlinear regression with a small number of the evaluated parameters and to the numerical or asymptotic study on the model peak functions - the eigenfunctions of the differential tasks and their fourier images [ru

Applications of Fourier transforms to generalized functions

CERN Document Server

Rahman, M

2011-01-01

This book explains how Fourier transforms can be applied to generalized functions. The generalized function is one of the important branches of mathematics and is applicable in many practical fields. Its applications to the theory of distribution and signal processing are especially important. The Fourier transform is a mathematical procedure that can be thought of as transforming a function from its time domain to the frequency domain.The book contains six chapters and three appendices. Chapter 1 deals with preliminary remarks on Fourier series from a general point of view and also contains an introduction to the first generalized function. Chapter 2 is concerned with the generalized functions and their Fourier transforms. Chapter 3 contains the Fourier transforms of particular generalized functions. The author has stated and proved 18 formulas dealing with the Fourier transforms of generalized functions, and demonstrated some important problems of practical interest. Chapter 4 deals with the asymptotic esti...

Nonlinear Fourier transform for dual-polarization optical communication system

DEFF Research Database (Denmark)

Gaiarin, Simone

communication is considered an emerging paradigm in fiber-optic communications that could potentially overcome these limitations. It relies on a mathematical technique called “inverse scattering transform” or “nonlinear Fourier transform (NFT)” to exploit the “hidden” linearity of the nonlinear Schrödinger...

Discrete Fourier Transform in a Complex Vector Space

Science.gov (United States)

Dean, Bruce H. (Inventor)

2015-01-01

An image-based phase retrieval technique has been developed that can be used on board a space based iterative transformation system. Image-based wavefront sensing is computationally demanding due to the floating-point nature of the process. The discrete Fourier transform (DFT) calculation is presented in "diagonal" form. By diagonal we mean that a transformation of basis is introduced by an application of the similarity transform of linear algebra. The current method exploits the diagonal structure of the DFT in a special way, particularly when parts of the calculation do not have to be repeated at each iteration to converge to an acceptable solution in order to focus an image.

Implementation of quantum and classical discrete fractional Fourier transforms

Science.gov (United States)

Weimann, Steffen; Perez-Leija, Armando; Lebugle, Maxime; Keil, Robert; Tichy, Malte; Gräfe, Markus; Heilmann, René; Nolte, Stefan; Moya-Cessa, Hector; Weihs, Gregor; Christodoulides, Demetrios N.; Szameit, Alexander

2016-01-01

Fourier transforms, integer and fractional, are ubiquitous mathematical tools in basic and applied science. Certainly, since the ordinary Fourier transform is merely a particular case of a continuous set of fractional Fourier domains, every property and application of the ordinary Fourier transform becomes a special case of the fractional Fourier transform. Despite the great practical importance of the discrete Fourier transform, implementation of fractional orders of the corresponding discrete operation has been elusive. Here we report classical and quantum optical realizations of the discrete fractional Fourier transform. In the context of classical optics, we implement discrete fractional Fourier transforms of exemplary wave functions and experimentally demonstrate the shift theorem. Moreover, we apply this approach in the quantum realm to Fourier transform separable and path-entangled biphoton wave functions. The proposed approach is versatile and could find applications in various fields where Fourier transforms are essential tools. PMID:27006089

Implementation of quantum and classical discrete fractional Fourier transforms.

Science.gov (United States)

Weimann, Steffen; Perez-Leija, Armando; Lebugle, Maxime; Keil, Robert; Tichy, Malte; Gräfe, Markus; Heilmann, René; Nolte, Stefan; Moya-Cessa, Hector; Weihs, Gregor; Christodoulides, Demetrios N; Szameit, Alexander

2016-03-23

Fourier transforms, integer and fractional, are ubiquitous mathematical tools in basic and applied science. Certainly, since the ordinary Fourier transform is merely a particular case of a continuous set of fractional Fourier domains, every property and application of the ordinary Fourier transform becomes a special case of the fractional Fourier transform. Despite the great practical importance of the discrete Fourier transform, implementation of fractional orders of the corresponding discrete operation has been elusive. Here we report classical and quantum optical realizations of the discrete fractional Fourier transform. In the context of classical optics, we implement discrete fractional Fourier transforms of exemplary wave functions and experimentally demonstrate the shift theorem. Moreover, we apply this approach in the quantum realm to Fourier transform separable and path-entangled biphoton wave functions. The proposed approach is versatile and could find applications in various fields where Fourier transforms are essential tools.

Rapid Quantification of Four Anthocyanins in Red Grape Wine by Hydrophilic Interaction Liquid Chromatography/Triple Quadrupole Linear Ion Trap Mass Spectrometry.

Science.gov (United States)

Sun, Yongming; Xia, Biqi; Chen, Xiangzhun; Duanmu, Chuansong; Li, Denghao; Han, Chao

2015-01-01

The identification and quantification of four anthocyanins (cyanidin-3-O-glucoside, peonidin-3-O-glucoside, delphinidin-3-O-glucoside, and malvidin-3-O-glucoside) in red grape wine were carried out by hydrophilic interaction liquid chromatography/triple quadrupole linear ion trap MS (HILIC/QTrap-MS/MS). Samples were diluted directly and separated on a Merck ZIC HILIC column with 20 mM ammonium acetate solution-acetonitrile mobile phase. Quantitative data acquisition was carried out in the multiple reaction monitoring mode. Additional identification and confirmation of target compounds were performed using the enhanced product ion mode of the linear ion trap. The LOQs were in the range 0.05-1.0 ng/mL. The average recoveries were in the range 94.6 to 104.5%. The HILIC/QTrap-MS/MS platform offers the best sensitivity and specificity for characterization and quantitative determination of the four anthocyanins in red grape wines and fulfills the quality criteria for routine laboratory application.

Alternating multivariate trigonometric functions and corresponding Fourier transforms

International Nuclear Information System (INIS)

Klimyk, A U; Patera, J

2008-01-01

We define and study multivariate sine and cosine functions, symmetric with respect to the alternating group A n , which is a subgroup of the permutation (symmetric) group S n . These functions are eigenfunctions of the Laplace operator. They determine Fourier-type transforms. There exist three types of such transforms: expansions into corresponding sine-Fourier and cosine-Fourier series, integral sine-Fourier and cosine-Fourier transforms, and multivariate finite sine and cosine transforms. In all these transforms, alternating multivariate sine and cosine functions are used as a kernel

Properties of the distributional finite Fourier transform

OpenAIRE

Carmichael, Richard D.

2016-01-01

The analytic functions in tubes which obtain the distributional finite Fourier transform as boundary value are shown to have a strong boundedness property and to be recoverable as a Fourier-Laplace transform, a distributional finite Fourier transform, and as a Cauchy integral of a distribution associated with the boundary value.

Fourier transform nuclear magnetic resonance

International Nuclear Information System (INIS)

Geick, R.

1981-01-01

This review starts with the basic principles of resonance phenomena in physical systems. Especially, the connection is shown between the properties of these systems and Fourier transforms. Next, we discuss the principles of nuclear magnetic resonance. Starting from the general properties of physical systems showing resonance phenomena and from the special properties of nuclear spin systems, the main part of this paper reviews pulse and Fourier methods in nuclear magnetic resonance. Among pulse methods, an introduction will be given to spin echoes, and, apart from the principle of Fourier transform nuclear magnetic resonance, an introduction to the technical problems of this method, e.g. resolution in the frequency domain, aliasing, phase and intensity errors, stationary state of the spin systems for repetitive measurements, proton decoupling, and application of Fourier methods to systems in a nonequilibrium state. The last section is devoted to special applications of Fourier methods and recent developments, e.g. measurement of relaxation times, solvent peak suppression, 'rapid scan'-method, methods for suppressing the effects of dipolar coupling in solids, two-dimensional Fourier transform nuclear magnetic resonance, and spin mapping or zeugmatography. (author)

Wigner distribution and fractional Fourier transform

NARCIS (Netherlands)

Alieva, T.; Bastiaans, M.J.; Boashash, B.

2003-01-01

We have described the relationship between the fractional Fourier transform and the Wigner distribution by using the Radon-Wigner transform, which is a set of projections of the Wigner distribution as well as a set of squared moduli of the fractional Fourier transform. We have introduced the concept

Dual-polarization nonlinear Fourier transform-based optical communication system

DEFF Research Database (Denmark)

Gaiarin, Simone; Perego, A. M.; da Silva, Edson Porto

2018-01-01

communication could potentially overcome these limitations. It relies on a mathematical technique called “nonlinear Fourier transform (NFT)” to exploit the “hidden” linearity of the nonlinear Schrödinger equation as the master model for signal propagation in an optical fiber. We present here the theoretical...

Scalable quantum search using trapped ions

International Nuclear Information System (INIS)

Ivanov, S. S.; Ivanov, P. A.; Linington, I. E.; Vitanov, N. V.

2010-01-01

We propose a scalable implementation of Grover's quantum search algorithm in a trapped-ion quantum information processor. The system is initialized in an entangled Dicke state by using adiabatic techniques. The inversion-about-average and oracle operators take the form of single off-resonant laser pulses. This is made possible by utilizing the physical symmetries of the trapped-ion linear crystal. The physical realization of the algorithm represents a dramatic simplification: each logical iteration (oracle and inversion about average) requires only two physical interaction steps, in contrast to the large number of concatenated gates required by previous approaches. This not only facilitates the implementation but also increases the overall fidelity of the algorithm.

Description of the electron-hydrogen collision by the Coulomb Fourier transform method

International Nuclear Information System (INIS)

Levin, S.B.

2005-01-01

A recently developed Coulomb Fourier Transform method is applied to the system containing one heavy ion and two electrons. The transformed Hamiltonian is described with a controlled accuracy in an effective finite basis set as a finite dimensional operator matrix. The kernels of interaction are formulated in terms of the so called Nordsieck integrals

Stability of Coulomb crystals in a linear Paul trap with storage-ring-like confinement

DEFF Research Database (Denmark)

Kjærgaard, Niels; Mølhave, Kristian; Drewsen, Michael

2002-01-01

We report experiments on the stability of ion Coulomb crystals in a linear Paul trap with storage-ring-like confinement. The transverse dynamics of charged particles in a trap of this type is analogous to that of a fast beam traveling through a channel with periodic, magnetic alternating gradient...... confinement. The experimentally observed stability conditions for stationary crystals comply remarkably well with current theory of crystalline plasmas and beams.......We report experiments on the stability of ion Coulomb crystals in a linear Paul trap with storage-ring-like confinement. The transverse dynamics of charged particles in a trap of this type is analogous to that of a fast beam traveling through a channel with periodic, magnetic alternating gradient...

Group-invariant finite Fourier transforms

International Nuclear Information System (INIS)

Shenefelt, M.H.

1988-01-01

The computation of the finite Fourier transform of functions is one of the most used computations in crystallography. Since the Fourier transform involved in 3-dimensional, the size of the computation becomes very large even for relatively few sample points along each edge. In this thesis, there is a family of algorithms that reduce the computation of Fourier transform of functions respecting the symmetries. Some properties of these algorithms are: (1) The algorithms make full use of the group of symmetries of a crystal. (2) The algorithms can be factored and combined according to the prime factorization of the number of points in the sample space. (3) The algorithms are organized into a family using the group structure of the crystallographic groups to make iterative procedures possible

Simulating first order optical systems—algorithms for and composition of discrete linear canonical transforms

Science.gov (United States)

Healy, John J.

2018-01-01

The linear canonical transforms (LCTs) are a parameterised group of linear integral transforms. The LCTs encompass a number of well-known transformations as special cases, including the Fourier transform, fractional Fourier transform, and the Fresnel integral. They relate the scalar wave fields at the input and output of systems composed of thin lenses and free space, along with other quadratic phase systems. In this paper, we perform a systematic search of all algorithms based on up to five stages of magnification, chirp multiplication and Fourier transforms. Based on that search, we propose a novel algorithm, for which we present numerical results. We compare the sampling requirements of three algorithms. Finally, we discuss some issues surrounding the composition of discrete LCTs.

On the inverse windowed Fourier transform

OpenAIRE

Rebollo Neira, Laura; Fernández Rubio, Juan Antonio

1999-01-01

The inversion problem concerning the windowed Fourier transform is considered. It is shown that, out of the infinite solutions that the problem admits, the windowed Fourier transform is the "optimal" solution according to a maximum-entropy selection criterion. Peer Reviewed

(Anti)symmetric multivariate exponential functions and corresponding Fourier transforms

International Nuclear Information System (INIS)

Klimyk, A U; Patera, J

2007-01-01

We define and study symmetrized and antisymmetrized multivariate exponential functions. They are defined as determinants and antideterminants of matrices whose entries are exponential functions of one variable. These functions are eigenfunctions of the Laplace operator on the corresponding fundamental domains satisfying certain boundary conditions. To symmetric and antisymmetric multivariate exponential functions there correspond Fourier transforms. There are three types of such Fourier transforms: expansions into the corresponding Fourier series, integral Fourier transforms and multivariate finite Fourier transforms. Eigenfunctions of the integral Fourier transforms are found

Non-thermalization in trapped atomic ion spin chains

Science.gov (United States)

Hess, P. W.; Becker, P.; Kaplan, H. B.; Kyprianidis, A.; Lee, A. C.; Neyenhuis, B.; Pagano, G.; Richerme, P.; Senko, C.; Smith, J.; Tan, W. L.; Zhang, J.; Monroe, C.

2017-10-01

Linear arrays of trapped and laser-cooled atomic ions are a versatile platform for studying strongly interacting many-body quantum systems. Effective spins are encoded in long-lived electronic levels of each ion and made to interact through laser-mediated optical dipole forces. The advantages of experiments with cold trapped ions, including high spatio-temporal resolution, decoupling from the external environment and control over the system Hamiltonian, are used to measure quantum effects not always accessible in natural condensed matter samples. In this review, we highlight recent work using trapped ions to explore a variety of non-ergodic phenomena in long-range interacting spin models, effects that are heralded by the memory of out-of-equilibrium initial conditions. We observe long-lived memory in static magnetizations for quenched many-body localization and prethermalization, while memory is preserved in the periodic oscillations of a driven discrete time crystal state. This article is part of the themed issue 'Breakdown of ergodicity in quantum systems: from solids to synthetic matter'.

Ejection of Coulomb Crystals from a Linear Paul Ion Trap for Ion-Molecule Reaction Studies.

Science.gov (United States)

Meyer, K A E; Pollum, L L; Petralia, L S; Tauschinsky, A; Rennick, C J; Softley, T P; Heazlewood, B R

2015-12-17

Coulomb crystals are being increasingly employed as a highly localized source of cold ions for the study of ion-molecule chemical reactions. To extend the scope of reactions that can be studied in Coulomb crystals-from simple reactions involving laser-cooled atomic ions, to more complex systems where molecular reactants give rise to multiple product channels-sensitive product detection methodologies are required. The use of a digital ion trap (DIT) and a new damped cosine trap (DCT) are described, which facilitate the ejection of Coulomb-crystallized ions onto an external detector for the recording of time-of-flight (TOF) mass spectra. This enables the examination of reaction dynamics and kinetics between Coulomb-crystallized ions and neutral molecules: ionic products are typically cotrapped, thus ejecting the crystal onto an external detector reveals the masses, identities, and quantities of all ionic species at a selected point in the reaction. Two reaction systems are examined: the reaction of Ca(+) with deuterated isotopologues of water, and the charge exchange between cotrapped Xe(+) with deuterated isotopologues of ammonia. These reactions are examples of two distinct types of experiment, the first involving direct reaction of the laser-cooled ions, and the second involving reaction of sympathetically-cooled heavy ions to form a mixture of light product ions. Extensive simulations are conducted to interpret experimental results and calculate optimal operating parameters, facilitating a comparison between the DIT and DCT approaches. The simulations also demonstrate a correlation between crystal shape and image shape on the detector, suggesting a possible means for determining crystal geometry for nonfluorescing ions.

Boosting Sensitivity in Liquid Chromatography–Fourier Transform Ion Cyclotron Resonance–Tandem Mass Spectrometry for Product Ion Analysis of Monoterpene Indole Alkaloids

Directory of Open Access Journals (Sweden)

Ryo eNakabayashi

2015-12-01

Full Text Available In metabolomics, the analysis of product ions in tandem mass spectrometry (MS/MS is noteworthy to chemically assign structural information. However, the development of relevant analytical methods are less advanced. Here, we developed a method to boost sensitivity in liquid chromatography–Fourier transform ion cyclotron resonance–tandem mass spectrometry analysis (MS/MS boost analysis. To verify the MS/MS boost analysis, both quercetin and uniformly labeled 13C quercetin were analyzed, revealing that the origin of the product ions is not the instrument, but the analyzed compounds resulting in sensitive product ions. Next, we applied this method to the analysis of monoterpene indole alkaloids (MIAs. The comparative analyses of MIAs having indole basic skeleton (ajmalicine, catharanthine, hirsuteine, and hirsutine and oxindole skeleton (formosanine, isoformosanine, pteropodine, isopteropodine, rhynchophylline, isorhynchophylline, and mitraphylline identified 86 and 73 common monoisotopic ions, respectively. The comparative analyses of the three pairs of stereoisomers showed more than 170 common monoisotopic ions in each pair. This method was also applied to the targeted analysis of MIAs in Catharanthus roseus and Uncaria rhynchophylla to profile indole and oxindole compounds using the product ions. This analysis is suitable for chemically assigning features of the metabolite groups, which contributes to targeted metabolome analysis.

Boosting Sensitivity in Liquid Chromatography–Fourier Transform Ion Cyclotron Resonance–Tandem Mass Spectrometry for Product Ion Analysis of Monoterpene Indole Alkaloids

Science.gov (United States)

Nakabayashi, Ryo; Tsugawa, Hiroshi; Kitajima, Mariko; Takayama, Hiromitsu; Saito, Kazuki

2015-01-01

In metabolomics, the analysis of product ions in tandem mass spectrometry (MS/MS) is noteworthy to chemically assign structural information. However, the development of relevant analytical methods are less advanced. Here, we developed a method to boost sensitivity in liquid chromatography–Fourier transform ion cyclotron resonance–tandem mass spectrometry analysis (MS/MS boost analysis). To verify the MS/MS boost analysis, both quercetin and uniformly labeled 13C quercetin were analyzed, revealing that the origin of the product ions is not the instrument, but the analyzed compounds resulting in sensitive product ions. Next, we applied this method to the analysis of monoterpene indole alkaloids (MIAs). The comparative analyses of MIAs having indole basic skeleton (ajmalicine, catharanthine, hirsuteine, and hirsutine) and oxindole skeleton (formosanine, isoformosanine, pteropodine, isopteropodine, rhynchophylline, isorhynchophylline, and mitraphylline) identified 86 and 73 common monoisotopic ions, respectively. The comparative analyses of the three pairs of stereoisomers showed more than 170 common monoisotopic ions in each pair. This method was also applied to the targeted analysis of MIAs in Catharanthus roseus and Uncaria rhynchophylla to profile indole and oxindole compounds using the product ions. This analysis is suitable for chemically assigning features of the metabolite groups, which contributes to targeted metabolome analysis. PMID:26734034

Ion trap architectures and new directions

Science.gov (United States)

Siverns, James D.; Quraishi, Qudsia

2017-12-01

Trapped ion technology has seen advances in performance, robustness and versatility over the last decade. With increasing numbers of trapped ion groups worldwide, a myriad of trap architectures are currently in use. Applications of trapped ions include: quantum simulation, computing and networking, time standards and fundamental studies in quantum dynamics. Design of such traps is driven by these various research aims, but some universally desirable properties have lead to the development of ion trap foundries. Additionally, the excellent control achievable with trapped ions and the ability to do photonic readout has allowed progress on quantum networking using entanglement between remotely situated ion-based nodes. Here, we present a selection of trap architectures currently in use by the community and present their most salient characteristics, identifying features particularly suited for quantum networking. We also discuss our own in-house research efforts aimed at long-distance trapped ion networking.

Ions kinematics in an electrostatic ion beam trap

Energy Technology Data Exchange (ETDEWEB)

Attia, D

2004-06-01

In this study, I have tried to provide a better understanding of the dynamics of ions inside an electrostatic ion beam trap. The electrostatic ion trap allows to store ions moving between two electrostatic mirrors. Although the trap has been developed already seven years ago, no direct measurement of the transversal velocity distribution of the ions has been performed. Such quantity is central for understanding the conditions under which a beam should be produced (mainly emittance) in order to be trapped by such a device. The data I have obtained during the course of this work are based on an experimental technique which relies on the direct imaging of the particles exiting the trap, as well as on numerical simulations of the ion trajectories inside the trap. I have personally been involved in the hardware development of the imaging system, the data acquisition and analysis of the data as well as il all numerical calculations presented here. These results allow us to obtain, for the first time, experimental information on the transverse phase space of the trap, and contribute to the overall understanding of the ion motion in this system. (author)

Chemical Mass Shifts in a Digital Linear Ion Trap as Analytical Identity of o-, m-, and p-Xylene

Science.gov (United States)

Sun, Lulu; Xue, Bing; Huang, Zhengxu; Cheng, Ping; Ma, Li; Ding, Li; Zhou, Zhen

2018-04-01

Chemical mass shifts between isomeric ions of o-, m-, and p-xylene were measured using a digital linear ion trap, and the directions and values of the shifts were found to be correlated to the collision cross sections of the isomers. Both forward and reverse scans were used and the chemical shifts for each pair of isomers in scans of opposite directions were in opposite signs. Using different voltage settings (namely the voltage dividing ratio-VDR) of the ion trap allows adding high order field components in the quadrupole field and results in larger chemical mass shifts. The differential chemical mass shift which combined the shifts from forward and reverse scans doubled the amount of chemical shift, e.g., 0.077 Th between o- and p-xylene, enough for identification of the type of isomer without using an additional ion mobility spectrometer. The feature of equal and opposite chemical mass shifts also allowed to null out the chemical mass shift by calculating the mean m/z value between the two opposite scans and remove or reduce the mass error caused by chemical mass shift. [Figure not available: see fulltext.

Chemical Mass Shifts in a Digital Linear Ion Trap as Analytical Identity of o-, m-, and p-Xylene.

Science.gov (United States)

Sun, Lulu; Xue, Bing; Huang, Zhengxu; Cheng, Ping; Ma, Li; Ding, Li; Zhou, Zhen

2018-07-01

Chemical mass shifts between isomeric ions of o-, m-, and p-xylene were measured using a digital linear ion trap, and the directions and values of the shifts were found to be correlated to the collision cross sections of the isomers. Both forward and reverse scans were used and the chemical shifts for each pair of isomers in scans of opposite directions were in opposite signs. Using different voltage settings (namely the voltage dividing ratio-VDR) of the ion trap allows adding high order field components in the quadrupole field and results in larger chemical mass shifts. The differential chemical mass shift which combined the shifts from forward and reverse scans doubled the amount of chemical shift, e.g., 0.077 Th between o- and p-xylene, enough for identification of the type of isomer without using an additional ion mobility spectrometer. The feature of equal and opposite chemical mass shifts also allowed to null out the chemical mass shift by calculating the mean m/z value between the two opposite scans and remove or reduce the mass error caused by chemical mass shift. Graphical Abstract ᅟ.

On the finite Fourier transforms of functions with infinite discontinuities

Directory of Open Access Journals (Sweden)

Branko Saric

2002-01-01

Full Text Available The introductory part of the paper is provided to give a brief review of the stability theory of a matrix pencil for discrete linear time-invariant singular control systems, based on the causal relationship between Jordan's theorem from the theory of Fourier series and Laurent's theorem from the calculus of residues. The main part is concerned with the theory of the integral transforms, which has proved to be a powerful tool in the control systems theory. On the basis of a newly defined notion of the total value of improper integrals, throughout the main part of the paper, an attempt has been made to present the global theory of the integral transforms, which are slightly more general with respect to the Laplace and Fourier transforms. The paper ends with examples by which the results of the theory are verified.

On the windowed Fourier transform as an interpolation of the Gabor transform

NARCIS (Netherlands)

Bastiaans, M.J.; Prochßzka, A.; Uhlør, J.; Sovka, P.

1997-01-01

The windowed Fourier transform and its sampled version - the Gabor transform - are introduced. With the help of Gabor's signal expansion, an interpolation function is derived with which the windowed Fourier transform can be constructed from the Gabor transform. Using the Zak transform, it is shown

An integrated ion trap and time-of-flight mass spectrometer for chemical and photo- reaction dynamics studies

International Nuclear Information System (INIS)

Schowalter, Steven J.; Chen Kuang; Rellergert, Wade G.; Sullivan, Scott T.; Hudson, Eric R.

2012-01-01

We demonstrate the integration of a linear quadrupole trap with a simple time-of-flight mass spectrometer with medium-mass resolution (m/Δm∼ 50) geared towards the demands of atomic, molecular, and chemical physics experiments. By utilizing a novel radial ion extraction scheme from the linear quadrupole trap into the mass analyzer, a device with large trap capacity and high optical access is realized without sacrificing mass resolution. This provides the ability to address trapped ions with laser light and facilitates interactions with neutral background gases prior to analyzing the trapped ions. Here, we describe the construction and implementation of the device as well as present representative ToF spectra. We conclude by demonstrating the flexibility of the device with proof-of-principle experiments that include the observation of molecular-ion photodissociation and the measurement of trapped-ion chemical reaction rates.

New macroscopic theory of anamalous diffusion induced by the dissipative trapped-ion instability

International Nuclear Information System (INIS)

Wimmel, H.K.

1975-03-01

For an axisymmetric toroidal plasma of the TOKAMAK type a new set of dissipative trapped-fluid equations is established. In addition to E vector x B vector drifts and collisions of the trapped particles, these equations take full account of the effect of Esub(//) (of the trapped ion modes) on free and trapped particles, and of the effect of grad delta 0 (delta 0 = equilibrium fraction of trapped particles). From the new equations the linear-mode properties of the dissipative trapped-ion instability and the anomalous diffusion flux of the trapped particles are derived. (orig.) [de

Surface Fourier-transform lens using a metasurface

International Nuclear Information System (INIS)

Li, Yun Bo; Cai, Ben Geng; Cheng, Qiang; Cui, Tie Jun

2015-01-01

We propose a surface (or 2D) Fourier-transform lens using a gradient refractive index (GRIN) metasurface in the microwave band, which is composed of sub-wavelength quasi-periodical metallic patches on a grounded dielectric substrate. Such a metasurface supports the transverse magnetic (TM) modes of surface waves. To gradually change the size of textures, we obtain different surface refractive indices, which can be tailored to fit the required refractive-index profile of a surface Fourier-transform lens. According to the theory of spatial Fourier transformation, we make use of the proposed lens to realize surface plane-wave scanning under different feeding locations. The simulation and experimental results jointly confirm the validity of the surface Fourier-transform lens. The proposed method can also be extended to the terahertz frequency. (paper)

Products of multiple Fourier series with application to the multiblade transformation

Science.gov (United States)

Kunz, D. L.

1981-01-01

A relatively simple and systematic method for forming the products of multiple Fourier series using tensor like operations is demonstrated. This symbolic multiplication can be performed for any arbitrary number of series, and the coefficients of a set of linear differential equations with periodic coefficients from a rotating coordinate system to a nonrotating system is also demonstrated. It is shown that using Fourier operations to perform this transformation make it easily understood, simple to apply, and generally applicable.

Ion trap device

Science.gov (United States)

Ibrahim, Yehia M.; Smith, Richard D.

2016-01-26

An ion trap device is disclosed. The device includes a series of electrodes that define an ion flow path. A radio frequency (RF) field is applied to the series of electrodes such that each electrode is phase shifted approximately 180 degrees from an adjacent electrode. A DC voltage is superimposed with the RF field to create a DC gradient to drive ions in the direction of the gradient. A second RF field or DC voltage is applied to selectively trap and release the ions from the device. Further, the device may be gridless and utilized at high pressure.

An integrated ion trap and time-of-flight mass spectrometer for chemical and photo- reaction dynamics studies.

Science.gov (United States)

Schowalter, Steven J; Chen, Kuang; Rellergert, Wade G; Sullivan, Scott T; Hudson, Eric R

2012-04-01

We demonstrate the integration of a linear quadrupole trap with a simple time-of-flight mass spectrometer with medium-mass resolution (m/Δm ∼ 50) geared towards the demands of atomic, molecular, and chemical physics experiments. By utilizing a novel radial ion extraction scheme from the linear quadrupole trap into the mass analyzer, a device with large trap capacity and high optical access is realized without sacrificing mass resolution. This provides the ability to address trapped ions with laser light and facilitates interactions with neutral background gases prior to analyzing the trapped ions. Here, we describe the construction and implementation of the device as well as present representative ToF spectra. We conclude by demonstrating the flexibility of the device with proof-of-principle experiments that include the observation of molecular-ion photodissociation and the measurement of trapped-ion chemical reaction rates. © 2012 American Institute of Physics

Fourier transforms in radar and signal processing

CERN Document Server

Brandwood, David

2011-01-01

Fourier transforms are used widely, and are of particular value in the analysis of single functions and combinations of functions found in radar and signal processing. Still, many problems that could have been tackled by using Fourier transforms may have gone unsolved because they require integration that is difficult and tedious. This newly revised and expanded edition of a classic Artech House book provides you with an up-to-date, coordinated system for performing Fourier transforms on a wide variety of functions. Along numerous updates throughout the book, the Second Edition includes a crit

Integrated System Technologies for Modular Trapped Ion Quantum Information Processing

Science.gov (United States)

Crain, Stephen G.

Although trapped ion technology is well-suited for quantum information science, scalability of the system remains one of the main challenges. One of the challenges associated with scaling the ion trap quantum computer is the ability to individually manipulate the increasing number of qubits. Using micro-mirrors fabricated with micro-electromechanical systems (MEMS) technology, laser beams are focused on individual ions in a linear chain and steer the focal point in two dimensions. Multiple single qubit gates are demonstrated on trapped 171Yb+ qubits and the gate performance is characterized using quantum state tomography. The system features negligible crosstalk to neighboring ions (technologies demonstrated in this thesis can be integrated to form a single quantum register with all of the necessary resources to perform local gates as well as high fidelity readout and provide a photon link to other systems.

Quantum arithmetic with the Quantum Fourier Transform

OpenAIRE

Ruiz-Perez, Lidia; Garcia-Escartin, Juan Carlos

2014-01-01

The Quantum Fourier Transform offers an interesting way to perform arithmetic operations on a quantum computer. We review existing Quantum Fourier Transform adders and multipliers and propose some modifications that extend their capabilities. Among the new circuits, we propose a quantum method to compute the weighted average of a series of inputs in the transform domain.

Clifford Fourier transform on vector fields.

Science.gov (United States)

Ebling, Julia; Scheuermann, Gerik

2005-01-01

Image processing and computer vision have robust methods for feature extraction and the computation of derivatives of scalar fields. Furthermore, interpolation and the effects of applying a filter can be analyzed in detail and can be advantages when applying these methods to vector fields to obtain a solid theoretical basis for feature extraction. We recently introduced the Clifford convolution, which is an extension of the classical convolution on scalar fields and provides a unified notation for the convolution of scalar and vector fields. It has attractive geometric properties that allow pattern matching on vector fields. In image processing, the convolution and the Fourier transform operators are closely related by the convolution theorem and, in this paper, we extend the Fourier transform to include general elements of Clifford Algebra, called multivectors, including scalars and vectors. The resulting convolution and derivative theorems are extensions of those for convolution and the Fourier transform on scalar fields. The Clifford Fourier transform allows a frequency analysis of vector fields and the behavior of vector-valued filters. In frequency space, vectors are transformed into general multivectors of the Clifford Algebra. Many basic vector-valued patterns, such as source, sink, saddle points, and potential vortices, can be described by a few multivectors in frequency space.

Collision-induced dissociation with Fourier transform mass spectrometry

International Nuclear Information System (INIS)

Cody, R.B.; Burnier, R.C.; Freiser, B.S.

1982-01-01

Collision-induced dissociations (CID) is demonstrated on a number of primary and secondary ions using a Nicolet prototype Fourier transform mass spectrometer (FT-MS). Like the triple quadrupole technique, CID using FT-MS is a relatively low energy and efficient process. The ability to study a wide range of ion-molecule reaction products is exemplified by results on proton-bound dimers and transition metal containing ionic species. Variation of collision energy by varying the RF irradiation level can provide information about product distributions as a function of energy as well as yield ion structural information. Like the triple quadrupole technique, no slits are employed and virtually all of the fragment ions formed by the CID process may be detected. Unlike all previous mass spectrometric techniques for studying CID, a tandem instrument is not required, and different experiments are performed by making software modifications rather than hardware modifications

A new trapped-ion instability with large frequency and radial wavenumber

International Nuclear Information System (INIS)

Tagger, M.

1979-01-01

The need for theoretical previsions concerning anomalous transport in large Tokamaks, as well as the recent results of PLT, ask the question of the process responsible for non-linear saturation of trapped-ion instabilities. This in turn necessitates the knowledge of the linear behaviour of these waves at large frequencies and large radial wavenumbers. We study the linear dispersion relation of these modes, in the radially local approximation, but including a term due to a new physical effect, combining finite banana-width and bounce resonances. Limiting ourselves presently to the first harmonic expansion of the bounce motion of trapped ions, we show that the effect of finite banana-width on the usual trapped-ion mode is complex and quite different from what is generally expected. In addition we show, analytically and numerically, the appearance of a nex branch of this instability. Essentially due to this new effect, it involves large frequencies (ω approximately ωsub(b) and is destabilized by large radial wavelengths (ksub(x) Λ approximately 1, where Λ is the typical banana-width). We discuss the nature of this new mode and its potential relevance of the experiments

q-Generalization of the inverse Fourier transform

International Nuclear Information System (INIS)

Jauregui, M.; Tsallis, C.

2011-01-01

A wide class of physical distributions appears to follow the q-Gaussian form, which plays the role of attractor according to a q-generalized Central Limit Theorem, where a q-generalized Fourier transform plays an important role. We introduce here a method which determines a distribution from the knowledge of its q-Fourier transform and some supplementary information. This procedure involves a recently q-generalized representation of the Dirac delta and the class of functions on which it acts. The present method conveniently extends the inverse of the standard Fourier transform, and is therefore expected to be very useful in the study of many complex systems. - Highlights: → We present a method to invert the q-Fourier transform of a distribution. → We illustrate when Dirac delta can be represented using q-exponentials. → We describe a family of functions for which this new representation works.

Ring-shaped Wigner crystals of trapped ions at the micronscale

Science.gov (United States)

Li, Haokun; Urban, Erik; Noel, Crystal; Chuang, Alexander; Xia, Yang; Hemmerling, Borge; Wang, Yuan; Zhang, Xiang; Haeffner, Hartmut

Trapped ion crystals are ideal platforms to study many-body physics and quantum information processing, with both the internal electronic states and external motional degree-of-freedoms controllable at the single quantum level. In contrast to conventional, finite, linear chains of ions, a ring topology exhibiting periodic boundary conditions and rotational symmetry opens up a new directions to diverse topics. However, previous implementations of ion rings result in small aspect ratios (electrode distance to ring diameter, making the rotational symmetry of the ion crystals prone to stray electric fields from imperfections of the trap electrodes, particularly evident at low temperatures. Here, using a new trap design with a 60-fold improvement of this aspect ratio, we demonstrate crystallization of 40Ca+ ions in a ring with rotational energy barriers comparable to the thermal energy of Doppler laser cooled ion crystals. When further reducing the rotational energy barriers, we observe delocalization of the ion rings. With this result, we enter a regime where quantum topological effects can be studied and novel quantum computation and simulation experiments can be implemented.

Screening and confirmation criteria for hormone residue analysis using liquid chromatography accurate mass time-of-flight, Fourier transform ion cyclotron resonance and orbitrap mass spectrometry techniques

NARCIS (Netherlands)

Nielen, M.W.F.; Engelen, M.C. van; Zuiderent, R.; Ramaker, R.

2007-01-01

An emerging trend is recognised in hormone and veterinary drug residue analysis from liquid chromatography tandem mass spectrometry (LC/MS/MS) based screening and confirmation towards accurate mass alternatives such as LC coupled with time-of-flight (TOF), Fourier transform ion cyclotron resonance

Application of high-performance liquid chromatography-tandem mass spectrometry with a quadrupole/linear ion trap instrument for the analysis of pesticide residues in olive oil.

Science.gov (United States)

Hernando, M D; Ferrer, C; Ulaszewska, M; García-Reyes, J F; Molina-Díaz, A; Fernández-Alba, A R

2007-11-01

This article describes the development of an enhanced liquid chromatography-mass spectrometry (LC-MS) method for the analysis of pesticides in olive oil. One hundred pesticides belonging to different classes and that are currently used in agriculture have been included in this method. The LC-MS method was developed using a hybrid quadrupole/linear ion trap (QqQ(LIT)) analyzer. Key features of this technique are the rapid scan acquisition times, high specificity and high sensitivity it enables when the multiple reaction monitoring (MRM) mode or the linear ion-trap operational mode is employed. The application of 5 ms dwell times using a linearly accelerating (LINAC) high-pressure collision cell enabled the analysis of a high number of pesticides, with enough data points acquired for optimal peak definition in MRM operation mode and for satisfactory quantitative determinations to be made. The method quantifies over a linear dynamic range of LOQs (0.03-10 microg kg(-1)) up to 500 microg kg(-1). Matrix effects were evaluated by comparing the slopes of matrix-matched and solvent-based calibration curves. Weak suppression or enhancement of signals was observed (ion (EPI) and MS3 were developed.

Fourier imaging of non-linear structure formation

Energy Technology Data Exchange (ETDEWEB)

Brandbyge, Jacob; Hannestad, Steen, E-mail: jacobb@phys.au.dk, E-mail: sth@phys.au.dk [Department of Physics and Astronomy, University of Aarhus, Ny Munkegade 120, DK-8000 Aarhus C (Denmark)

2017-04-01

We perform a Fourier space decomposition of the dynamics of non-linear cosmological structure formation in ΛCDM models. From N -body simulations involving only cold dark matter we calculate 3-dimensional non-linear density, velocity divergence and vorticity Fourier realizations, and use these to calculate the fully non-linear mode coupling integrals in the corresponding fluid equations. Our approach allows for a reconstruction of the amount of mode coupling between any two wavenumbers as a function of redshift. With our Fourier decomposition method we identify the transfer of power from larger to smaller scales, the stable clustering regime, the scale where vorticity becomes important, and the suppression of the non-linear divergence power spectrum as compared to linear theory. Our results can be used to improve and calibrate semi-analytical structure formation models.

Fourier imaging of non-linear structure formation

International Nuclear Information System (INIS)

Brandbyge, Jacob; Hannestad, Steen

2017-01-01

We perform a Fourier space decomposition of the dynamics of non-linear cosmological structure formation in ΛCDM models. From N -body simulations involving only cold dark matter we calculate 3-dimensional non-linear density, velocity divergence and vorticity Fourier realizations, and use these to calculate the fully non-linear mode coupling integrals in the corresponding fluid equations. Our approach allows for a reconstruction of the amount of mode coupling between any two wavenumbers as a function of redshift. With our Fourier decomposition method we identify the transfer of power from larger to smaller scales, the stable clustering regime, the scale where vorticity becomes important, and the suppression of the non-linear divergence power spectrum as compared to linear theory. Our results can be used to improve and calibrate semi-analytical structure formation models.

Application of the fractional Fourier transform to image reconstruction in MRI.

Science.gov (United States)

Parot, Vicente; Sing-Long, Carlos; Lizama, Carlos; Tejos, Cristian; Uribe, Sergio; Irarrazaval, Pablo

2012-07-01

The classic paradigm for MRI requires a homogeneous B(0) field in combination with linear encoding gradients. Distortions are produced when the B(0) is not homogeneous, and several postprocessing techniques have been developed to correct them. Field homogeneity is difficult to achieve, particularly for short-bore magnets and higher B(0) fields. Nonlinear magnetic components can also arise from concomitant fields, particularly in low-field imaging, or intentionally used for nonlinear encoding. In any of these situations, the second-order component is key, because it constitutes the first step to approximate higher-order fields. We propose to use the fractional Fourier transform for analyzing and reconstructing the object's magnetization under the presence of quadratic fields. The fractional fourier transform provides a precise theoretical framework for this. We show how it can be used for reconstruction and for gaining a better understanding of the quadratic field-induced distortions, including examples of reconstruction for simulated and in vivo data. The obtained images have improved quality compared with standard Fourier reconstructions. The fractional fourier transform opens a new paradigm for understanding the MR signal generated by an object under a quadratic main field or nonlinear encoding. Copyright © 2011 Wiley Periodicals, Inc.

Second order oscillations of a Vlasov-Poisson plasma in the Fourier transformed space

International Nuclear Information System (INIS)

Sedlacek, Z.; Nocera, L.

1991-05-01

The Vlasov-Poisson system of equations in the Fourier-transformed velocity space is studied. At first some results of the linear theory are reformulated: in the new representation the Van Kampen eigenmodes and their adjoint are found to be ordinary functions with convenient piece-wise continuity properties. A transparent derivation is given of the free-streaming temporal echo in terms of the kinematics of wave packets in the Fourier-transformed velocity space. This analysis is further extended to include Coulomb interactions which allows to establish a connection between the echo theory, the second order oscillations of Best and the phenomenon of linear sidebands. The calculation of the time evolution of the global second order electric field is performed in detail in the case of a Maxwellian equilibrium distribution function. It is concluded that the phenomenon of linear sidebands may be properly explained in terms of the intrinsic features of the equilibrium distribution function. (author) 5 figs., 32 refs

Studies of the trapped particle and ion temperature gradient instabilities in the Columbia Linear Machine

International Nuclear Information System (INIS)

Mathey, O.H.

1989-01-01

In the first part of the work, the effects of weak Coulomb and neutral collisions on the collisionless curvature driven trapped particle mode are studied in the Columbia Linear Machine (CLM) [Phys. Rev. Lett. 57, 1729, (1986)]. Low Coulomb collisionality yields a small stabilizing correction to the magnetohydrodynamic (MHD) collisionless mode, which scales as v, using the Krook model, and ν ec 1/2 using a Lorentz pitch angle operator. In higher collisionality regimes, both models tend to yield similar scalings. In view of relative high neutral collisionality in CLM, both types of collisionality are then combined, modeling neutral collisions with the conserving Krook and Coulomb collisions with a Lorentz model. The dispersion relation is then integrated over velocity space. This combination yields results in very good accord with the available experimental data. The Ion Temperature Gradient Instability is then investigated. It is shown that anisotropy in gradient has a substantial effect on the ion temperature gradient driven mode. A gradient in the parallel temperature is needed for an instability to occur, and a gradient in the perpendicular temperature gradient further enhances the instability indirectly as long as the frequency of the mode is near ion resonance. The physical reason for this important role difference is presented. The Columbia Linear Machine is being redesigned to produce and identify the ion temperature gradient driven η i mode. Using the expected parameters, the author has developed detailed predictions of the mode characteristics in the CLM. Strong multi mode instabilities are expected. As the ion parallel and perpendicular ion temperature gradients are expected to differ significantly, we differentiate between η i parallel and ν i perpendicular and explore the physical differences between them, which leads to a scheme for stabilization of the mode

UV Photodissociation Action Spectroscopy of Haloanilinium Ions in a Linear Quadrupole Ion Trap Mass Spectrometer

Science.gov (United States)

Hansen, Christopher S.; Kirk, Benjamin B.; Blanksby, Stephen J.; O'Hair, Richard. A. J.; Trevitt, Adam J.

2013-06-01

UV-vis photodissociation action spectroscopy is becoming increasingly prevalent because of advances in, and commercial availability of, ion trapping technologies and tunable laser sources. This study outlines in detail an instrumental arrangement, combining a commercial ion-trap mass spectrometer and tunable nanosecond pulsed laser source, for performing fully automated photodissociation action spectroscopy on gas-phase ions. The components of the instrumentation are outlined, including the optical and electronic interfacing, in addition to the control software for automating the experiment and performing online analysis of the spectra. To demonstrate the utility of this ensemble, the photodissociation action spectra of 4-chloroanilinium, 4-bromoanilinium, and 4-iodoanilinium cations are presented and discussed. Multiple photoproducts are detected in each case and the photoproduct yields are followed as a function of laser wavelength. It is shown that the wavelength-dependent partitioning of the halide loss, H loss, and NH3 loss channels can be broadly rationalized in terms of the relative carbon-halide bond dissociation energies and processes of energy redistribution. The photodissociation action spectrum of (phenyl)Ag2 + is compared with a literature spectrum as a further benchmark.

Rainbow Fourier Transform

Science.gov (United States)

Alexandrov, Mikhail D.; Cairns, Brian; Mishchenko, Michael I.

2012-01-01

We present a novel technique for remote sensing of cloud droplet size distributions. Polarized reflectances in the scattering angle range between 135deg and 165deg exhibit a sharply defined rainbow structure, the shape of which is determined mostly by single scattering properties of cloud particles, and therefore, can be modeled using the Mie theory. Fitting the observed rainbow with such a model (computed for a parameterized family of particle size distributions) has been used for cloud droplet size retrievals. We discovered that the relationship between the rainbow structures and the corresponding particle size distributions is deeper than it had been commonly understood. In fact, the Mie theory-derived polarized reflectance as a function of reduced scattering angle (in the rainbow angular range) and the (monodisperse) particle radius appears to be a proxy to a kernel of an integral transform (similar to the sine Fourier transform on the positive semi-axis). This approach, called the rainbow Fourier transform (RFT), allows us to accurately retrieve the shape of the droplet size distribution by the application of the corresponding inverse transform to the observed polarized rainbow. While the basis functions of the proxy-transform are not exactly orthogonal in the finite angular range, this procedure needs to be complemented by a simple regression technique, which removes the retrieval artifacts. This non-parametric approach does not require any a priori knowledge of the droplet size distribution functional shape and is computationally fast (no look-up tables, no fitting, computations are the same as for the forward modeling).

Fourier series, Fourier transform and their applications to mathematical physics

CERN Document Server

Serov, Valery

2017-01-01

This text serves as an introduction to the modern theory of analysis and differential equations with applications in mathematical physics and engineering sciences.  Having outgrown from a series of half-semester courses given at University of Oulu, this book consists of four self-contained parts. The first part, Fourier Series and the Discrete Fourier Transform, is devoted to the classical one-dimensional trigonometric Fourier series with some applications to PDEs and signal processing.  The second part, Fourier Transform and Distributions, is concerned with distribution theory of L. Schwartz and its applications to the Schrödinger and magnetic Schrödinger operations.  The third part, Operator Theory and Integral Equations, is devoted mostly to the self-adjoint but unbounded operators in Hilbert spaces and their applications to integral equations in such spaces. The fourth and final part, Introduction to Partial Differential Equations, serves as an introduction to modern methods for classical theory o...

Fourier transform and its application to 1D and 2D NMR

International Nuclear Information System (INIS)

Canet, D.

1988-01-01

In this review article, the following points are developed: Pulsed NMR and Fourier transform; Fourier transform and two-dimensional spectroscopy; Mathematical properties of Fourier transform; Fourier transform of a sine function- one dimensional NMR; Fourier transform of a product of sine functions - two-dimensional NMR; Data manipulations in the time domain; Numerical Fourier transform [fr

Spin resonance with trapped ions

Energy Technology Data Exchange (ETDEWEB)

Wunderlich, Ch; Balzer, Ch; Hannemann, T; Mintert, F; Neuhauser, W; Reiss, D; Toschek, P E [Institut fuer Laser-Physik, Universitaet Hamburg, Jungiusstrasse 9, 20355 Hamburg (Germany)

2003-03-14

A modified ion trap is described where experiments (in particular related to quantum information processing) that usually require optical radiation can be carried out using microwave or radio frequency electromagnetic fields. Instead of applying the usual methods for coherent manipulation of trapped ions, a string of ions in such a modified trap can be treated like a molecule in nuclear magnetic resonance experiments taking advantage of spin-spin coupling. The collection of trapped ions can be viewed as an N-qubit molecule with adjustable spin-spin coupling constants. Given N identically prepared quantum mechanical two-level systems (qubits), the optimal strategy to estimate their quantum state requires collective measurements. Using the ground state hyperfine levels of electrodynamically trapped {sup 171}Yb{sup +}, we have implemented an adaptive algorithm for state estimation involving sequential measurements on arbitrary qubit states.

Spin resonance with trapped ions

International Nuclear Information System (INIS)

Wunderlich, Ch; Balzer, Ch; Hannemann, T; Mintert, F; Neuhauser, W; Reiss, D; Toschek, P E

2003-01-01

A modified ion trap is described where experiments (in particular related to quantum information processing) that usually require optical radiation can be carried out using microwave or radio frequency electromagnetic fields. Instead of applying the usual methods for coherent manipulation of trapped ions, a string of ions in such a modified trap can be treated like a molecule in nuclear magnetic resonance experiments taking advantage of spin-spin coupling. The collection of trapped ions can be viewed as an N-qubit molecule with adjustable spin-spin coupling constants. Given N identically prepared quantum mechanical two-level systems (qubits), the optimal strategy to estimate their quantum state requires collective measurements. Using the ground state hyperfine levels of electrodynamically trapped 171 Yb + , we have implemented an adaptive algorithm for state estimation involving sequential measurements on arbitrary qubit states

Replica Fourier Transform: Properties and applications

International Nuclear Information System (INIS)

Crisanti, A.; De Dominicis, C.

2015-01-01

The Replica Fourier Transform is the generalization of the discrete Fourier Transform to quantities defined on an ultrametric tree. It finds use in conjunction of the replica method used to study thermodynamics properties of disordered systems such as spin glasses. Its definition is presented in a systematic and simple form and its use illustrated with some representative examples. In particular we give a detailed discussion of the diagonalization in the Replica Fourier Space of the Hessian matrix of the Gaussian fluctuations about the mean field saddle point of spin glass theory. The general results are finally discussed for a generic spherical spin glass model, where the Hessian can be computed analytically

Multi-band Image Registration Method Based on Fourier Transform

Institute of Scientific and Technical Information of China (English)

庹红娅; 刘允才

2004-01-01

This paper presented a registration method based on Fourier transform for multi-band images which is involved in translation and small rotation. Although different band images differ a lot in the intensity and features,they contain certain common information which we can exploit. A model was given that the multi-band images have linear correlations under the least-square sense. It is proved that the coefficients have no effect on the registration progress if two images have linear correlations. Finally, the steps of the registration method were proposed. The experiments show that the model is reasonable and the results are satisfying.

Novel control modes to improve the performance of rectilinear ion trap mass spectrometer with dual pressure chambers

Science.gov (United States)

Huo, Xinming; Tang, Fei; Zhang, Xiaohua; Chen, Jin; Zhang, Yan; Guo, Cheng'an; Wang, Xiaohao

2016-10-01

The rectilinear ion trap (RIT) has gradually become one of the preferred mass analyzers for portable mass spectrometers because of its simple configuration. In order to enhance the performance, including sensitivity, quantitation capability, throughput, and resolution, a novel RIT mass spectrometer with dual pressure chambers was designed and characterized. The studied system constituted a quadrupole linear ion trap (QLIT) in the first chamber and a RIT in the second chamber. Two control modes are hereby proposed: Storage Quadrupole Linear Ion Trap-Rectilinear Ion Trap (SQLIT-RIT) mode, in which the QLIT was used at high pressure for ion storage and isolation, and the RIT was used for analysis; and Analysis Quadrupole Linear Ion Trap-Rectilinear Ion Trap (AQLIT-RIT) mode, in which the QLIT was used for ion storage and cooling. Subsequently, synchronous scanning and analysis were carried out by QLIT and RIT. In SQLIT-RIT mode, signal intensity was improved by a factor of 30; the limit of quantitation was reduced more than tenfold to 50 ng mL-1, and an optimal duty cycle of 96.4% was achieved. In AQLIT-RIT mode, the number of ions coexisting in the RIT was reduced, which weakened the space-charge effect and reduced the mass shift. Furthermore, the mass resolution was enhanced by a factor of 3. The results indicate that the novel control modes achieve satisfactory performance without adding any system complexity, which provides a viable pathway to guarantee good analytical performance in miniaturization of the mass spectrometer.

Laser induced fluorescence of trapped molecular ions

Energy Technology Data Exchange (ETDEWEB)

Grieman, F.J.

1979-10-01

An experimental apparatus for obtaining the optical spectra of molecular ions is described. The experimental technique includes the use of three dimensional ion trapping, laser induced fluorescence, and gated photon counting methods. The ions, which are produced by electron impact, are confined in a radio-frequency quadrupole ion trap of cylindrical design. Because the quadrupole ion trap allows mass selection of the molecular ion desired for study, the analysis of the spectra obtained is greatly simplified. The ion trap also confines the ions to a region easily probed by a laser beam. 18 references.

Laser induced fluorescence of trapped molecular ions

International Nuclear Information System (INIS)

Grieman, F.J.

1979-10-01

An experimental apparatus for obtaining the optical spectra of molecular ions is described. The experimental technique includes the use of three dimensional ion trapping, laser induced fluorescence, and gated photon counting methods. The ions, which are produced by electron impact, are confined in a radio-frequency quadrupole ion trap of cylindrical design. Because the quadrupole ion trap allows mass selection of the molecular ion desired for study, the analysis of the spectra obtained is greatly simplified. The ion trap also confines the ions to a region easily probed by a laser beam. 18 references

Optimization and simulation of MEMS rectilinear ion trap

Directory of Open Access Journals (Sweden)

Huang Gang

2015-04-01

Full Text Available In this paper, the design of a MEMS rectilinear ion trap was optimized under simulated conditions. The size range of the MEMS rectilinear ion trap’s electrodes studied in this paper is measured at micron scale. SIMION software was used to simulate the MEMS rectilinear ion trap with different sizes and different radio-frequency signals. The ion-trapping efficiencies of the ion trap under these different simulation conditions were obtained. The ion-trapping efficiencies were compared to determine the performance of the MEMS rectilinear ion trap in different conditions and to find the optimum conditions. The simulation results show that for the ion trap at micron scale or smaller, the optimized length–width ratio was 0.8, and a higher frequency of radio-frequency signal is necessary to obtain a higher ion-trapping efficiency. These results have a guiding role in the process of developing MEMS rectilinear ion traps, and great application prospects in the research fields of the MEMS rectilinear ion trap and the MEMS mass spectrometer.

Systems and Methods for Ejection of Ions from an Ion Trap

Science.gov (United States)

Cooks, Robert Graham (Inventor); Snyder, Dalton (Inventor)

2018-01-01

The invention generally relates to systems and methods for ejection of ions from an ion trap. In certain embodiments, systems and methods of the invention sum two different frequency signals into a single summed signal that is applied to an ion trap. In other embodiments, an amplitude of a single frequency signal is modulated as the single frequency signal is being applied to the ion trap. In other embodiments, a first alternating current (AC) signal is applied to an ion trap that varies as a function of time, while a constant radio frequency (RF) signal is applied to the ion trap.

Fourier transforms in NMR, optical, and mass spectrometry

International Nuclear Information System (INIS)

Marshall, A.G.; Verdun, F.R.; Ohio State Univ., Columbus, OH

1990-01-01

This book is a teaching and reference text for Fourier transform methods as they are applied in spectroscopy. It offers a unified treatment of the three most popular types of FT/spectroscopy. Non-ideal effects are treated in detail: noise (source- and detector-limited); non-linear response; limits to spectrometer performance based on finite detection period, finite data size, mis-phasing, etc. Common puzzles and paradoxes are explained: e.g., use of mathematically complex variables to represent physically real quantities; interpretation of negative frequency signals; on-resonance versus off-resonance response; interpolation; ultimate accuracy of discrete representation of an analog signal; differences between linearly- and circularly-polarized radiation; multiplex advantage or disadvantage, etc. (author). refs.; figs.; tabs

A Fourier Transform Spectrometer Based on an Electrothermal MEMS Mirror with Improved Linear Scan Range

Directory of Open Access Journals (Sweden)

Wei Wang

2016-09-01

Full Text Available A Fourier transform spectrometer (FTS that incorporates a closed-loop controlled, electrothermally actuated microelectromechanical systems (MEMS micromirror is proposed and experimentally verified. The scan range and the tilting angle of the mirror plate are the two critical parameters for MEMS-based FTS. In this work, the MEMS mirror with a footprint of 4.3 mm × 3.1 mm is based on a modified lateral-shift-free (LSF bimorph actuator design with large piston and reduced tilting. Combined with a position-sensitive device (PSD for tilt angle sensing, the feedback controlled MEMS mirror generates a 430 µm stable linear piston scan with the mirror plate tilting angle less than ±0.002°. The usable piston scan range is increased to 78% of the MEMS mirror’s full scan capability, and a spectral resolution of 0.55 nm at 531.9 nm wavelength, has been achieved. It is a significant improvement compared to the prior work.

Novel Ion Trap Design for Strong Ion-Cavity Coupling

Directory of Open Access Journals (Sweden)

Alejandro Márquez Seco

2016-04-01

Full Text Available We present a novel ion trap design which facilitates the integration of an optical fiber cavity into the trap structure. The optical fibers are confined inside hollow electrodes in such a way that tight shielding and free movement of the fibers are simultaneously achievable. The latter enables in situ optimization of the overlap between the trapped ions and the cavity field. Through numerical simulations, we systematically analyze the effects of the electrode geometry on the trapping characteristics such as trap depths, secular frequencies and the optical access angle. Additionally, we simulate the effects of the presence of the fibers and confirm the robustness of the trapping potential. Based on these simulations and other technical considerations, we devise a practical trap configuration that isviable to achieve strong coupling of a single ion.

The Aarhus Ion Micro-Trap Project

DEFF Research Database (Denmark)

Miroshnychenko, Yevhen; Nielsen, Otto; Poulsen, Gregers

As part of our involvement in the EU MICROTRAP project, we have designed, manufactured and assembled a micro-scale ion trap with integrated optical fibers. These prealigned fibers will allow delivering cooling laser light to single ions. Therefore, such a trap will not require any direct optical...... and installed in an ultra high vacuum chamber, which includes an ablation oven for all-optical loading of the trap [2]. The next steps on the project are to demonstrate the operation of the micro-trap and the cooling of ions using fiber delivered light. [1] D. Grant, Development of Micro-Scale Ion traps, Master...... Thesis (2008). [2] R.J. Hendricks, D.M. Grant, P.F. Herskind, A. Dantan and M. Drewsen, An all-optical ion-loading technique for scalable microtrap architectures, Applied Physics B, 88, 507 (2007)....

A gain and bandwidth enhanced transimpedance preamplifier for Fourier-transform ion cyclotron resonance mass spectrometry

International Nuclear Information System (INIS)

Lin, Tzu-Yung; Green, Roger J.; O'Connor, Peter B.

2011-01-01

The nature of the ion signal from a 12-T Fourier-transform ion cyclotron resonance mass spectrometer and the electronic noise were studied to further understand the electronic detection limit. At minimal cost, a new transimpedance preamplifier was designed, computer simulated, built, and tested. The preamplifier design pushes the electronic signal-to-noise performance at room temperature to the limit, because of its enhanced tolerance of the capacitance of the detection device, lower intrinsic noise, and larger flat mid-band gain (input current noise spectral density of around 1 pA/√(Hz) when the transimpedance is about 85 dBΩ). The designed preamplifier has a bandwidth of ∼3 kHz to 10 MHz, which corresponds to the mass-to-charge ratio, m/z, of approximately 18 to 61 k at 12 T. The transimpedance and the bandwidth can be easily adjusted by changing the value of passive components. The feedback limitation of the circuit is discussed. With the maximum possible transimpedance of 5.3 MΩ when using an 0402 surface mount resistor, the preamplifier was estimated to be able to detect ∼110 charges in a single scan.

Fast inverse nonlinear Fourier transformation using exponential one-step methods : Darboux transformation

NARCIS (Netherlands)

Vaibhav, V.K.

2017-01-01

This paper considers the non-Hermitian Zakharov-Shabat (ZS) scattering problem which forms the basis for defining the SU(2) nonlinear Fourier transformation (NFT). The theoretical underpinnings of this generalization of the conventional Fourier transformation are quite well established in the

Bioconversion of red ginseng saponins in the gastro-intestinal tract in vitro model studied by high-performance liquid chromatography-high resolution Fourier transform ion cyclotron resonance mass spectrometry

NARCIS (Netherlands)

Kong, H.; Wang, M.; Venema, K.; Maathuis, A.; Heijden, R. van der; Greef, J. van der; Xu, G.; Hankemeier, T.

2009-01-01

A high-performance liquid chromatography-high resolution Fourier transform ion cyclotron resonance mass spectrometry (HPLC-FTICR-MS) method was developed to investigate the metabolism of ginsenosides in in vitro models of the gastro-intestinal tract. The metabolites were identified by

2D non-separable linear canonical transform (2D-NS-LCT) based cryptography

Science.gov (United States)

Zhao, Liang; Muniraj, Inbarasan; Healy, John J.; Malallah, Ra'ed; Cui, Xiao-Guang; Ryle, James P.; Sheridan, John T.

2017-05-01

The 2D non-separable linear canonical transform (2D-NS-LCT) can describe a variety of paraxial optical systems. Digital algorithms to numerically evaluate the 2D-NS-LCTs are not only important in modeling the light field propagations but also of interest in various signal processing based applications, for instance optical encryption. Therefore, in this paper, for the first time, a 2D-NS-LCT based optical Double-random- Phase-Encryption (DRPE) system is proposed which offers encrypting information in multiple degrees of freedom. Compared with the traditional systems, i.e. (i) Fourier transform (FT); (ii) Fresnel transform (FST); (iii) Fractional Fourier transform (FRT); and (iv) Linear Canonical transform (LCT), based DRPE systems, the proposed system is more secure and robust as it encrypts the data with more degrees of freedom with an augmented key-space.

Linear transforms for Fourier data on the sphere: application to high angular resolution diffusion MRI of the brain.

Science.gov (United States)

Haldar, Justin P; Leahy, Richard M

2013-05-01

This paper presents a novel family of linear transforms that can be applied to data collected from the surface of a 2-sphere in three-dimensional Fourier space. This family of transforms generalizes the previously-proposed Funk-Radon Transform (FRT), which was originally developed for estimating the orientations of white matter fibers in the central nervous system from diffusion magnetic resonance imaging data. The new family of transforms is characterized theoretically, and efficient numerical implementations of the transforms are presented for the case when the measured data is represented in a basis of spherical harmonics. After these general discussions, attention is focused on a particular new transform from this family that we name the Funk-Radon and Cosine Transform (FRACT). Based on theoretical arguments, it is expected that FRACT-based analysis should yield significantly better orientation information (e.g., improved accuracy and higher angular resolution) than FRT-based analysis, while maintaining the strong characterizability and computational efficiency of the FRT. Simulations are used to confirm these theoretical characteristics, and the practical significance of the proposed approach is illustrated with real diffusion weighted MRI brain data. These experiments demonstrate that, in addition to having strong theoretical characteristics, the proposed approach can outperform existing state-of-the-art orientation estimation methods with respect to measures such as angular resolution and robustness to noise and modeling errors. Copyright © 2013 Elsevier Inc. All rights reserved.

Characterization of non-polar aromatic hydrocarbons in crude oil using atmospheric pressure laser ionization and Fourier transform ion cyclotron resonance mass spectrometry (APLI FT-ICR MS).

Science.gov (United States)

Schrader, Wolfgang; Panda, Saroj K; Brockmann, Klaus J; Benter, Thorsten

2008-07-01

We report on the successful application of the recently introduced atmospheric pressure laser ionization (APLI) method as a novel tool for the analysis of crude oil and its components. Using Fourier transform ion cyclotron resonance mass spectrometry, unambiguous determination of key compounds in this complex matrix with unprecedented sensitivity is presented.

A highly miniaturized vacuum package for a trapped ion atomic clock

Energy Technology Data Exchange (ETDEWEB)

Schwindt, Peter D. D., E-mail: pschwin@sandia.gov; Jau, Yuan-Yu; Partner, Heather; Casias, Adrian; Wagner, Adrian R.; Moorman, Matthew; Manginell, Ronald P. [Sandia National Laboratories, Albuquerque, New Mexico 87185 (United States); Kellogg, James R.; Prestage, John D. [Jet Propulsion Laboratory, Pasadena, California 91109 (United States)

2016-05-15

We report on the development of a highly miniaturized vacuum package for use in an atomic clock utilizing trapped ytterbium-171 ions. The vacuum package is approximately 1 cm{sup 3} in size and contains a linear quadrupole RF Paul ion trap, miniature neutral Yb sources, and a non-evaporable getter pump. We describe the fabrication process for making the Yb sources and assembling the vacuum package. To prepare the vacuum package for ion trapping, it was evacuated, baked at a high temperature, and then back filled with a helium buffer gas. Once appropriate vacuum conditions were achieved in the package, it was sealed with a copper pinch-off and was subsequently pumped only by the non-evaporable getter. We demonstrated ion trapping in this vacuum package and the operation of an atomic clock, stabilizing a local oscillator to the 12.6 GHz hyperfine transition of {sup 171}Y b{sup +}. The fractional frequency stability of the clock was measured to be 2 × 10{sup −11}/τ{sup 1/2}.

Spectroscopy with trapped highly charged ions

International Nuclear Information System (INIS)

Beiersdorfer, Peter

2009-01-01

We give an overview of atomic spectroscopy performed on electron beam ion traps at various locations throughout the world. Spectroscopy at these facilities contributes to various areas of science and engineering, including but not limited to basic atomic physics, astrophysics, extreme ultraviolet lithography, and the development of density and temperature diagnostics of fusion plasmas. These contributions are accomplished by generating, for example, spectral surveys, making precise radiative lifetime measurements, accounting for radiative power emitted in a given wavelength band, illucidating isotopic effects, and testing collisional-radiative models. While spectroscopy with electron beam ion traps had originally focused on the x-ray emission from highly charged ions interacting with the electron beam, the operating modes of such devices have expanded to study radiation in almost all wavelength bands from the visible to the hard x-ray region; and at several facilities the ions can be studied even in the absence of an electron beam. Photon emission after charge exchange or laser excitation has been observed; and the work is no longer restricted to highly charged ions. Much of the experimental capabilities are unique to electron beam ion traps, and the work performed with these devices cannot be undertaken elsewhere. However, in other areas the work on electron beam ion traps rivals the spectroscopy performed with conventional ion traps or heavy-ion storage rings. The examples we present highlight many of the capabilities of the existing electron beam ion traps and their contributions to physics.

Time-Frequency Analysis of Non-Stationary Biological Signals with Sparse Linear Regression Based Fourier Linear Combiner

Directory of Open Access Journals (Sweden)

Yubo Wang

2017-06-01

Full Text Available It is often difficult to analyze biological signals because of their nonlinear and non-stationary characteristics. This necessitates the usage of time-frequency decomposition methods for analyzing the subtle changes in these signals that are often connected to an underlying phenomena. This paper presents a new approach to analyze the time-varying characteristics of such signals by employing a simple truncated Fourier series model, namely the band-limited multiple Fourier linear combiner (BMFLC. In contrast to the earlier designs, we first identified the sparsity imposed on the signal model in order to reformulate the model to a sparse linear regression model. The coefficients of the proposed model are then estimated by a convex optimization algorithm. The performance of the proposed method was analyzed with benchmark test signals. An energy ratio metric is employed to quantify the spectral performance and results show that the proposed method Sparse-BMFLC has high mean energy (0.9976 ratio and outperforms existing methods such as short-time Fourier transfrom (STFT, continuous Wavelet transform (CWT and BMFLC Kalman Smoother. Furthermore, the proposed method provides an overall 6.22% in reconstruction error.

Time-Frequency Analysis of Non-Stationary Biological Signals with Sparse Linear Regression Based Fourier Linear Combiner.

Science.gov (United States)

Wang, Yubo; Veluvolu, Kalyana C

2017-06-14

It is often difficult to analyze biological signals because of their nonlinear and non-stationary characteristics. This necessitates the usage of time-frequency decomposition methods for analyzing the subtle changes in these signals that are often connected to an underlying phenomena. This paper presents a new approach to analyze the time-varying characteristics of such signals by employing a simple truncated Fourier series model, namely the band-limited multiple Fourier linear combiner (BMFLC). In contrast to the earlier designs, we first identified the sparsity imposed on the signal model in order to reformulate the model to a sparse linear regression model. The coefficients of the proposed model are then estimated by a convex optimization algorithm. The performance of the proposed method was analyzed with benchmark test signals. An energy ratio metric is employed to quantify the spectral performance and results show that the proposed method Sparse-BMFLC has high mean energy (0.9976) ratio and outperforms existing methods such as short-time Fourier transfrom (STFT), continuous Wavelet transform (CWT) and BMFLC Kalman Smoother. Furthermore, the proposed method provides an overall 6.22% in reconstruction error.

Asymmetric ion trap

Science.gov (United States)

Barlow, Stephan E.; Alexander, Michael L.; Follansbee, James C.

1997-01-01

An ion trap having two end cap electrodes disposed asymmetrically about a center of a ring electrode. The inner surface of the end cap electrodes are conformed to an asymmetric pair of equipotential lines of the harmonic formed by the application of voltages to the electrodes. The asymmetry of the end cap electrodes allows ejection of charged species through the closer of the two electrodes which in turn allows for simultaneously detecting anions and cations expelled from the ion trap through the use of two detectors charged with opposite polarity.

Image reconstruction from pairs of Fourier-transform magnitude

International Nuclear Information System (INIS)

Hunt, B.R.; Overman, T.L.; Gough, P.

1998-01-01

The retrieval of phase information from only the magnitude of the Fourier transform of a signal remains an important problem for many applications. We present an algorithm for phase retrieval when there exist two related sets of Fourier-transform magnitude data. The data are assumed to come from a single object observed in two different polarizations through a distorting medium, so the phase component of the Fourier transform of the object is corrupted. Phase retrieval is accomplished by minimization of a suitable criterion function, which can take three different forms. copyright 1998 Optical Society of America

Food contaminant analysis at ultra-high mass resolution: application of hybrid linear ion trap - orbitrap mass spectrometry for the determination of the polyether toxins, azaspiracids, in shellfish.

LENUS (Irish Health Repository)

2010-10-30

The biotoxins, azaspiracids (AZAs), from marine phytoplankton accumulate in shellfish and affect human health by causing severe gastrointestinal disturbance, diarrhea, nausea and vomiting. Specific and sensitive methods have been developed and validated for the determination of the most commonly occurring azaspiracid analogs. An LTQ Orbitrap mass spectrometer is a hybrid instrument that combines linear ion trap (LIT) mass spectrometry (MS) with high-resolution Fourier transform (FT) MS and this was exploited to perform simultaneous ultra-high-resolution full-scan MS analysis and collision-induced dissociation (CID) tandem mass spectrometry (MS\\/MS). Using the highest mass resolution setting (100,000 FWHM) in full-scan mode, the methodology was validated for the determination of six AZAs in mussel (Mytilus galloprovincialis) tissue extracts. Ultra-high mass resolution, together with a narrow mass tolerance window of ±2 mDa, dramatically improved detection sensitivity. In addition to employing chromatographic resolution to distinguish between the isomeric azaspiracid analogs, AZA1\\/AZA6 and AZA4\\/AZA5, higher energy collisionally induced dissociation (HCD) fragmentation on selected precursor ions were performed in parallel with full-scan FTMS. Using HCD MS\\/MS, most precursor and product ion masses were determined within 1 ppm of the theoretical m\\/z values throughout the mass spectral range and this enhanced the reliability of analyte identity.For the analysis of mussels (M. galloprovincialis), the method limit of quantitation (LOQ) was 0.010 µg\\/g using full-scan FTMS and this was comparable with the LOQ (0.007 µg\\/g) using CID MS\\/MS. The repeatability data were; intra-day RSD% (1.8-4.4%; n = 6) and inter-day RSD% (4.7-8.6%; n = 3). Application of these methods to the analysis of mussels (M. edulis) that were naturally contaminated with azaspiracids, using high-resolution full-scan Orbitrap MS and low-resolution CID MS\\/MS, produced

Sympathetic cooling of ions in a hybrid atom ion trap

Energy Technology Data Exchange (ETDEWEB)

Hoeltkemeier, Bastian

2016-10-27

In this thesis the dynamics of a trapped ion immersed in a spatially localized buffer gas is investigated. For a homogeneous buffer gas, the ion's energy distribution reaches a stable equilibrium only if the mass of the buffer gas atoms is below a critical value. This limitation can be overcome by using multipole traps in combination and/or a spatially confined buffer gas. Using a generalized model for elastic collisions of the ion with the buffer gas atoms, the ion's energy distribution is numerically determined for arbitrary buffer gas distributions and trap parameters. Three regimes characterized by the respective analytic form of the ion's equilibrium energy distribution are found. One of these is a novel regime at large atom-to-ion mass ratios where the final ion temperature can tuned by adiabatically decreasing the spatial extension of the buffer gas and the effective ion trap depth (forced sympathetic cooling). The second part of the thesis presents a hybrid atom ion trap designed for sympathetic cooling of hydroxide anions. In this hybrid trap the anions are immersed in a cloud of laser cooled rubidium atoms. The translational and rovibrational temperatures of the anions is probed by photodetachment tomography and spectroscopy which shows the first ever indication of sympathetic cooling of anions by laser cooled atoms.

The relationship between shock response spectrum and fast Fourier transform

International Nuclear Information System (INIS)

Zola, Maurizio

2001-01-01

In this paper the basic relationship between response spectrum and fast Fourier transform is laid down. Since a long time the response spectrum has been used by structural engineers in the seismic domain and nowadays it is going to be used to define transient motions. This way to define the excitation is more general and more real than the use of classical shape pulses for the reproduction of real environment. Nevertheless the response spectrum of a real excitation represents a loss of some information with respect to the Fourier transform. A useful discussion could arise from these observations. Appendix A gives the relationship between the mathematic Fourier transform and the digital Fourier transform given by computers, while Appendix B gives some examples of response spectra and Fourier transforms of simple functions. (author)

Experiments with trapped ions and ultrafast laser pulses

Science.gov (United States)

Johnson, Kale Gifford

Since the dawn of quantum information science, laser-cooled trapped atomic ions have been one of the most compelling systems for the physical realization of a quantum computer. By applying qubit state dependent forces to the ions, their collective motional modes can be used as a bus to realize entangling quantum gates. Ultrafast state-dependent kicks [1] can provide a universal set of quantum logic operations, in conjunction with ultrafast single qubit rotations [2], which uses only ultrafast laser pulses. This may present a clearer route to scaling a trapped ion processor [3]. In addition to the role that spin-dependent kicks (SDKs) play in quantum computation, their utility in fundamental quantum mechanics research is also apparent. In this thesis, we present a set of experiments which demonstrate some of the principle properties of SDKs including ion motion independence (we demonstrate single ion thermometry from the ground state to near room temperature and the largest Schrodinger cat state ever created in an oscillator), high speed operations (compared with conventional atom-laser interactions), and multi-qubit entanglement operations with speed that is not fundamentally limited by the trap oscillation frequency. We also present a method to provide higher stability in the radial mode ion oscillation frequencies of a linear radiofrequency (rf) Paul trap-a crucial factor when performing operations on the rf-sensitive modes. Finally, we present the highest atomic position sensitivity measurement of an isolated atom to date of 0.5 nm Hz. (-1/2) with a minimum uncertaintyof 1.7 nm using a 0.6 numerical aperature (NA) lens system, along with a method to correct aberrations and a direct position measurement of ion micromotion (the inherent oscillations of an ion trapped in an oscillating rf field). This development could be used to directly image atom motion in the quantum regime, along with sensing forces at the yoctonewton [10. (-24) N)] scale forgravity sensing

A Simplified Proof of Uncertainty Principle for Quaternion Linear Canonical Transform

Directory of Open Access Journals (Sweden)

Mawardi Bahri

2016-01-01

Full Text Available We provide a short and simple proof of an uncertainty principle associated with the quaternion linear canonical transform (QLCT by considering the fundamental relationship between the QLCT and the quaternion Fourier transform (QFT. We show how this relation allows us to derive the inverse transform and Parseval and Plancherel formulas associated with the QLCT. Some other properties of the QLCT are also studied.

Fourier-based reconstruction via alternating direction total variation minimization in linear scan CT

International Nuclear Information System (INIS)

Cai, Ailong; Wang, Linyuan; Yan, Bin; Zhang, Hanming; Li, Lei; Xi, Xiaoqi; Li, Jianxin

2015-01-01

In this study, we consider a novel form of computed tomography (CT), that is, linear scan CT (LCT), which applies a straight line trajectory. Furthermore, an iterative algorithm is proposed for pseudo-polar Fourier reconstruction through total variation minimization (PPF-TVM). Considering that the sampled Fourier data are distributed in pseudo-polar coordinates, the reconstruction model minimizes the TV of the image subject to the constraint that the estimated 2D Fourier data for the image are consistent with the 1D Fourier transform of the projection data. PPF-TVM employs the alternating direction method (ADM) to develop a robust and efficient iteration scheme, which ensures stable convergence provided that appropriate parameter values are given. In the ADM scheme, PPF-TVM applies the pseudo-polar fast Fourier transform and its adjoint to iterate back and forth between the image and frequency domains. Thus, there is no interpolation in the Fourier domain, which makes the algorithm both fast and accurate. PPF-TVM is particularly useful for limited angle reconstruction in LCT and it appears to be robust against artifacts. The PPF-TVM algorithm was tested with the FORBILD head phantom and real data in comparisons with state-of-the-art algorithms. Simulation studies and real data verification suggest that PPF-TVM can reconstruct higher accuracy images with lower time consumption

Application of Fourier-transform ion cyclotron resonance mass spectrometry to metabolic profiling and metabolite identification.

Science.gov (United States)

Ohta, Daisaku; Kanaya, Shigehiko; Suzuki, Hideyuki

2010-02-01

Metabolomics, as an essential part of genomics studies, intends holistic understanding of metabolic networks through simultaneous analysis of a myriad of both known and unknown metabolites occurring in living organisms. The initial stage of metabolomics was designed for the reproducible analyses of known metabolites based on their comparison to available authentic compounds. Such metabolomics platforms were mostly based on mass spectrometry (MS) technologies enabled by a combination of different ionization methods together with a variety of separation steps including LC, GC, and CE. Among these, Fourier-transform ion cyclotron resonance MS (FT-ICR/MS) is distinguished from other MS technologies by its ultrahigh resolution power in mass to charge ratio (m/z). The potential of FT-ICR/MS as a distinctive metabolomics tool has been demonstrated in nontargeted metabolic profiling and functional characterization of novel genes. Here, we discuss both the advantages and difficulties encountered in the FT-ICR/MS metabolomics studies.

Application of Fourier transform to MHD flow over an accelerated plate with partial-slippage

Directory of Open Access Journals (Sweden)

Salman Ahmad

2014-06-01

Full Text Available Magneto-Hydrodynamic (MHD flow over an accelerated plate is investigated with partial slip conditions. Generalized Fourier Transform is used to get the exact solution not only for uniform acceleration but also for variable acceleration. The numerical solution is obtained by using linear finite element method in space and One-Step-θ-scheme in time. The resulting discretized algebraic systems are solved by applying geometric-multigrid approach. Numerical solutions are compared with the obtained Fourier transform results. Many interesting results related with slippage and MHD effects are discussed in detail through graphical sketches and tables. Application of Dirac-Delta function is one of the main features of present work.

Direct fourier method reconstruction based on unequally spaced fast fourier transform

International Nuclear Information System (INIS)

Wu Xiaofeng; Zhao Ming; Liu Li

2003-01-01

First, We give an Unequally Spaced Fast Fourier Transform (USFFT) method, which is more exact and theoretically more comprehensible than its former counterpart. Then, with an interesting interpolation scheme, we discusse how to apply USFFT to Direct Fourier Method (DFM) reconstruction of parallel projection data. At last, an emulation experiment result is given. (authors)

A discrete Fourier transform for virtual memory machines

Science.gov (United States)

Galant, David C.

1992-01-01

An algebraic theory of the Discrete Fourier Transform is developed in great detail. Examination of the details of the theory leads to a computationally efficient fast Fourier transform for the use on computers with virtual memory. Such an algorithm is of great use on modern desktop machines. A FORTRAN coded version of the algorithm is given for the case when the sequence of numbers to be transformed is a power of two.

Comparison of Fourier transform and continuous wavelet transform to study echo-planar imaging flow maps

Energy Technology Data Exchange (ETDEWEB)

Rodriguez G, A.; Bowtell, R.; Mansfield, P. [Area de Procesamiento Digital de Senales e Imagenes Biomedicas. Universidad Autonoma Metropolitana Iztapalapa. Mexico D.F. 09340 Mexico (Mexico)

1998-12-31

Velocity maps were studied combining Doyle and Mansfield method (1986) with each of the following transforms: Fourier, window Fourier and wavelet (Mexican hat). Continuous wavelet transform was compared against the two Fourier transform to determine which technique is best suited to study blood maps generated by Half Fourier Echo-Planar Imaging. Coefficient images were calculated and plots of the pixel intensity variation are presented. Finally, contour maps are shown to visualize the behavior of the blood flow in the cardiac chambers for the wavelet technique. (Author)

Comparison of Fourier transform and continuous wavelet transform to study echo-planar imaging flow maps

International Nuclear Information System (INIS)

Rodriguez G, A.; Bowtell, R.; Mansfield, P.

1998-01-01

Velocity maps were studied combining Doyle and Mansfield method (1986) with each of the following transforms: Fourier, window Fourier and wavelet (Mexican hat). Continuous wavelet transform was compared against the two Fourier transform to determine which technique is best suited to study blood maps generated by Half Fourier Echo-Planar Imaging. Coefficient images were calculated and plots of the pixel intensity variation are presented. Finally, contour maps are shown to visualize the behavior of the blood flow in the cardiac chambers for the wavelet technique. (Author)

Wigner distribution and fractional Fourier transform

NARCIS (Netherlands)

Alieva, T.; Bastiaans, M.J.

2001-01-01

The connection between the Wigner distribution and the squared modulus of the fractional Fourier transform - which are both well-known time-frequency representations of a signal - is established. In particular the Radon-Wigner transform is used, which relates projections of the Wigner distribution

Convolution Theorem of Fractional Fourier Transformation Derived by Representation Transformation in Quantum Mechancis

International Nuclear Information System (INIS)

Fan Hongyi; Hao Ren; Lu Hailiang

2008-01-01

Based on our previous paper (Commun. Theor. Phys. 39 (2003) 417) we derive the convolution theorem of fractional Fourier transformation in the context of quantum mechanics, which seems a convenient and neat way. Generalization of this method to the complex fractional Fourier transformation case is also possible

The application and improvement of Fourier transform spectrometer experiment

Science.gov (United States)

Liu, Zhi-min; Gao, En-duo; Zhou, Feng-qi; Wang, Lan-lan; Feng, Xiao-hua; Qi, Jin-quan; Ji, Cheng; Wang, Luning

2017-08-01

According to teaching and experimental requirements of Optoelectronic information science and Engineering, in order to consolidate theoretical knowledge and improve the students practical ability, the Fourier transform spectrometer ( FTS) experiment, its design, application and improvement are discussed in this paper. The measurement principle and instrument structure of Fourier transform spectrometer are introduced, and the spectrums of several common Laser devices are measured. Based on the analysis of spectrum and test, several possible improvement methods are proposed. It also helps students to understand the application of Fourier transform in physics.

Geometric Representations for Discrete Fourier Transforms

Science.gov (United States)

Cambell, C. W.

1986-01-01

Simple geometric representations show symmetry and periodicity of discrete Fourier transforms (DFT's). Help in visualizing requirements for storing and manipulating transform value in computations. Representations useful in any number of dimensions, but particularly in one-, two-, and three-dimensional cases often encountered in practice.

Quantum simulation of spin models on an arbitrary lattice with trapped ions

International Nuclear Information System (INIS)

Korenblit, S; Kafri, D; Campbell, W C; Islam, R; Edwards, E E; Monroe, C; Gong, Z-X; Lin, G-D; Duan, L-M; Kim, J; Kim, K

2012-01-01

A collection of trapped atomic ions represents one of the most attractive platforms for the quantum simulation of interacting spin networks and quantum magnetism. Spin-dependent optical dipole forces applied to an ion crystal create long-range effective spin–spin interactions and allow the simulation of spin Hamiltonians that possess nontrivial phases and dynamics. Here we show how the appropriate design of laser fields can provide for arbitrary multidimensional spin–spin interaction graphs even for the case of a linear spatial array of ions. This scheme uses currently available trap technology and is scalable to levels where the classical methods of simulation are intractable. (paper)

The quantum state vector in phase space and Gabor's windowed Fourier transform

International Nuclear Information System (INIS)

Bracken, A J; Watson, P

2010-01-01

Representations of quantum state vectors by complex phase space amplitudes, complementing the description of the density operator by the Wigner function, have been defined by applying the Weyl-Wigner transform to dyadic operators, linear in the state vector and anti-linear in a fixed 'window state vector'. Here aspects of this construction are explored, and a connection is established with Gabor's 'windowed Fourier transform'. The amplitudes that arise for simple quantum states from various choices of windows are presented as illustrations. Generalized Bargmann representations of the state vector appear as special cases, associated with Gaussian windows. For every choice of window, amplitudes lie in a corresponding linear subspace of square-integrable functions on phase space. A generalized Born interpretation of amplitudes is described, with both the Wigner function and a generalized Husimi function appearing as quantities linear in an amplitude and anti-linear in its complex conjugate. Schroedinger's time-dependent and time-independent equations are represented on phase space amplitudes, and their solutions described in simple cases.

A cryogenic electrostatic trap for long-time storage of keV ion beams

Science.gov (United States)

Lange, M.; Froese, M.; Menk, S.; Varju, J.; Bastert, R.; Blaum, K.; López-Urrutia, J. R. Crespo; Fellenberger, F.; Grieser, M.; von Hahn, R.; Heber, O.; Kühnel, K.-U.; Laux, F.; Orlov, D. A.; Rappaport, M. L.; Repnow, R.; Schröter, C. D.; Schwalm, D.; Shornikov, A.; Sieber, T.; Toker, Y.; Ullrich, J.; Wolf, A.; Zajfman, D.

2010-05-01

We report on the realization and operation of a fast ion beam trap of the linear electrostatic type employing liquid helium cooling to reach extremely low blackbody radiation temperature and residual gas density and, hence, long storage times of more than 5 min which are unprecedented for keV ion beams. Inside a beam pipe that can be cooled to temperatures <15 K, with 1.8 K reached in some locations, an ion beam pulse can be stored at kinetic energies of 2-20 keV between two electrostatic mirrors. Along with an overview of the cryogenic trap design, we present a measurement of the residual gas density inside the trap resulting in only 2×103 cm-3, which for a room temperature environment corresponds to a pressure in the 10-14 mbar range. The device, called the cryogenic trap for fast ion beams, is now being used to investigate molecules and clusters at low temperatures, but has also served as a design prototype for the cryogenic heavy-ion storage ring currently under construction at the Max-Planck Institute for Nuclear Physics.

Sawtooth activity of the ion cloud in an electron-beam ion trap

International Nuclear Information System (INIS)

Radtke, R.; Biedermann, C.

2003-01-01

The dynamics of an ensemble of highly charged Ar and Ba ions in an electron-beam ion trap (EBIT) was studied by recording time-resolved x-ray spectra emitted from trapped ions. Sawtoothlike signatures manifest in the spectra for a variety of EBIT operating conditions indicating a sudden collapse of the ion inventory in the trap. The collapse occurs on a time scale of approximately 100 ms and the evolution of the sawteeth is very sensitive to parameters such as electron-beam current and axial trap depth. Analysis of the measurements is based on a time-dependent calculation of the trapping process showing that sawtooth activity is caused by the feedback between the low-Z argon and high-Z barium ions. This unexpected behavior demonstrates the importance of nonlinear effects in electron-beam traps containing more than a single ion species

Ball-grid array architecture for microfabricated ion traps

Science.gov (United States)

Guise, Nicholas D.; Fallek, Spencer D.; Stevens, Kelly E.; Brown, K. R.; Volin, Curtis; Harter, Alexa W.; Amini, Jason M.; Higashi, Robert E.; Lu, Son Thai; Chanhvongsak, Helen M.; Nguyen, Thi A.; Marcus, Matthew S.; Ohnstein, Thomas R.; Youngner, Daniel W.

2015-05-01

State-of-the-art microfabricated ion traps for quantum information research are approaching nearly one hundred control electrodes. We report here on the development and testing of a new architecture for microfabricated ion traps, built around ball-grid array (BGA) connections, that is suitable for increasingly complex trap designs. In the BGA trap, through-substrate vias bring electrical signals from the back side of the trap die to the surface trap structure on the top side. Gold-ball bump bonds connect the back side of the trap die to an interposer for signal routing from the carrier. Trench capacitors fabricated into the trap die replace area-intensive surface or edge capacitors. Wirebonds in the BGA architecture are moved to the interposer. These last two features allow the trap die to be reduced to only the area required to produce trapping fields. The smaller trap dimensions allow tight focusing of an addressing laser beam for fast single-qubit rotations. Performance of the BGA trap as characterized with 40Ca+ ions is comparable to previous surface-electrode traps in terms of ion heating rate, mode frequency stability, and storage lifetime. We demonstrate two-qubit entanglement operations with 171Yb+ ions in a second BGA trap.

Ball-grid array architecture for microfabricated ion traps

International Nuclear Information System (INIS)

Guise, Nicholas D.; Fallek, Spencer D.; Stevens, Kelly E.; Brown, K. R.; Volin, Curtis; Harter, Alexa W.; Amini, Jason M.; Higashi, Robert E.; Lu, Son Thai; Chanhvongsak, Helen M.; Nguyen, Thi A.; Marcus, Matthew S.; Ohnstein, Thomas R.; Youngner, Daniel W.

2015-01-01

State-of-the-art microfabricated ion traps for quantum information research are approaching nearly one hundred control electrodes. We report here on the development and testing of a new architecture for microfabricated ion traps, built around ball-grid array (BGA) connections, that is suitable for increasingly complex trap designs. In the BGA trap, through-substrate vias bring electrical signals from the back side of the trap die to the surface trap structure on the top side. Gold-ball bump bonds connect the back side of the trap die to an interposer for signal routing from the carrier. Trench capacitors fabricated into the trap die replace area-intensive surface or edge capacitors. Wirebonds in the BGA architecture are moved to the interposer. These last two features allow the trap die to be reduced to only the area required to produce trapping fields. The smaller trap dimensions allow tight focusing of an addressing laser beam for fast single-qubit rotations. Performance of the BGA trap as characterized with 40 Ca + ions is comparable to previous surface-electrode traps in terms of ion heating rate, mode frequency stability, and storage lifetime. We demonstrate two-qubit entanglement operations with 171 Yb + ions in a second BGA trap

Fourier Transforms Simplified: Computing an Infrared Spectrum from an Interferogram

Science.gov (United States)

Hanley, Quentin S.

2012-01-01

Fourier transforms are used widely in chemistry and allied sciences. Examples include infrared, nuclear magnetic resonance, and mass spectroscopies. A thorough understanding of Fourier methods assists the understanding of microscopy, X-ray diffraction, and diffraction gratings. The theory of Fourier transforms has been presented in this "Journal",…

Quantum computing with trapped ions

Energy Technology Data Exchange (ETDEWEB)

Hughes, R.J.

1998-01-01

The significance of quantum computation for cryptography is discussed. Following a brief survey of the requirements for quantum computational hardware, an overview of the ion trap quantum computation project at Los Alamos is presented. The physical limitations to quantum computation with trapped ions are analyzed and an assessment of the computational potential of the technology is made.

Lifetime measurements in an electrostatic ion beam trap using image charge monitoring

International Nuclear Information System (INIS)

Rahinov, Igor; Toker, Yoni; Heber, Oded; Rappaport, Michael; Zajfman, Daniel; Strasser, Daniel; Schwalm, Dirk

2012-01-01

A technique for mass-selective lifetime measurements of keV ions in a linear electrostatic ion beam trap is presented. The technique is based on bunching the ions using a weak RF potential and non-destructive ion detection by a pick-up electrode. This method has no mass-limitation, possesses the advantage of inherent mass-selectivity, and offers a possibility of measuring simultaneously the lifetimes of different ion species with no need for prior mass-selection.

On integral and finite Fourier transforms of continuous q-Hermite polynomials

International Nuclear Information System (INIS)

Atakishiyeva, M. K.; Atakishiyev, N. M.

2009-01-01

We give an overview of the remarkably simple transformation properties of the continuous q-Hermite polynomials H n (x vertical bar q) of Rogers with respect to the classical Fourier integral transform. The behavior of the q-Hermite polynomials under the finite Fourier transform and an explicit form of the q-extended eigenfunctions of the finite Fourier transform, defined in terms of these polynomials, are also discussed.

Limited-angle three-dimensional reconstructions using Fourier transform iterations and Radon transform iterations

International Nuclear Information System (INIS)

Tam, K.C.; Perez-Mendez, V.

1981-01-01

The principles of limited-angle reconstruction of space-limited objects using the concepts of allowed cone and missing cone in Fourier space are discussed. The distortion of a point source resulting from setting the Fourier components in the missing cone to zero has been calculated mathematically, and its bearing on the convergence of an iteration scheme involving Fourier transforms has been analyzed in detail. it was found that the convergence rate is fairly insensitive to the position of the point source within the boundary of the object, apart from an edge effect which tends to enhance some parts of the boundary in reconstructing the object. Another iteration scheme involving Radon transforms was introduced and compared to the Fourier transform method in such areas as root mean square error, stability with respect to noise, and computer reconstruction time

Limited-angle 3-D reconstructions using Fourier transform iterations and Radon transform iterations

International Nuclear Information System (INIS)

Tam, K.C.; Perez-Mendez, V.

1979-12-01

The principles of limited-angle reconstruction of space-limited objects using the concepts of allowed cone and missing cone in Fourier space are discussed. The distortion of a point source resulting from setting the Fourier components in the missing cone to zero was calculated mathematically, and its bearing on the convergence of an iteration scheme involving Fourier transforms was analyzed in detail. It was found that the convergence rate is fairly insensitive to the position of the point source within the boundary of the object, apart from an edge effect that tends to enhance some parts of the boundary in reconstructing the object. Another iteration scheme involving Radon transforms was introduced and compared to the Fourier transform method in such areas as root mean square error, stability with respect to noise, and computer reconstruction time. 8 figures, 2 tables

The ion circus: A novel circular Paul trap to resolve isobaric contamination

Energy Technology Data Exchange (ETDEWEB)

Ramirez, E. Minaya [CSNSM-IN2P3/CNRS, Bat. 108, Universite de Paris Sud, 91405 Orsay (France)], E-mail: minaya@csnsm.in2p3.fr; Cabaret, S.; Lunney, D. [CSNSM-IN2P3/CNRS, Bat. 108, Universite de Paris Sud, 91405 Orsay (France)

2008-10-15

The ion circus is a miniature storage ring formed by a segmented radiofrequency mass filter bent into a circle. The primary goal of this unique device is to perform high-resolution mass separation with small transmission loss since the resolving power is increased while the orbiting ions cool in the ring. Contrary to its linear brother, this circular Paul trap is designed to cool and mass separate the ions over a much longer flight path, thus requiring lower buffer gas pressure. Ions can be accumulated in the ring and extracted either in tangential or perpendicular directions. This way, the trap also serves as a versatile beam distribution device. Design principles are presented and the prototype instrument, under test in Orsay, is described.

Scaling ion traps for quantum computing

CSIR Research Space (South Africa)

Uys, H

2010-09-01

Full Text Available The design, fabrication and preliminary testing of a chipscale, multi-zone, surface electrode ion trap is reported. The modular design and fabrication techniques used are anticipated to advance scalability of ion trap quantum computing architectures...

Observation of a structural transition for coulomb crystals in a linear Paul trap

DEFF Research Database (Denmark)

Kjærgaard, N.; Drewsen, M.

2003-01-01

A structural transition for laser cooled ion Coulomb crystals in a linear Paul trap just above the stability limit of parametrically resonant excitation of bulk plasma modes has been observed. In contrast to the usual spheroidal shell structures present below the stability limit, the ions arrange...... in a "string-of-disks" configuration. The spheroidal envelopes of the string-of-disks structures are in agreement with results from cold fluid theory usually valid for ion Coulomb crystals if the ion systems are assumed to be rotating collectively....

Observation of a structural transition for Coulomb crystals in a linear Paul trap

International Nuclear Information System (INIS)

Kjaergaard, Niels; Drewsen, Michael

2003-01-01

A structural transition for laser cooled ion Coulomb crystals in a linear Paul trap just above the stability limit of parametrically resonant excitation of bulk plasma modes has been observed. In contrast to the usual spheroidal shell structures present below the stability limit, the ions arrange in a 'string-of-disks' configuration. The spheroidal envelopes of the string-of-disks structures are in agreement with results from cold fluid theory usually valid for ion Coulomb crystals if the ion systems are assumed to be rotating collectively

Trapped ion depletion by anomalous diffusion due to the dissipative trapped ion instability

International Nuclear Information System (INIS)

Wimmel, H.K.

1975-07-01

At high temperatures the KADOMTSEV-POGUTSE diffusion in tokamaks can become so large as to cause depletion of trapped ions if these are replaced with free ions by means of collisions rather than being directly recycled or injected. Modified KADOMTSEV-POGUTSE diffusion formulas are employed in order to estimate this effect in the cases of classical and anomalous collisions. The maximum trapped-ion depletion is estimated from the PENROSE stability condition. For anomalous collisions a BOHM-type diffusion is derived. Numerical examples are given for JET-like parameters (JET = Joint European Torus). Depletion is found to reduce diffusion by factors of up to 10 and more. (orig.) [de

Reducing aberration effect of Fourier transform lens by modifying Fourier spectrum of diffractive optical element in beam shaping optical system.

Science.gov (United States)

Zhang, Fang; Zhu, Jing; Song, Qiang; Yue, Weirui; Liu, Jingdan; Wang, Jian; Situ, Guohai; Huang, Huijie

2015-10-20

In general, Fourier transform lenses are considered as ideal in the design algorithms of diffractive optical elements (DOEs). However, the inherent aberrations of a real Fourier transform lens disturb the far field pattern. The difference between the generated pattern and the expected design will impact the system performance. Therefore, a method for modifying the Fourier spectrum of DOEs without introducing other optical elements to reduce the aberration effect of the Fourier transform lens is proposed. By applying this method, beam shaping performance is improved markedly for the optical system with a real Fourier transform lens. The experiments carried out with a commercial Fourier transform lens give evidence for this method. The method is capable of reducing the system complexity as well as improving its performance.

Trapped Ion Qubits

Energy Technology Data Exchange (ETDEWEB)

Maunz, Peter Lukas Wilhelm

2017-04-01

Qubits can be encoded in clock states of trapped ions. These states are well isolated from the environment resulting in long coherence times [1] while enabling efficient high-fidelity qubit interactions mediated by the Coulomb coupled motion of the ions in the trap. Quantum states can be prepared with high fidelity and measured efficiently using fluorescence detection. State preparation and detection with 99.93% fidelity have been realized in multiple systems [1,2]. Single qubit gates have been demonstrated below rigorous fault-tolerance thresholds [1,3]. Two qubit gates have been realized with more than 99.9% fidelity [4,5]. Quantum algorithms have been demonstrated on systems of 5 to 15 qubits [6–8].

Stable Trapping of Multielectron Helium Bubbles in a Paul Trap

Science.gov (United States)

Joseph, E. M.; Vadakkumbatt, V.; Pal, A.; Ghosh, A.

2017-06-01

In a recent experiment, we have used a linear Paul trap to store and study multielectron bubbles (MEBs) in liquid helium. MEBs have a charge-to-mass ratio (between 10^{-4} and 10^{-2} C/kg) which is several orders of magnitude smaller than ions (between 10^6 and 10^8 C/kg) studied in traditional ion traps. In addition, MEBs experience significant drag force while moving through the liquid. As a result, the experimental parameters for stable trapping of MEBs, such as magnitude and frequency of the applied electric fields, are very different from those used in typical ion trap experiments. The purpose of this paper is to model the motion of MEBs inside a linear Paul trap in liquid helium, determine the range of working parameters of the trap, and compare the results with experiments.

Sawteeth stabilization by energetic trapped ions

International Nuclear Information System (INIS)

Samain, A.; Edery, D.; Garbet, X.; Roubin, J.P.

1991-01-01

The analysis of a possible stabilization of sawteeth by a population of energetic ions is performed by using the Lagrangian of the electromagnetic perturbation. It is shown that the trapped component of such a population has a small influence compared to that of the passing component. The stabilization threshold is calculated assuming a non linear regime in the q=1 resonant layer. The energetic population must create a stable tearing structure if the average curvature effect on thermal particles in the layer is small. However, this effect decreases the actual threshold

Experimental investigation of the stability diagram for Paul traps in the case of praseodymium ions

International Nuclear Information System (INIS)

Koczorowski, W.; Szawiola, G.; Walaszyk, A.; Buczek, A.; Stefanska, D.; Stachowska, E.

2006-01-01

The present paper describes an investigation of non-linear resonances of praseodymium ion clouds stored in a Paul trap as a function of the storage parameters. These have been observed in traps with different ring electrode diameters. In these different traps the resonances occur for different values of the operating parameters. Discrepancies with the approximation model for one ion have been found. The intensity of the fluorescence signal and the Doppler half width have been recorded as a function of one of the storage parameters: q. We use our results to optimize the fluorescence signal of the stored ions, which is especially useful in the case of the double-resonance method.

Generalized Fourier transforms Fk,a

DEFF Research Database (Denmark)

Salem, Ben Said; Kobayashi, Toshiyuki; Ørsted, Bent

2009-01-01

We construct a two-parameter family of actions ωk,a of the Lie algebra by differential-difference operators on . Here, k is a multiplicity-function for the Dunkl operators, and a>0 arises from the interpolation of the Weil representation and the minimal unitary representation of the conformal gro...... of our semigroup Ωk,a provides us with (k,a) -generalized Fourier transforms , which includes the Dunkl transform ( a=2 ) and a new unitary operator ( a=1 ) as a Dunkl-type generalization of the classical Hankel transform....

Microfabricated Microwave-Integrated Surface Ion Trap

Science.gov (United States)

Revelle, Melissa C.; Blain, Matthew G.; Haltli, Raymond A.; Hollowell, Andrew E.; Nordquist, Christopher D.; Maunz, Peter

2017-04-01

Quantum information processing holds the key to solving computational problems that are intractable with classical computers. Trapped ions are a physical realization of a quantum information system in which qubits are encoded in hyperfine energy states. Coupling the qubit states to ion motion, as needed for two-qubit gates, is typically accomplished using Raman laser beams. Alternatively, this coupling can be achieved with strong microwave gradient fields. While microwave radiation is easier to control than a laser, it is challenging to precisely engineer the radiated microwave field. Taking advantage of Sandia's microfabrication techniques, we created a surface ion trap with integrated microwave electrodes with sub-wavelength dimensions. This multi-layered device permits co-location of the microwave antennae and the ion trap electrodes to create localized microwave gradient fields and necessary trapping fields. Here, we characterize the trap design and present simulated microwave performance with progress towards experimental results. This research was funded, in part, by the Office of the Director of National Intelligence (ODNI), Intelligence Advanced Research Projects Activity (IARPA).

A fractional Fourier transform analysis of the scattering of ultrasonic waves

Science.gov (United States)

Tant, Katherine M.M.; Mulholland, Anthony J.; Langer, Matthias; Gachagan, Anthony

2015-01-01

Many safety critical structures, such as those found in nuclear plants, oil pipelines and in the aerospace industry, rely on key components that are constructed from heterogeneous materials. Ultrasonic non-destructive testing (NDT) uses high-frequency mechanical waves to inspect these parts, ensuring they operate reliably without compromising their integrity. It is possible to employ mathematical models to develop a deeper understanding of the acquired ultrasonic data and enhance defect imaging algorithms. In this paper, a model for the scattering of ultrasonic waves by a crack is derived in the time–frequency domain. The fractional Fourier transform (FrFT) is applied to an inhomogeneous wave equation where the forcing function is prescribed as a linear chirp, modulated by a Gaussian envelope. The homogeneous solution is found via the Born approximation which encapsulates information regarding the flaw geometry. The inhomogeneous solution is obtained via the inverse Fourier transform of a Gaussian-windowed linear chirp excitation. It is observed that, although the scattering profile of the flaw does not change, it is amplified. Thus, the theory demonstrates the enhanced signal-to-noise ratio permitted by the use of coded excitation, as well as establishing a time–frequency domain framework to assist in flaw identification and classification. PMID:25792967

Active stabilization of ion trap radiofrequency potentials

Energy Technology Data Exchange (ETDEWEB)

Johnson, K. G.; Wong-Campos, J. D.; Restelli, A.; Landsman, K. A.; Neyenhuis, B.; Mizrahi, J.; Monroe, C. [Joint Quantum Institute and University of Maryland Department of Physics, College Park, Maryland 20742 (United States)

2016-05-15

We actively stabilize the harmonic oscillation frequency of a laser-cooled atomic ion confined in a radiofrequency (rf) Paul trap by sampling and rectifying the high voltage rf applied to the trap electrodes. We are able to stabilize the 1 MHz atomic oscillation frequency to be better than 10 Hz or 10 ppm. This represents a suppression of ambient noise on the rf circuit by 34 dB. This technique could impact the sensitivity of ion trap mass spectrometry and the fidelity of quantum operations in ion trap quantum information applications.

The Fourier Transform for Certain HyperKähler Fourfolds

NARCIS (Netherlands)

Shen, M.; Vial, C.

2016-01-01

Using a codimension-1 algebraic cycle obtained from the Poincaré line bundle, Beauville defined the Fourier transform on the Chow groups of an abelian variety A and showed that the Fourier transform induces a decomposition of the Chow ring CH∗(A). By using a codimension-2 algebraic cycle

Fourier-based linear systems description of free-breathing pulmonary magnetic resonance imaging

Science.gov (United States)

Capaldi, D. P. I.; Svenningsen, S.; Cunningham, I. A.; Parraga, G.

2015-03-01

Fourier-decomposition of free-breathing pulmonary magnetic resonance imaging (FDMRI) was recently piloted as a way to provide rapid quantitative pulmonary maps of ventilation and perfusion without the use of exogenous contrast agents. This method exploits fast pulmonary MRI acquisition of free-breathing proton (1H) pulmonary images and non-rigid registration to compensate for changes in position and shape of the thorax associated with breathing. In this way, ventilation imaging using conventional MRI systems can be undertaken but there has been no systematic evaluation of fundamental image quality measurements based on linear systems theory. We investigated the performance of free-breathing pulmonary ventilation imaging using a Fourier-based linear system description of each operation required to generate FDMRI ventilation maps. Twelve subjects with chronic obstructive pulmonary disease (COPD) or bronchiectasis underwent pulmonary function tests and MRI. Non-rigid registration was used to co-register the temporal series of pulmonary images. Pulmonary voxel intensities were aligned along a time axis and discrete Fourier transforms were performed on the periodic signal intensity pattern to generate frequency spectra. We determined the signal-to-noise ratio (SNR) of the FDMRI ventilation maps using a conventional approach (SNRC) and using the Fourier-based description (SNRF). Mean SNR was 4.7 ± 1.3 for subjects with bronchiectasis and 3.4 ± 1.8, for COPD subjects (p>.05). SNRF was significantly different than SNRC (p<.01). SNRF was approximately 50% of SNRC suggesting that the linear system model well-estimates the current approach.

Application of the fractional Fourier transform to the design of LCOS based optical interconnects and fiber switches.

Science.gov (United States)

Robertson, Brian; Zhang, Zichen; Yang, Haining; Redmond, Maura M; Collings, Neil; Liu, Jinsong; Lin, Ruisheng; Jeziorska-Chapman, Anna M; Moore, John R; Crossland, William A; Chu, D P

2012-04-20

It is shown that reflective liquid crystal on silicon (LCOS) spatial light modulator (SLM) based interconnects or fiber switches that use defocus to reduce crosstalk can be evaluated and optimized using a fractional Fourier transform if certain optical symmetry conditions are met. Theoretically the maximum allowable linear hologram phase error compared to a Fourier switch is increased by a factor of six before the target crosstalk for telecom applications of -40 dB is exceeded. A Gerchberg-Saxton algorithm incorporating a fractional Fourier transform modified for use with a reflective LCOS SLM is used to optimize multi-casting holograms in a prototype telecom switch. Experiments are in close agreement to predicted performance.

Towards a wire-mediated coupling of trapped ions

Science.gov (United States)

Clark, Robert; Lee, Tony; Daniilidis, Nikos; Sankaranarayanan, S.; Häffner, Hartmut

2008-03-01

Most schemes for ion trap quantum computation rely upon the exchange of information between ion-qubits in the same trap region, mediated by their shared vibrational mode. An alternative way to achieve this coupling is via the image charges induced in a conducting wire that connects different traps. This was shown to be theoretically possible by Heinzen and Wineland in 1990, but some important practical questions have remained unaddressed. Among these are how the presence of such a wire modifies the motional frequencies and heating rates of trapped ions. We thus have realized this system as a 1 mm-scale planar segmented rf ion trap combined with an electrically floating gold wire of 25 microns diameter and length 1 cm. This wire is placed close to trapped ions using a set of piezoelectric nanopositioners. We present here experimental measurements of the motional frequencies and heating rates of a single trapped calcium ion as the wire is moved from 3.0 mm to 0.2 mm away from the ion. We discuss the implications of these results for achieving wire-mediated coupling in the present apparatus, as well as in future improved setups.

Ion traps fabricated in a CMOS foundry

Energy Technology Data Exchange (ETDEWEB)

Mehta, K. K.; Ram, R. J. [Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (United States); Eltony, A. M.; Chuang, I. L. [Center for Ultracold Atoms, Research Laboratory of Electronics and Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (United States); Bruzewicz, C. D.; Sage, J. M., E-mail: jsage@ll.mit.edu; Chiaverini, J., E-mail: john.chiaverini@ll.mit.edu [Lincoln Laboratory, Massachusetts Institute of Technology, Lexington, Massachusetts 02420 (United States)

2014-07-28

We demonstrate trapping in a surface-electrode ion trap fabricated in a 90-nm CMOS (complementary metal-oxide-semiconductor) foundry process utilizing the top metal layer of the process for the trap electrodes. The process includes doped active regions and metal interconnect layers, allowing for co-fabrication of standard CMOS circuitry as well as devices for optical control and measurement. With one of the interconnect layers defining a ground plane between the trap electrode layer and the p-type doped silicon substrate, ion loading is robust and trapping is stable. We measure a motional heating rate comparable to those seen in surface-electrode traps of similar size. This demonstration of scalable quantum computing hardware utilizing a commercial CMOS process opens the door to integration and co-fabrication of electronics and photonics for large-scale quantum processing in trapped-ion arrays.

Discrete fourier transform (DFT) analysis for applications using iterative transform methods

Science.gov (United States)

Dean, Bruce H. (Inventor)

2012-01-01

According to various embodiments, a method is provided for determining aberration data for an optical system. The method comprises collecting a data signal, and generating a pre-transformation algorithm. The data is pre-transformed by multiplying the data with the pre-transformation algorithm. A discrete Fourier transform of the pre-transformed data is performed in an iterative loop. The method further comprises back-transforming the data to generate aberration data.

From Fourier Transforms to Singular Eigenfunctions for Multigroup Transport

International Nuclear Information System (INIS)

Ganapol, B.D.

2001-01-01

A new Fourier transform approach to the solution of the multigroup transport equation with anisotropic scattering and isotropic source is presented. Through routine analytical continuation, the inversion contour is shifted from the real line to produce contributions from the poles and cuts in the complex plane. The integrand along the branch cut is then recast in terms of matrix continuum singular eigenfunctions, demonstrating equivalence of Fourier transform inversion and the singular eigenfunction expansion. The significance of this paper is that it represents the initial step in revealing the intimate connection between the Fourier transform and singular eigenfunction approaches as well as serves as a basis for a numerical algorithm

Ion Trapping, Storage, and Ejection in Structures for Lossless Ion Manipulations.

Science.gov (United States)

Zhang, Xinyu; Garimella, Sandilya V B; Prost, Spencer A; Webb, Ian K; Chen, Tsung-Chi; Tang, Keqi; Tolmachev, Aleksey V; Norheim, Randolph V; Baker, Erin S; Anderson, Gordon A; Ibrahim, Yehia M; Smith, Richard D

2015-06-16

A new Structures for Lossless Ion Manipulations (SLIM) module, having electrode arrays patterned on a pair of parallel printed circuit boards (PCB), was constructed and utilized to investigate capabilities for ion trapping at a pressure of 4 Torr. Positive ions were confined by application of RF voltages to a series of inner rung electrodes with alternating phase on adjacent electrodes, in conjunction with positive DC potentials on surrounding guard electrodes on each PCB. An axial DC field was also introduced by stepwise varying the DC potentials applied to the inner rung electrodes to control the ion transport and accumulation inside the ion trapping region. We show that ions can be trapped and accumulated with up to 100% efficiency, stored for at least 5 h with no significant losses, and then could be rapidly ejected from the SLIM trap. The present results provide a foundation for the development of much more complex SLIM devices that facilitate extended ion manipulations.

Dioxin analysis by gas chromatography-Fourier transform ion cyclotron resonance mass spectrometry (GC-FTICRMS).

Science.gov (United States)

Taguchi, Vince Y; Nieckarz, Robert J; Clement, Ray E; Krolik, Stefan; Williams, Robert

2010-11-01

The feasibility of utilizing a gas chromatograph-tandem quadrupole-Fourier transform ion cyclotron resonance mass spectrometer (GC-MS/MS-FTICRMS) to analyze chlorinated-dioxins/furans (CDDs/CDFs) and mixed halogenated dioxins/furans (HDDs/HDFs) was investigated by operating the system in the GC-FTICRMS mode. CDDs/CDFs and mixed HDDs/HDFs could be analyzed at 50,000 to 100,000 resolving power (RP) on the capillary gas chromatographic time scale. Initial experiments demonstrated that 1 pg of 2,3,7,8-tetrachlorodibenzo-p-dioxin (TCDD) and 5 pg of 2-bromo-3,7,8-trichlorodibenzo-p-dioxin (BTrCDD) could be detected. The feasibility of utilizing an FTICRMS for screening of CDDs/CDFs, HDDs/HDFs and related compounds was also investigated by analyzing an extract from vegetation exposed to fall-out from an industrial fire. CDDs/CDFs, chlorinated pyrenes and chlorinated tetracenes could be detected from a Kendrick plot analysis of the ultrahigh resolution mass spectra. Mass accuracies were of the order of 0.5 ppm on standards with external mass calibration and 1 ppm on a sample with internal mass calibration. Copyright © 2010 American Society for Mass Spectrometry. Published by Elsevier Inc. All rights reserved.

Fourier transform ion cyclotron resonance mass spectrometry: the analytical tool for heavy oil and bitumen characterization

Energy Technology Data Exchange (ETDEWEB)

Oldenburg, Thomas B.P; Brown, Melisa; Hsieh, Ben; Larter, Steve [Petroleum Reservoir Group (prg), Department of Geoscience, University of Calgary, Alberta (Canada)

2011-07-01

The Fourier Transform Ion Cyclotron Resonance Mass Spectrometry (FTICRMS), developed in the 1970's by Marshall and Comisarow at the University of British Columbia, has become a commercially available tool capable of analyzing several hundred thousand components in a petroleum mixture at once. This analytical technology will probably usher a dramatic revolution in geochemical capability, equal to or greater than the molecular revolution that occurred when GCMS technologies became cheaply available. The molecular resolution and information content given by the FTICRMS petroleum analysis can be compared to the information in the human genome. With current GCMS-based petroleum geochemical protocols perhaps a few hundred components can be quantitatively determined, but with FTICRMS, 1000 times this number of components could possibly be resolved. However, fluid and other properties depend on interaction of this multitude of hydrocarbon and non-hydrocarbon components, not the components themselves, and access to the full potential of this new petroleomics will depend on the definition of this interactome.

Two Dimensional Symmetric Correlation Functions of the S Operator and Two Dimensional Fourier Transforms: Considering the Line Coupling for P and R Lines of Linear Molecules

Science.gov (United States)

Ma, Q.; Boulet, C.; Tipping, R. H.

2014-01-01

The refinement of the Robert-Bonamy (RB) formalism by considering the line coupling for isotropic Raman Q lines of linear molecules developed in our previous study [Q. Ma, C. Boulet, and R. H. Tipping, J. Chem. Phys. 139, 034305 (2013)] has been extended to infrared P and R lines. In these calculations, the main task is to derive diagonal and off-diagonal matrix elements of the Liouville operator iS1 - S2 introduced in the formalism. When one considers the line coupling for isotropic Raman Q lines where their initial and final rotational quantum numbers are identical, the derivations of off-diagonal elements do not require extra correlation functions of the ^S operator and their Fourier transforms except for those used in deriving diagonal elements. In contrast, the derivations for infrared P and R lines become more difficult because they require a lot of new correlation functions and their Fourier transforms. By introducing two dimensional correlation functions labeled by two tensor ranks and making variable changes to become even functions, the derivations only require the latters' two dimensional Fourier transforms evaluated at two modulation frequencies characterizing the averaged energy gap and the frequency detuning between the two coupled transitions. With the coordinate representation, it is easy to accurately derive these two dimensional correlation functions. Meanwhile, by using the sampling theory one is able to effectively evaluate their two dimensional Fourier transforms. Thus, the obstacles in considering the line coupling for P and R lines have been overcome. Numerical calculations have been carried out for the half-widths of both the isotropic Raman Q lines and the infrared P and R lines of C2H2 broadened by N2. In comparison with values derived from the RB formalism, new calculated values are significantly reduced and become closer to measurements.

High-fidelity operations in microfabricated surface ion traps

Science.gov (United States)

Maunz, Peter

2017-04-01

Trapped ion systems can be used to implement quantum computation as well as quantum simulation. To scale these systems to the number of qubits required to solve interesting problems in quantum chemistry or solid state physics, the use of large multi-zone ion traps has been proposed. Microfabrication enables the realization of surface electrode ion traps with complex electrode structures. While these traps may enable the scaling of trapped ion quantum information processing (QIP), microfabricated ion traps also pose several technical challenges. Here, we present Sandia's trap fabrication capabilities and characterize trap properties and shuttling operations in our most recent high optical access trap (HOA-2). To demonstrate the viability of Sandia's microfabricated ion traps for QIP we realize robust single and two-qubit gates and characterize them using gate set tomography (GST). In this way we are able to demonstrate the first single qubit gates with a diamond norm of less than 1 . 7 ×10-4 , below a rigorous fault tolerance threshold for general noise of 6 . 7 ×10-4. Furthermore, we realize Mølmer-Sørensen two qubit gates with a process fidelity of 99 . 58(6) % also characterized by GST. These results demonstrate the viability of microfabricated surface traps for state of the art quantum information processing demonstrations. This research was funded, in part, by the Office of the Director of National Intelligence (ODNI), Intelligence Advanced Research Projects Activity (IARPA).

Atmospheric pressure chemical ionization Fourier transform ion cyclotron resonance mass spectrometry for complex thiophenic mixture analysis

KAUST Repository

Hourani, Nadim

2013-10-01

Rationale Polycyclic aromatic sulfur heterocycles (PASHs) are detrimental species for refining processes in petroleum industry. Current mass spectrometric Methods that determine their composition are often preceded by derivatization and dopant addition approaches. Different ionization Methods have different impact on the molecular assignment of complex PASHs. The analysis of such species under atmospheric pressure chemical ionization (APCI) is still considered limited due to uncontrolled ion generation with low- and high-mass PASHs. Methods The ionization behavior of a model mixture of five selected PASH standards was investigated using an APCI source with nitrogen as the reagent gas. A complex thiophenic fraction was separated from a vacuum gas oil (VGO) and injected using the same method. The samples were analyzed using Fourier transform ion cyclotron resonance mass spectrometry (FTICR MS). RESULTS PASH model analytes were successfully ionized and mainly [M + H]+ ions were produced. The same ionization pattern was observed for the real thiophenic sample. It was found that S1 class species were the major sulfur-containing species found in the VGO sample. These species indicated the presence of alkylated benzothiophenic (BT), dibenzothiophenic (DBT) and benzonaphthothiophenic (BNT) series that were detected by APCI-FTICR MS. CONCLUSIONS This study provides an established APCI-FTICR MS method for the analysis of complex PASHs. PASHs were detected without using any derivatization and without fragmentation. The method can be used for the analysis of S-containing crude oil samples. © 2013 John Wiley & Sons, Ltd.

Achieving Translationally Invariant Trapped Ion Rings

Science.gov (United States)

Urban, Erik; Li, Hao-Kun; Noel, Crystal; Hemmerling, Boerge; Zhang, Xiang; Haeffner, Hartmut

2017-04-01

We present the design and implementation of a novel surface ion trap design in a ring configuration. By eliminating the need for wire bonds through the use of electrical vias and using a rotationally invariant electrode configuration, we have realized a trap that is able to trap up to 20 ions in a ring geometry 45um in diameter, 400um above the trap surface. This large trapping height to ring diameter ratio allows for global addressing of the ring with both lasers and electric fields in the chamber, thereby increasing our ability to control the ring as a whole. Applying compensating electric fields, we measure very low tangential trap frequencies (less than 20kHz) corresponding to rotational barriers down to 4mK. This measurement is currently limited by the temperature of the ions but extrapolation indicates the barrier can be reduced much further with more advanced cooling techniques. Finally, we show that we are able to reduce this energy barrier sufficiently such that the ions are able to overcome it either through thermal motion or rotational motion and delocalize over the full extent of the ring. This work was funded by the Keck Foundation and the NSF.

A cryogenic electrostatic trap for long-time storage of keV ion beams.

Science.gov (United States)

Lange, M; Froese, M; Menk, S; Varju, J; Bastert, R; Blaum, K; López-Urrutia, J R Crespo; Fellenberger, F; Grieser, M; von Hahn, R; Heber, O; Kühnel, K-U; Laux, F; Orlov, D A; Rappaport, M L; Repnow, R; Schröter, C D; Schwalm, D; Shornikov, A; Sieber, T; Toker, Y; Ullrich, J; Wolf, A; Zajfman, D

2010-05-01

We report on the realization and operation of a fast ion beam trap of the linear electrostatic type employing liquid helium cooling to reach extremely low blackbody radiation temperature and residual gas density and, hence, long storage times of more than 5 min which are unprecedented for keV ion beams. Inside a beam pipe that can be cooled to temperatures <15 K, with 1.8 K reached in some locations, an ion beam pulse can be stored at kinetic energies of 2-20 keV between two electrostatic mirrors. Along with an overview of the cryogenic trap design, we present a measurement of the residual gas density inside the trap resulting in only 2 x 10(3) cm(-3), which for a room temperature environment corresponds to a pressure in the 10(-14) mbar range. The device, called the cryogenic trap for fast ion beams, is now being used to investigate molecules and clusters at low temperatures, but has also served as a design prototype for the cryogenic heavy-ion storage ring currently under construction at the Max-Planck Institute for Nuclear Physics.

Comparative study on γ energy spectrum denoise by fourier and wavelet transforms

International Nuclear Information System (INIS)

Shi Dongsheng; Di Yuming; Zhou Chunlin

2007-01-01

This paper introduces the basic principle of wavelet and Fourier transforms, applies wavelet transform method to denoise γ energy spectrum of 60 Co and compares it with Fourier transform method. The result of simulation with MATLAB software tool showed that as compared with traditional Fourier transform, wavelet transform has comparatively higher accuracy for γ energy spectrum denoising and is more feasible to γ energy spectrum denoising. (authors)

Fast and accurate algorithm for the computation of complex linear canonical transforms.

Science.gov (United States)

Koç, Aykut; Ozaktas, Haldun M; Hesselink, Lambertus

2010-09-01

A fast and accurate algorithm is developed for the numerical computation of the family of complex linear canonical transforms (CLCTs), which represent the input-output relationship of complex quadratic-phase systems. Allowing the linear canonical transform parameters to be complex numbers makes it possible to represent paraxial optical systems that involve complex parameters. These include lossy systems such as Gaussian apertures, Gaussian ducts, or complex graded-index media, as well as lossless thin lenses and sections of free space and any arbitrary combinations of them. Complex-ordered fractional Fourier transforms (CFRTs) are a special case of CLCTs, and therefore a fast and accurate algorithm to compute CFRTs is included as a special case of the presented algorithm. The algorithm is based on decomposition of an arbitrary CLCT matrix into real and complex chirp multiplications and Fourier transforms. The samples of the output are obtained from the samples of the input in approximately N log N time, where N is the number of input samples. A space-bandwidth product tracking formalism is developed to ensure that the number of samples is information-theoretically sufficient to reconstruct the continuous transform, but not unnecessarily redundant.

On the Scaled Fractional Fourier Transformation Operator

International Nuclear Information System (INIS)

Hong-Yi, Fan; Li-Yun, Hu

2008-01-01

Based on our previous study [Chin. Phys. Lett. 24 (2007) 2238] in which the Fresnel operator corresponding to classical Fresnel transform was introduced, we derive the fractional Fourier transformation operator, and the optical operator method is then enriched

Fourier transformations for difference analogs of the harmonic oscillator

International Nuclear Information System (INIS)

Askey, R.; Atakishiyev, N.M.

1995-01-01

The relation between the Mehler bilinear generating function for the Hermite polynomials and the kernel of the Fourier transformation that connect the spaces of coordinate and momentum is discussed. On the base of the relation the discrete analogs of the Fourier transformation for the Kravchuk and Charlier functions are considered. 6 refs

Highly charged ion trapping and cooling

International Nuclear Information System (INIS)

Beck, B. R.; Church, D. A.; Gruber, L.; Holder, J. P.; Schneider, D.; Steiger, J.

1998-01-01

In the past few years a cryogenic Penning trap (RETRAP) has been operational at the Electron Beam Ion Trap (EBIT) facility at Lawrence Livermore National Laboratory. The combination of RETRAP and EBIT provides a unique possibility of producing and re-trapping highly charged ions and cooling them to very low temperatures. Due to the high Coulomb potentials in such an ensemble of cold highly charged ions the Coulomb coupling parameter (the ratio of Coulomb potential to the thermal energy) can easily reach values of 172 and more. To study such systems is not only of interest in astrophysics to simulate White Dwarf star interiors but opens up new possibilities in a variety of areas (e.g. laser spectroscopy), cold highly charged ion beams

The finite Fourier transform of classical polynomials

OpenAIRE

Dixit, Atul; Jiu, Lin; Moll, Victor H.; Vignat, Christophe

2014-01-01

The finite Fourier transform of a family of orthogonal polynomials $A_{n}(x)$, is the usual transform of the polynomial extended by $0$ outside their natural domain. Explicit expressions are given for the Legendre, Jacobi, Gegenbauer and Chebyshev families.

Ion trapping in one-minimum potentials via charge-exchange collisions

International Nuclear Information System (INIS)

Maier, H.; Kuhn, S.

1994-01-01

A (1 d, 2 v), electrostatic, kinetics model for time-independent single-ended Q-machine states with a positively biased cold plate and a single internal minimum near the hot plate is presented. While the electrons are treated as collisionless, charge-exchange collisions between the ions and the neutral background gas atoms are taken into account by means of a linearized Boltzmann collision operator. The self-consistent plasma states are found by using an iterative analytic-numerical trajectory-simulation method in which the charge-density and potential distributions are alternately determined numerical results clearly demonstrate the sensitive role that trapped ions play in shaping the microscopic and macroscopic properties of the dc states under study. The trapped-ion distributions themselves are shown to be controlled critically by the detailed scattering conditions, which in turn are determined by the choice of the background properties. (author). 10 refs, 3 figs

Fast Fourier transform telescope

International Nuclear Information System (INIS)

Tegmark, Max; Zaldarriaga, Matias

2009-01-01

We propose an all-digital telescope for 21 cm tomography, which combines key advantages of both single dishes and interferometers. The electric field is digitized by antennas on a rectangular grid, after which a series of fast Fourier transforms recovers simultaneous multifrequency images of up to half the sky. Thanks to Moore's law, the bandwidth up to which this is feasible has now reached about 1 GHz, and will likely continue doubling every couple of years. The main advantages over a single dish telescope are cost and orders of magnitude larger field-of-view, translating into dramatically better sensitivity for large-area surveys. The key advantages over traditional interferometers are cost (the correlator computational cost for an N-element array scales as Nlog 2 N rather than N 2 ) and a compact synthesized beam. We argue that 21 cm tomography could be an ideal first application of a very large fast Fourier transform telescope, which would provide both massive sensitivity improvements per dollar and mitigate the off-beam point source foreground problem with its clean beam. Another potentially interesting application is cosmic microwave background polarization.

The PROSAIC Laplace and Fourier Transform

International Nuclear Information System (INIS)

Smith, G.A.

1994-01-01

Integral Transform methods play an extremely important role in many branches of science and engineering. The ease with which many problems may be solved using these techniques is well known. In Electrical Engineering especially, Laplace and Fourier Transforms have been used for a long time as a way to change the solution of differential equations into trivial algebraic manipulations or to provide alternate representations of signals and data. These techniques, while seemingly overshadowed by today's emphasis on digital analysis, still form an invaluable basis in the understanding of systems and circuits. A firm grasp of the practical aspects of these subjects provides valuable conceptual tools. This tutorial paper is a review of Laplace and Fourier Transforms from an applied perspective with an emphasis on engineering applications. The interrelationship of the time and frequency domains will be stressed, in an attempt to comfort those who, after living so much of their lives in the time domain, find thinking in the frequency domain disquieting

Fourier transforms and convolutions for the experimentalist

CERN Document Server

Jennison, RC

1961-01-01

Fourier Transforms and Convolutions for the Experimentalist provides the experimentalist with a guide to the principles and practical uses of the Fourier transformation. It aims to bridge the gap between the more abstract account of a purely mathematical approach and the rule of thumb calculation and intuition of the practical worker. The monograph springs from a lecture course which the author has given in recent years and for which he has drawn upon a number of sources, including a set of notes compiled by the late Dr. I. C. Browne from a series of lectures given by Mr. J . A. Ratcliffe of t

Space-charge effects in Penning ion traps

Science.gov (United States)

Porobić, T.; Beck, M.; Breitenfeldt, M.; Couratin, C.; Finlay, P.; Knecht, A.; Fabian, X.; Friedag, P.; Fléchard, X.; Liénard, E.; Ban, G.; Zákoucký, D.; Soti, G.; Van Gorp, S.; Weinheimer, Ch.; Wursten, E.; Severijns, N.

2015-06-01

The influence of space-charge on ion cyclotron resonances and magnetron eigenfrequency in a gas-filled Penning ion trap has been investigated. Off-line measurements with K39+ using the cooling trap of the WITCH retardation spectrometer-based setup at ISOLDE/CERN were performed. Experimental ion cyclotron resonances were compared with ab initio Coulomb simulations and found to be in agreement. As an important systematic effect of the WITCH experiment, the magnetron eigenfrequency of the ion cloud was studied under increasing space-charge conditions. Finally, the helium buffer gas pressure in the Penning trap was determined by comparing experimental cooling rates with simulations.

Implementation schemes for unsharp measurements with trapped ions

CSIR Research Space (South Africa)

Choudhary, SK

2013-01-01

Full Text Available trapped ion. The schemes rely on introducing weak entanglement between the state of a target ion and that of an auxiliary ion, using standard ion-trap quantum logic operations, and then realizing an unsharp measurement through projective measurement...

Application of linear discriminant analysis and Attenuated Total Reflectance Fourier Transform Infrared microspectroscopy for diagnosis of colon cancer.

Science.gov (United States)

Khanmohammadi, Mohammadreza; Bagheri Garmarudi, Amir; Samani, Simin; Ghasemi, Keyvan; Ashuri, Ahmad

2011-06-01

Attenuated Total Reflectance Fourier Transform Infrared (ATR-FTIR) microspectroscopy was applied for detection of colon cancer according to the spectral features of colon tissues. Supervised classification models can be trained to identify the tissue type based on the spectroscopic fingerprint. A total of 78 colon tissues were used in spectroscopy studies. Major spectral differences were observed in 1,740-900 cm(-1) spectral region. Several chemometric methods such as analysis of variance (ANOVA), cluster analysis (CA) and linear discriminate analysis (LDA) were applied for classification of IR spectra. Utilizing the chemometric techniques, clear and reproducible differences were observed between the spectra of normal and cancer cases, suggesting that infrared microspectroscopy in conjunction with spectral data processing would be useful for diagnostic classification. Using LDA technique, the spectra were classified into cancer and normal tissue classes with an accuracy of 95.8%. The sensitivity and specificity was 100 and 93.1%, respectively.

Causal Correlation Functions and Fourier Transforms: Application in Calculating Pressure Induced Shifts

Science.gov (United States)

Ma, Q.; Tipping, R. H.; Lavrentieva, N. N.

2012-01-01

By adopting a concept from signal processing, instead of starting from the correlation functions which are even, one considers the causal correlation functions whose Fourier transforms become complex. Their real and imaginary parts multiplied by 2 are the Fourier transforms of the original correlations and the subsequent Hilbert transforms, respectively. Thus, by taking this step one can complete the two previously needed transforms. However, to obviate performing the Cauchy principal integrations required in the Hilbert transforms is the greatest advantage. Meanwhile, because the causal correlations are well-bounded within the time domain and band limited in the frequency domain, one can replace their Fourier transforms by the discrete Fourier transforms and the latter can be carried out with the FFT algorithm. This replacement is justified by sampling theory because the Fourier transforms can be derived from the discrete Fourier transforms with the Nyquis rate without any distortions. We apply this method in calculating pressure induced shifts of H2O lines and obtain more reliable values. By comparing the calculated shifts with those in HITRAN 2008 and by screening both of them with the pair identity and the smooth variation rules, one can conclude many of shift values in HITRAN are not correct.

Ion effects in future circular and linear accelerators

International Nuclear Information System (INIS)

Raubenheimer, T.O.

1995-05-01

In this paper, the author discusses ion effects relevant to future storage rings and linear colliders. The author first reviews the conventional ion effects observed in present storage rings and then discusses how these effects will differ in the next generation of rings and linacs. These future accelerators operate in a new regime because of the high current long bunch trains and the very small transverse beam emittances. Usually, storage rings are designed with ion clearing gaps to prevent ion trapping between bunch trains or beam revolutions. Regardless, ions generated within a single bunch train can have significant effects. The same is true in transport lines and linacs, where typical vacuum pressures are relatively high. Amongst other effects, the author addresses the tune spreads due to the ions and the resulting filamentation which can severely limit emittance correction techniques in future linear colliders, the bunch-to-bunch coupling due to the ions which can cause a multi-bunch instability with fast growth rates, and the betatron coupling and beam halo creation which limit the vertical emittance and beam lifetimes

Fourier optics along a hybrid optical fiber for Bessel-like beam generation and its applications in multiple-particle trapping.

Science.gov (United States)

Kim, Jongki; Jeong, Yoonseob; Lee, Sejin; Ha, Woosung; Shin, Jeon-Soo; Oh, Kyunghwan

2012-02-15

Highly efficient Bessel-like beam generation was achieved based on a new all-fiber method that implements Fourier transformation of a micro annular aperture along a concatenated composite optical fiber. The beam showed unique characteristics of tilted washboard optical potential in the transverse plane and sustained a nondiffracting length over 400 μm along the axial direction. Optical trapping of multiple dielectric particles and living Jurkat cells were successfully demonstrated along the axial direction of the beam in the water.

Ion trapping in the high-energy storage ring HESR

Energy Technology Data Exchange (ETDEWEB)

Hinterberger, Frank [Bonn Univ. (Germany). Helmholtz-Institut fuer Strahlen- und Kernphysik

2011-10-15

The problem of ion trapping in the high-energy storage ring HESR is studied in the present report. Positive ions are trapped in the negative potential well of the antiproton beam. The ions are produced by the interaction between the antiproton beam and the residual gas. The adverse effects of ion trapping like tune shifts, tune spreads and coherent instabilities are reviewed. The ion production rate by ionization of the residual gas molecules is estimated. The negative potential well and the corresponding electric fields of the antiproton beam are evaluated in order to study the transverse and longitudinal motion of the ions and the accumulation in trapping pockets. The removal of ions can be achieved using clearing electrodes and under certain conditions resonant transverse beam shaking. Diagnostic tools and measurements of trapped ion effects are sketched. (orig.)

FOURIER SERIES MODELS THROUGH TRANSFORMATION

African Journals Online (AJOL)

DEPT

monthly temperature data (1996 – 2005) collected from the National Root ... KEY WORDS: Fourier series, square transformation, multiplicative model, ... fluctuations or movements are often periodic(Ekpeyong,2005). .... significant trend or not, if the trend is not significant, the grand mean may be used as an estimate of trend.

Fourier transform in multimode systems in the Bargmann representation

International Nuclear Information System (INIS)

Lei, C; Vourdas, A

2007-01-01

A Fourier transform in a multimode system is studied, using the Bargmann representation. The growth of a Bargmann function is shown to be related to the second-order correlation of the corresponding state. Both the total growth and the total second-order correlation remain unchanged under the Fourier transform. Examples with coherent states, squeezed states and Mittag-Leffler states are discussed

Utilization of the ion traps by SPIRAL

International Nuclear Information System (INIS)

Le Brun, C.; Lienard, E.; Mauger, F.; Tamain, B.

1997-01-01

An ion trap is a device capable of confine particles, ions or atoms in a well-controlled environment isolated from any exterior perturbations. There are different traps. They are utilized to collect or stock ions, to cool them after in order to subject them to high precision measurement of masses, magnetic moments, hyperfine properties, beta decay properties, etc. Some dozen of traps are currently used all over the world to study stable or radioactive ions.. SPIRAL has been designed and built to produce radioactive ions starting from various heavy ion beams. SPIRAL has the advantage that the projectile parameters, the target and the energy can be chosen to optimize the production in various regions of the nuclear chart. Also, in SPIRAL it is possible to extract more rapidly the radioactive ions formed in the targets. In addition, in SPIRAL the multicharged ion production in a ECR source is possible. The utilization of multicharged ions is indeed very useful for fast mass measurements or for the study of the interaction between the nucleus and the electronic cloud. Finally, utilization of a ion trap on SPIRAL can be designed first at the level of production target by installing a low energy output line. Than, the trap system could be up-graded and brought to its full utilization behind of the recoil spectrometer. It must be capable of selecting and slowing down the ions produced in the reactions (fusion transfer, very inelastic collisions, etc.) induced by the radioactive ions accelerated in CIME. At present, the collaboration is debating on the most favored subject to study and the most suited experimental setups. The following subjects were selected: ion capture, purification and manipulation; isomers (separation and utilization); mass measurements; hyperfine interactions; lifetimes, nuclear electric cloud; β decays; study of the N = Z nuclei close to the proton drip line; physical and chemical properties of transuranium systems

Fourier transform infrared spectra applications to chemical systems

CERN Document Server

Ferraro, John R

1978-01-01

Fourier Transform Infrared Spectroscopy: Applications to Chemical Systems presents the chemical applications of the Fourier transform interferometry (FT-IR).The book contains discussions on the applications of FT-IR in the fields of chromatography FT-IR, polymers and biological macromolecules, emission spectroscopy, matrix isolation, high-pressure interferometry, and far infrared interferometry. The final chapter is devoted to the presentation of the use of FT-IR in solving national technical problems such as air pollution, space exploration, and energy related subjects.Researc

Fourier transform infrared spectra applications to chemical systems

CERN Document Server

Ferraro, John R

1985-01-01

The final and largest volume to complete this four-volume treatise is published in response to the intense commercial and research interest in Fourier Transform Interferometry.Presenting current information from leading experts in the field, Volume 4 introduces new information on, for example, applications of Diffuse Reflectance Spectroscopy in the Far-Infrared Region. The editors place emphasis on surface studies and address advances in Capillary Gas Chromatography - Fourier Transform Interferometry.Volume 4 especially benefits spectroscopists and physicists, as well as researchers

Cryptography, quantum computation and trapped ions

Energy Technology Data Exchange (ETDEWEB)

Hughes, Richard J.

1998-03-01

The significance of quantum computation for cryptography is discussed. Following a brief survey of the requirements for quantum computational hardware, an overview of the ion trap quantum computation project at Los Alamos is presented. The physical limitations to quantum computation with trapped ions are analyzed and an assessment of the computational potential of the technology is made.

Multichannel Dynamic Fourier-Transform IR Spectrometer

Science.gov (United States)

Balashov, A. A.; Vaguine, V. A.; Golyak, Il. S.; Morozov, A. N.; Khorokhorin, A. I.

2017-09-01

A design of a multichannel continuous scan Fourier-transform IR spectrometer for simultaneous recording and analysis of the spectral characteristics of several objects is proposed. For implementing the design, a multi-probe fiber is used, constructed from several optical fibers connected into a single optical connector and attached at the output of the interferometer. The Fourier-transform spectrometer is used as a signal modulator. Each fiber is individually mated with an investigated sample and a dedicated radiation detector. For the developed system, the radiation intensity of the spectrometer is calculated from the condition of the minimum spectral resolution and parameters of the optical fibers. Using the proposed design, emission spectra of a gas-discharge neon lamp have been recorded using a single fiber 1 mm in diameter with a numerical aperture NA = 0.22.

Theoretical examination of the trapping of ion-implanted hydrogen in metals

International Nuclear Information System (INIS)

Myers, S.M.; Nordlander, P.; Besenbacher, F.; Norskov, J.K.

1986-01-01

Theoretical analysis of the defect trapping of ion-implanted hydrogen in metals has been extended in two respects. A new transport formalism has been developed which takes account not only of the diffusion, trapping, and surface release of the hydrogen, which were included in earlier treatments, but also the diffusion, recombination, agglomeration, and surface annihilation of the vacancy and interstitial traps. In addition, effective-medium theory has been used to examine multiple hydrogen occupancy of the vacancy, and, for the fcc structure, appreciable binding enthalpies relative to the solution site have been found for occupancies of up to six. These extensions have been employed to model the depth distribution of ion-implanted hydrogen in Ni and Al during linear ramping of temperature, and the results have been used to interpret previously published data from these metals. The agreement between theory and experiment is good for both systems. In the case of Ni, the two experimentally observed hydrogen-release stages are both accounted for in terms of trapping at vacancies with a binding enthalpy that depends upon occupancy in accord with effective-medium theory

Evaporative cooling of highly charged ions in EBIT [Electron Beam Ion Trap]: An experimental realization

International Nuclear Information System (INIS)

Schneider, M.B.; Levine, M.A.; Bennett, C.L.; Henderson, J.R.; Knapp, D.A.; Marrs, R.E.

1988-01-01

Both the total number and trapping lifetime of near-neon-like gold ions held in an electron beam ion trap have been greatly increased by a process of 'evaporative cooling'. A continuous flow of low-charge-state ions into the trap cools the high-charge-state ions in the trap. Preliminary experimental results using titanium ions as a coolant are presented. 8 refs., 6 figs., 2 tabs

Solution of 3-dimensional diffusion equation by finite Fourier transformation

International Nuclear Information System (INIS)

Krishnani, P.D.

1978-01-01

Three dimensional diffusion equation in Cartesian co-ordinates is solved by using the finite Fourier transformation. This method is different from the usual Fourier transformation method in the sense that the solutions are obtained without performing the inverse Fourier transformation. The advantage has been taken of the fact that the flux is finite and integrable in the finite region. By applying this condition, a two-dimensional integral equation, involving flux and its normal derivative at the boundary, is obtained. By solving this equation with given boundary conditions, all of the boundary values are determined. In order to calculate the flux inside the region, flux is expanded into three-dimensional Fourier series. The Fourier coefficients of the flux in the region are calculated from the boundary values. The advantage of this method is that the integrated flux is obtained without knowing the fluxes inside the region as in the case of finite difference method. (author)

[Screening and confirmation of 24 hormones in cosmetics by ultra high performance liquid chromatography-linear ion trap/orbitrap high resolution mass spectrometry].

Science.gov (United States)

Li, Zhaoyong; Wang, Fengmei; Niu, Zengyuan; Luo, Xin; Zhang, Gang; Chen, Junhui

2014-05-01

A method of ultra high performance liquid chromatography-linear ion trap/orbitrap high resolution mass spectrometry (UPLC-LTQ/Orbitrap MS) was established to screen and confirm 24 hormones in cosmetics. Various cosmetic samples were extracted with methanol. The extract was loaded onto a Waters ACQUITY UPLC BEH C18 column (50 mm x 2.1 mm, 1.7 microm) using a gradient elution of acetonitrile/water containing 0.1% (v/v) formic acid for the separation. The accurate mass of quasi-molecular ion was acquired by full scanning of electrostatic field orbitrap. The rapid screening was carried out by the accurate mass of quasi-molecular ion. The confirmation analysis for targeted compounds was performed with the retention time and qualitative fragments obtained by data dependent scan mode. Under the optimal conditions, the 24 hormones were routinely detected with mass accuracy error below 3 x 10(-6) (3 ppm), and good linearities were obtained in their respective linear ranges with correlation coefficients higher than 0.99. The LODs (S/N = 3) of the 24 compounds were hormones in 50 cosmetic samples. The results demonstrate that the method is a useful tool for the rapid screening and identification of the hormones in cosmetics.

A Fourier transform method for Vsin i estimations under nonlinear Limb-Darkening laws

Energy Technology Data Exchange (ETDEWEB)

Levenhagen, R. S., E-mail: ronaldo.levenhagen@gmail.com [Universidade Federal de São Paulo, Depto. Ciências Exatas e da Terra, Rua Prof. Arthur Riedel, 275, Jd. Eldorado, CEP 09972-270 Diadema, SP (Brazil)

2014-12-10

Star rotation offers us a large horizon for the study of many important physical issues pertaining to stellar evolution. Currently, four methods are widely used to infer rotation velocities, namely those related to line width calibrations, on the fitting of synthetic spectra, interferometry, and on Fourier transforms (FTs) of line profiles. Almost all of the estimations of stellar projected rotation velocities using the Fourier method in the literature have been addressed with the use of linear limb-darkening (LD) approximations during the evaluation of rotation profiles and their cosine FTs, which in certain cases, lead to discrepant velocity estimates. In this work, we introduce new mathematical expressions of rotation profiles and their Fourier cosine transforms assuming three nonlinear LD laws—quadratic, square-root, and logarithmic—and study their applications with and without gravity-darkening (GD) and geometrical flattening (GF) effects. Through an analysis of He I models in the visible range accounting for both limb and GD, we find out that, for classical models without rotationally driven effects, all the Vsin i values are too close to each other. On the other hand, taking into account GD and GF, the Vsin i obtained with the linear law result in Vsin i values that are systematically smaller than those obtained with the other laws. As a rule of thumb, we apply these expressions to the FT method to evaluate the projected rotation velocity of the emission B-type star Achernar (α Eri).

A quadrupole ion trap as low-energy cluster ion beam source

CERN Document Server

Uchida, N; Kanayama, T

2003-01-01

Kinetic energy distribution of ion beams was measured by a retarding field energy analyzer for a mass-selective cluster ion beam deposition system that uses a quadrupole ion trap as a cluster ion beam source. The results indicated that the system delivers a cluster-ion beam with energy distribution of approx 2 eV, which corresponded well to the calculation results of the trapping potentials in the ion trap. Using this deposition system, mass-selected hydrogenated Si cluster ions Si sub n H sub x sup + were actually deposited on Si(111)-(7x7) surfaces at impact kinetic energy E sub d of 3-30 eV. Observation by using a scanning tunneling microscope (STM) demonstrated that Si sub 6 H sub x sup + cluster ions landed on the surface without decomposition at E sub d =3 eV, while the deposition was destructive at E sub d>=18 eV. (author)

Metabolic profile of Kudiezi injection in rats by UHPLC coupled with Fourier transform ion cyclotron resonance mass spectrometry.

Science.gov (United States)

Zhang, Jingdan; Zhang, Xiaoxue; Zhao, Yangyang; Song, Aihua; Sun, Wei; Yin, Ran

2018-02-01

In this study, a reliable and sensitive ultra-high performance liquid chromatography coupled with fourier transform ion cyclotron resonance mass spectrometry method was developed for the systematic study of the metabolic profile of Kudiezi injection in rat plasma, bile, urine, and feces after intravenous administration of a single dose. The chromatographic separation was performed on an Agilent Eclipse Plus C 18 column (4.6 mm × 50 mm, 1.8 μm) and the identification of prototype components and metabolites was achieved on a Bruker Solarix 7.0 T ultra-high resolution spectrometer in negative ion mode. Results indicated that a total of 76 constituents including 29 prototype compounds and 47 metabolites (10 phase I metabolites and 37 phase II metabolites) were tentatively identified. And the metabolic pathways of these prototype compounds including hydroxylation, dehydrogenation, glucuronidation, and sulfate conjugation. In conclusion, the developed method with high resolution and sensitivity was effective for screening and identification of prototypes and metabolites of Kudiezi injection in vivo. Moreover, these results would provide significant information for further pharmacokinetic and pharmacological research of Kudiezi injection in vivo. © 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Ion trapping within the dust grain plasma sheath

International Nuclear Information System (INIS)

Jovanovic, D.; Shukla, P.K.

2002-01-01

One of the most important and still unresolved problems in the physics of dusty plasmas is the determination of the dust charge. The grains are not directly accessible to measurements and it is necessary to have a reliable theoretical model of the electron and ion dynamics inside the Debye sphere for the interpretation of the relevant experimental data, which include also the effects of the surrounding electron and ion clouds. Recent computer simulations [6] and laboratory experiments [9] indicate that the plasma sheath is dominated by trapped ions, orbiting the grain on closed trajectories at distances smaller than the Debye radius, that cannot be accounted for by the classical theories. We present the first analytical, fully self-consistent, calculations of the electrostatic shielding of a charged dust grain in a collisional plasma. In the regime when the mean free path for the ion-dust collisions is larger than that for the ion-neutral collisions, we solve the kinetic equation for the ions, coupled with Boltzmann distributed electrons and Poisson's equation. The ion velocity distribution function, in the form of a spherically symmetric ion hole, is found to be anisotropic in the presence of charge-exchange collisions. The number of trapped ions and their spatial distribution are determined from the interplay between the collective plasma interaction and the collisional trapping/de-trapping. The stationary state results from the self-tuning of the trapped ion density by the feedback based on the nonlocality of the collisional integral, and on the ion mixing in the radial direction along elongated orbits. Our results confirm the existence of a strong Debye shielding of the dust charge, allowing also the over-population of the trapped ion distribution (ion hump)

A small trapped-ion quantum register

International Nuclear Information System (INIS)

Kielpinski, D

2003-01-01

We review experiments performed at the National Institute of Standards and Technology on entanglement, Bell's inequality and decoherence-free subspaces (DFSs) in a quantum register of trapped 9 Be + ions. The group of Dr David Wineland has demonstrated entanglement of up to four ions using the technique of Molmer and Sorensen. This method produces the state (|↓↓> + |↑↑>)/√2 for two ions and the state (|↓↓↓↓> + |↑↑↑↑>)/√2 for four ions. The entanglement was generated deterministically in each shot of the experiment. Measurements on the two-ion entangled state violate Bell's inequality at the 8σ level. Because of the high detector efficiency of the apparatus, this experiment closes the detector loophole for Bell's inequality measurements for the first time. This measurement is also the first violation of Bell's inequality by massive particles that does not implicitly assume results from quantum mechanics. The group also demonstrated measurement of an interferometric phase with precision better than the shot-noise limit using a two-ion entangled state. A large-scale version of this scheme could improve the signal-to-noise ratio of atomic clocks by orders of magnitude. Further experiments demonstrated reversible encoding of an arbitrary qubit, originally contained in one ion, into a DFS of two ions. The DFS-encoded qubit resists applied collective dephasing noise and retains coherence under ambient conditions 3.6 times longer than does an unencoded qubit. The encoding method, which uses single-ion gates and the two-ion entangling gate, demonstrates all the elements required for two-qubit universal quantum logic. Finally, we describe an architecture for a large-scale ion trap quantum computer. By performing logic gates on small numbers of ions trapped in separate regions of the array, we take advantage of existing techniques for manipulating small trapped-ion quantum registers while enabling massively parallel gate operation. Encoding the

The prosaic Laplace and Fourier transform

International Nuclear Information System (INIS)

Smith, G.A.

1995-01-01

Integral Transform methods play an extremely important role in many branches of science and engineering. The ease with which many problems may be solved using these techniques is well known. In Electrical Engineering especially, Laplace and Fourier Transforms have been used for a long time as a way to change the solution of differential equations into trivial algebraic manipulations or to provide alternate representations of signals and data. These techniques, while seemingly overshadowed by today's emphasis on digital analysis, still form an invaluable basis in the understanding of systems and circuits. A firm grasp of the practical aspects of these subjects provides valuable conceptual tools. This tutorial paper is a review of Laplace and Fourier Transforms from an applied perspective with an emphasis on engineering applications. The interrelationship of the time and frequency domains will be stressed, in an attempt to comfort those who, after living so much of their lives in the time domain, find thinking in the frequency domain disquieting. copyright 1995 American Institute of Physics

Precise and fast spatial-frequency analysis using the iterative local Fourier transform.

Science.gov (United States)

Lee, Sukmock; Choi, Heejoo; Kim, Dae Wook

2016-09-19

The use of the discrete Fourier transform has decreased since the introduction of the fast Fourier transform (fFT), which is a numerically efficient computing process. This paper presents the iterative local Fourier transform (ilFT), a set of new processing algorithms that iteratively apply the discrete Fourier transform within a local and optimal frequency domain. The new technique achieves 210 times higher frequency resolution than the fFT within a comparable computation time. The method's superb computing efficiency, high resolution, spectrum zoom-in capability, and overall performance are evaluated and compared to other advanced high-resolution Fourier transform techniques, such as the fFT combined with several fitting methods. The effectiveness of the ilFT is demonstrated through the data analysis of a set of Talbot self-images (1280 × 1024 pixels) obtained with an experimental setup using grating in a diverging beam produced by a coherent point source.

Improved implementation algorithms of the two-dimensional nonseparable linear canonical transform.

Science.gov (United States)

Ding, Jian-Jiun; Pei, Soo-Chang; Liu, Chun-Lin

2012-08-01

The two-dimensional nonseparable linear canonical transform (2D NSLCT), which is a generalization of the fractional Fourier transform and the linear canonical transform, is useful for analyzing optical systems. However, since the 2D NSLCT has 16 parameters and is very complicated, it is a great challenge to implement it in an efficient way. In this paper, we improved the previous work and propose an efficient way to implement the 2D NSLCT. The proposed algorithm can minimize the numerical error arising from interpolation operations and requires fewer chirp multiplications. The simulation results show that, compared with the existing algorithm, the proposed algorithms can implement the 2D NSLCT more accurately and the required computation time is also less.

Solution of multi-group diffusion equation in x-y-z geometry by finite Fourier transformation

International Nuclear Information System (INIS)

Kobayashi, Keisuke

1975-01-01

The multi-group diffusion equation in three-dimensional x-y-z geometry is solved by finite Fourier transformation. Applying the Fourier transformation to a finite region with constant nuclear cross sections, the fluxes and currents at the material boundaries are obtained in terms of the Fourier series. Truncating the series after the first term, and assuming that the source term is piecewise linear within each mesh box, a set of coupled equations is obtained in the form of three-point equations for each coordinate. These equations can be easily solved by the alternative direction implicit method. Thus a practical procedure is established that could be applied to replace the currently used difference equation. This equation is used to solve the multi-group diffusion equation by means of the source iteration method; and sample calculations for thermal and fast reactors show that the present method yields accurate results with a smaller number of mesh points than the usual finite difference equations. (auth.)

Simple optical setup implementation for digital Fourier transform holography

Energy Technology Data Exchange (ETDEWEB)

De Oliveira, G N [Pos-graduacao em Engenharia Mecanica, TEM/PGMEC, Universidade Federal Fluminense, Rua Passo da Patria, 156, Niteroi, R.J., Cep.: 24.210-240 (Brazil); Rodrigues, D M C; Dos Santos, P A M, E-mail: pams@if.uff.br [Instituto de Fisica, Laboratorio de Optica Nao-linear e Aplicada, Universidade Federal Fluminense, Av. Gal. Nilton Tavares de Souza, s/n, Gragoata, Niteroi, R.J., Cep.:24.210-346 (Brazil)

2011-01-01

In the present work a simple implementation of Digital Fourier Transform Holography (DFTH) setup is discussed. This is obtained making a very simple modification in the classical setup arquiteture of the Fourier Transform holography. It is also demonstrated the easy and practical viability of the setup in an interferometric application for mechanical parameters determination. The work is also proposed as an interesting advanced introductory training for graduated students in digital holography.

Quantum Information Experiments with Trapped Ions at NIST

Science.gov (United States)

Wilson, Andrew

2015-03-01

We present an overview of recent trapped-ion quantum information experiments at NIST. Advancing beyond few-qubit ``proof-of-principle'' experiments to the many-qubit systems needed for practical quantum simulation and information processing, without compromising on the performance demonstrated with small systems, remains a major challenge. One approach to scalable hardware development is surface-electrode traps. Micro-fabricated planar traps can have a number of useful features, including flexible electrode geometries, integrated microwave delivery, and spatio-temporal tuning of potentials for ion transport and spin-spin interactions. In this talk we report on a number of on-going investigations with surface traps. Experiments feature a multi-zone trap with closely spaced ions in a triangular arrangement (a first step towards 2D arrays of ions with tunable spin-spin interactions), a scheme for smooth transport through a junction in a 2D structure based on switchable RF potentials, and a micro-fabricated photo-detector integrated into a trap. We also give a progress report on our latest efforts to improve the fidelity of both optical and microwave 2-qubit gates. This work was supported by IARPA, ONR and the NIST Quantum Information Program. The 3-ion and switchable-RF-junction traps were developed in collaboration with Sandia National Laboratory.

Trapping of hydrogen isotopes in molybdenum and niobium predamaged by ion implantation

International Nuclear Information System (INIS)

Bottiger, J.; Picraux, S.T.; Rud, N.; Laursen, T.

1977-01-01

The trapping of hydrogen isotopes at defects in Mo and Nb have been studied. Ion beams of 11- and 18-keV He + , 55-keV O + and Ne + , and 500-keV Bi + were used to create defects. Subsequently H or D was injected at room temperature by use of molecular beams of 16-keV H + 2 and D + 2 . Appreciable enhancements were observed in the amount of H and D retained within the near-surface region of predamaged samples compared to samples with no prior damage. The total amount of D retained within the near-surface region was measured by means of the nuclear reaction D( 3 He,p) 4 He, and H depth profiles were measured via a resonance in the nuclear reaction 1 H( 19 F,αγ) 16 O. The H profiles correlate with the predicted predamaging ion profiles; however, appreciable tails to deeper depths for the hydrogen profiles are observed for the heavier predamaging ions. For a given predamage ion fluence, the amount of trapped deuterium increases linearly with incident deuterium fluence until a saturation in the enhancement is reached. The amount of deuterium trapped when saturation occurs increases with increasing predamage fluence. The experiments indicate that lighter ions, which create fewer primary displacements, are more effective per displacement in trapping hydrogen. An appreciable release of hydrogen is obtained upon annealing at 200 and 300 degreeC, and a preannealing experiment indicates this is due to detrapping rather than to any loss of traps. These temperatures suggest a much higher binding energy for the trapped hydrogen isotopes (approx.1.5 eV) than the available evidence gives for simple H-defect binding energies (approximately-less-than0.3 eV). The detailed trapping mechanism is not known. However, it is suggested on the basis of the high binding energies and the high concentrations of hydrogen which can be trapped that clusters of hydrogen may be formed

Identification of chemical components in Baidianling Capsule based on gas chromatography-mass spectrometry and high-performance liquid chromatography combined with Fourier transform ion cyclotron resonance mass spectrometry.

Science.gov (United States)

Wu, Wenying; Chen, Yu; Wang, Binjie; Sun, Xiaoyang; Guo, Ping; Chen, Xiaohui

2017-08-01

Baidianling Capsule, which is made from 16 Chinese herbs, has been widely used for treating vitiligo clinically. In this study, the sensitive and rapid method has been developed for the analysis of chemical components in Baidianling Capsule by gas chromatography-mass spectrometry in combination with retention indices and high-performance liquid chromatography combined with Fourier transform ion cyclotron resonance mass spectrometry. Firstly, a total of 110 potential volatile compounds obtained from different extraction procedures including alkanes, alkenes, alkynes, ketones, ethers, aldehydes, alcohols, phenols, organic acids, esters, furans, pyrrole, acid amides, heterocycles, and oxides were detected from Baidianling Capsule by gas chromatography-mass spectrometry, of which 75 were identified by mass spectrometry in combination with the retention index. Then, a total of 124 components were tentatively identified by high-performance liquid chromatography combined with Fourier transform ion cyclotron resonance mass spectrometry. Fifteen constituents from Baidianling Capsule were accurately identified by comparing the retention times with those of reference compounds, others were identified by comparing the retention times and mass spectrometry data, as well as retrieving the reference literature. This study provides a practical strategy for rapidly screening and identifying the multiple constituents of a complex traditional Chinese medicine. © 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Discrete Fourier transform in nanostructures using scattering

International Nuclear Information System (INIS)

Leuenberger, Michael N.; Flatte, Michael E.; Loss, Daniel; Awschalom, D.D.

2004-01-01

In this article, we show that the discrete Fourier transform (DFT) can be performed by scattering a coherent particle or laser beam off an electrically controllable two-dimensional (2D) potential that has the shape of rings or peaks. After encoding the initial vector into the two-dimensional potential by means of electric gates, the Fourier-transformed vector can be read out by detectors surrounding the potential. The wavelength of the laser beam determines the necessary accuracy of the 2D potential, which makes our method very fault-tolerant. Since the time to perform the DFT is much smaller than the clock cycle of today's computers, our proposed device performs DFTs at the frequency of the computer clock speed

Robust quantum gates between trapped ions using shaped pulses

Energy Technology Data Exchange (ETDEWEB)

Zou, Ping, E-mail: zouping@m.scnu.edu.cn; Zhang, Zhi-Ming, E-mail: zmzhang@scnu.edu.cn

2015-12-18

We improve two existing entangling gate schemes between trapped ion qubits immersed in a large linear crystal. Based on the existing two-qubit gate schemes by applying segmented forces on the individually addressed qubits, we present a systematic method to optimize the shapes of the forces to suppress the dominant source of infidelity. The spin-dependent forces in the scheme can be from periodic photon kicks or from continuous optical pulses. The entangling gates are fast, robust, and have high fidelity. They can be used to implement scalable quantum computation and quantum simulation. - Highlights: • We present a systematic method to optimize the shape of the pulses to decouple qubits from intermediary motional modes. • Our optimized scheme can be applied to both the ultrafast gate and fast gate. • Our optimized scheme can suppress the dominant source of infidelity to arbitrary order. • When the number of trapped ions increase, the number of needed segments increases slowly.

The Fourier transform of tubular densities

KAUST Repository

Prior, C B; Goriely, A

2012-01-01

molecules. We consider tubes of both finite radii and unrestricted radius. When there is overlap of the tube structure the net density is calculated using the super-position principle. The Fourier transform of this density is composed of two expressions, one

Spectrums Transform Operators in Bases of Fourier and Walsh Functions

Directory of Open Access Journals (Sweden)

V. V. Syuzev

2017-01-01

Full Text Available The problems of synthesis of the efficient algorithms for digital processing of discrete signals require transforming the signal spectra from one basis system into other. The rational solution to this problem is to construct the Fourier kernel, which is a spectrum of some basis functions, according to the system of functions of the other basis. However, Fourier kernel properties are not equally studied and described for all basis systems of practical importance. The article sets a task and presents an original way to solve the problem of mutual transformation of trigonometric Fourier spectrum into Walsh spectrum of different basis systems.The relevance of this theoretical and applied problem is stipulated, on the one hand, by the prevalence of trigonometric Fourier basis for harmonic representation of digital signals, and, on the other hand, by the fact that Walsh basis systems allow us to have efficient algorithms to simulate signals. The problem solution is achieved through building the Fourier kernel of a special structure that allows us to establish independent groups of Fourier and Walsh spectrum coefficients for further reducing the computational complexity of the transform algorithms.The article analyzes the properties of the system of trigonometric Fourier functions and shows its completeness. Considers the Walsh function basis systems in three versions, namely those of Hadamard, Paley, and Hartmut giving different ordering and analytical descriptions of the functions that make up the basis. Proves a completeness of these systems.Sequentially, for each of the three Walsh systems the analytical curves for the Fourier kernel components are obtained, and Fourier kernel themselves are built with binary rational number of samples of basis functions. The kernels are presented in matrix form and, as an example, recorded for a particular value of the discrete interval of N, equal to 8. The analysis spectral coefficients of the Fourier kernel

An analogue of a theorem of Titchmarsh for Walsh-Fourier transformations

International Nuclear Information System (INIS)

Golubov, B I

1998-01-01

Let f-hat c be the Fourier cosine transform of f. Then, as proved for functions of class L p (R + ) in Titchmarsh's book 'Introduction to the theory of Fourier integrals' (1937), the Hardy operator and the Hardy-Littlewood operator can be defined. In the present paper similar equalities are proved for functions of class L p (R + ), 1< p≤2, and the Walsh-Fourier transformation

Ions in the linacs of future linear colliders

International Nuclear Information System (INIS)

Raubenheimer, T.O.; Chen, P.

1992-01-01

Ions have been identified as a potential limitation in high current storage rings. In this paper we consider the effects of ions in the linacs of future linear colliders. Future linear collider designs call for long trains of closely spaced bunches and/or very dense bunches. Significant ion densities can be generated through the collisional ionization process and trapping in a long train of bunches or through tunneling ionization with very dense bunches. These ions provide skew fields which cause transverse betatron coupling and increase the vertical emittance of the flat beams, and they increase the rate of filamentation, making correction of the emittance dilutions more difficult. While transverse coupling can be alleviated by separating the horizontal and vertical phase advances, the increased filamentation will reduce the effectiveness of non-local correction techniques, leading to tighter alignment tolerances. To reduce the effect of the ions in the designs considered to the level of the intrinsic energy spread one would need to achieve vacuum pressures less than 10 -9 Torr. 5 figs., 5 refs

Application of High-Performance Liquid Chromatography Coupled with Linear Ion Trap Quadrupole Orbitrap Mass Spectrometry for Qualitative and Quantitative Assessment of Shejin-Liyan Granule Supplements

OpenAIRE

Jifeng Gu; Weijun Wu; Mengwei Huang; Fen Long; Xinhua Liu; Yizhun Zhu

2018-01-01

A method for high-performance liquid chromatography coupled with linear ion trap quadrupole Orbitrap high-resolution mass spectrometry (HPLC-LTQ-Orbitrap MS) was developed and validated for the qualitative and quantitative assessment of Shejin-liyan Granule. According to the fragmentation mechanism and high-resolution MS data, 54 compounds, including fourteen isoflavones, eleven ligands, eight flavonoids, six physalins, six organic acids, four triterpenoid saponins, two xanthones, two alkaloi...

Implementation of Period-Finding Algorithm by Means of Simulating Quantum Fourier Transform

Directory of Open Access Journals (Sweden)

Zohreh Moghareh Abed

2010-01-01

Full Text Available In this paper, we introduce quantum fourier transform as a key ingredient for many useful algorithms. These algorithms make a solution for problems which is considered to be intractable problems on a classical computer. Quantum Fourier transform is propounded as a key for quantum phase estimation algorithm. In this paper our aim is the implementation of period-finding algorithm.Quantum computer solves this problem, exponentially faster than classical one. Quantum phase estimation algorithm is the key for the period-finding problem .Therefore, by means of simulating quantum Fourier transform, we are able to implement the period-finding algorithm. In this paper, the simulation of quantum Fourier transform is carried out by Matlab software.

Electro-optic imaging Fourier transform spectrometer

Science.gov (United States)

Chao, Tien-Hsin (Inventor); Znod, Hanying (Inventor)

2009-01-01

An Electro-Optic Imaging Fourier Transform Spectrometer (EOIFTS) for Hyperspectral Imaging is described. The EOIFTS includes an input polarizer, an output polarizer, and a plurality of birefringent phase elements. The relative orientations of the polarizers and birefringent phase elements can be changed mechanically or via a controller, using ferroelectric liquid crystals, to substantially measure the spectral Fourier components of light propagating through the EIOFTS. When achromatic switches are used as an integral part of the birefringent phase elements, the EIOFTS becomes suitable for broadband applications, with over 1 micron infrared bandwidth.

Large quantum Fourier transforms are never exactly realized by braiding conformal blocks

International Nuclear Information System (INIS)

Freedman, Michael H.; Wang, Zhenghan

2007-01-01

Fourier transform is an essential ingredient in Shor's factoring algorithm. In the standard quantum circuit model with the gate set {U(2), controlled-NOT}, the discrete Fourier transforms F N =(ω ij ) NxN , i,j=0,1,...,N-1, ω=e 2πi at ∼sol∼ at N , can be realized exactly by quantum circuits of size O(n 2 ), n=ln N, and so can the discrete sine or cosine transforms. In topological quantum computing, the simplest universal topological quantum computer is based on the Fibonacci (2+1)-topological quantum field theory (TQFT), where the standard quantum circuits are replaced by unitary transformations realized by braiding conformal blocks. We report here that the large Fourier transforms F N and the discrete sine or cosine transforms can never be realized exactly by braiding conformal blocks for a fixed TQFT. It follows that an approximation is unavoidable in the implementation of Fourier transforms by braiding conformal blocks

Vector Radix 2 × 2 Sliding Fast Fourier Transform

Directory of Open Access Journals (Sweden)

Keun-Yung Byun

2016-01-01

Full Text Available The two-dimensional (2D discrete Fourier transform (DFT in the sliding window scenario has been successfully used for numerous applications requiring consecutive spectrum analysis of input signals. However, the results of conventional sliding DFT algorithms are potentially unstable because of the accumulated numerical errors caused by recursive strategy. In this letter, a stable 2D sliding fast Fourier transform (FFT algorithm based on the vector radix (VR 2 × 2 FFT is presented. In the VR-2 × 2 FFT algorithm, each 2D DFT bin is hierarchically decomposed into four sub-DFT bins until the size of the sub-DFT bins is reduced to 2 × 2; the output DFT bins are calculated using the linear combination of the sub-DFT bins. Because the sub-DFT bins for the overlapped input signals between the previous and current window are the same, the proposed algorithm reduces the computational complexity of the VR-2 × 2 FFT algorithm by reusing previously calculated sub-DFT bins in the sliding window scenario. Moreover, because the resultant DFT bins are identical to those of the VR-2 × 2 FFT algorithm, numerical errors do not arise; therefore, unconditional stability is guaranteed. Theoretical analysis shows that the proposed algorithm has the lowest computational requirements among the existing stable sliding DFT algorithms.

Sideband-cooling of trapped ytterbium-ions in the microwave regime

International Nuclear Information System (INIS)

Scharfenberger, Benedikt J.

2012-01-01

Trapped ions in a Paul trap are at present one of the most promising candidates for Quantum Information Processing (QIP). The technique that is used for this purpose in this experiment was introduced in 2001 by F. Mintert and Ch. Wunderlich. The core of this method is the use of atomic transitions in the radio- or microwave region, while a magnetic field gradient along the trap axis (where the ion chain is situated) lifts the degeneracy of the transition frequencies, such that the ions can be distinguished in frequency space; it also serves for the coupling of internal and external degrees of freedom of the ion chain. This method is called MAGIC (MAgnetic Gradient Induced Coupling). The performance of the measurements required that the apparatus of the experiment, which consists of laser sources, lambdameter, vacuum- and microwave system as well as imaging- and detection-units, had to be assembled and tested, which was an important prerequisite for the successful performance of the here described experiments. For the experiments it is advantageous to prepare the ions in an energetic state close to the motional ground state, which contributes to a reduction of the dephasing of the system while manipulating it with microwaves. By using the sideband-cooling technique to the sub-Doppler regime it is taken advantage of the fact, that ions in a linear trap are in good approximation situated in a harmonic oscillator potential and can therefore only populate discrete vibrational energy levels, whose frequency difference is given by the axial trap frequency ω z . If the system is excited by a microwave, which frequency is detuned from resonance to lower energies by a vibrational quantum, the ion looses one such phonon within each cooling-cycle. When this cycle is driven several times, the average phonon number and thus the temperature of the ion can be reduced efficiently and the ion can be initialized in a state close to the motional ground state. As sideband

Equivalence of linear canonical transform domains to fractional Fourier domains and the bicanonical width product: a generalization of the space-bandwidth product.

Science.gov (United States)

Oktem, Figen S; Ozaktas, Haldun M

2010-08-01

Linear canonical transforms (LCTs) form a three-parameter family of integral transforms with wide application in optics. We show that LCT domains correspond to scaled fractional Fourier domains and thus to scaled oblique axes in the space-frequency plane. This allows LCT domains to be labeled and ordered by the corresponding fractional order parameter and provides insight into the evolution of light through an optical system modeled by LCTs. If a set of signals is highly confined to finite intervals in two arbitrary LCT domains, the space-frequency (phase space) support is a parallelogram. The number of degrees of freedom of this set of signals is given by the area of this parallelogram, which is equal to the bicanonical width product but usually smaller than the conventional space-bandwidth product. The bicanonical width product, which is a generalization of the space-bandwidth product, can provide a tighter measure of the actual number of degrees of freedom, and allows us to represent and process signals with fewer samples.

Modular Universal Scalable Ion-trap Quantum Computer

Science.gov (United States)

2016-06-02

SECURITY CLASSIFICATION OF: The main goal of the original MUSIQC proposal was to construct and demonstrate a modular and universally- expandable ion...Distribution Unlimited UU UU UU UU 02-06-2016 1-Aug-2010 31-Jan-2016 Final Report: Modular Universal Scalable Ion-trap Quantum Computer The views...P.O. Box 12211 Research Triangle Park, NC 27709-2211 Ion trap quantum computation, scalable modular architectures REPORT DOCUMENTATION PAGE 11

Control of the conformations of ion Coulomb crystals in a Penning trap

Energy Technology Data Exchange (ETDEWEB)

Thompson, R. C.; Mavadia, S.; Goodwin, J. F.; Stutter, G.; Bharadia, S.; Crick, D. R.; Segal, D. M. [Blackett Laboratory, Imperial College London, London SW7 2AZ (United Kingdom)

2015-06-29

Ion Coulomb crystals containing small numbers of ions have been created and manipulated in a wide range of configurations in a Penning trap, from a linear string, through various three-dimensional conformations, to a planar crystal. We show that the dynamics of the system simplifies enormously in a frame which rotates at half the cyclotron frequency and we discuss the effect of the radial cooling laser beam in this frame. Simulations show that the crystal conformations can be reproduced by finding the minimum energy configuration in a frame whose radial potential is modified by the rotation of the ion crystal. The rotation frequency of the crystal deduced from the simulations is consistent with the known laser parameters. We also show that even though the number of ions in our system is small (typically less than 20), the system still behaves like a plasma and its static properties can be calculated using the standard model for a single-component plasma in a trap.

Control of the conformations of ion Coulomb crystals in a Penning trap

International Nuclear Information System (INIS)

Thompson, R. C.; Mavadia, S.; Goodwin, J. F.; Stutter, G.; Bharadia, S.; Crick, D. R.; Segal, D. M.

2015-01-01

Ion Coulomb crystals containing small numbers of ions have been created and manipulated in a wide range of configurations in a Penning trap, from a linear string, through various three-dimensional conformations, to a planar crystal. We show that the dynamics of the system simplifies enormously in a frame which rotates at half the cyclotron frequency and we discuss the effect of the radial cooling laser beam in this frame. Simulations show that the crystal conformations can be reproduced by finding the minimum energy configuration in a frame whose radial potential is modified by the rotation of the ion crystal. The rotation frequency of the crystal deduced from the simulations is consistent with the known laser parameters. We also show that even though the number of ions in our system is small (typically less than 20), the system still behaves like a plasma and its static properties can be calculated using the standard model for a single-component plasma in a trap

Positioning of the rf potential minimum line of a linear Paul trap with micrometer precision

DEFF Research Database (Denmark)

Herskind, Peter Fønss; Dantan, Aurélien; Albert, Magnus

2009-01-01

We demonstrate a general technique to achieve a precise radial displacement of the nodal line of the radiofrequency (rf) field in a linear Paul trap. The technique relies on the selective adjustment of the load capacitance of the trap electrodes, achieved through the addition of capacitors...... to the basic resonant rf circuit used to drive the trap. Displacements of up to ~100 µm with micrometer precision are measured using a combination of fluorescence images of ion Coulomb crystals and coherent coupling of such crystals to a mode of an optical cavity. The displacements are made without measurable...

The RC Circuit: An Approach with Fourier Transforms In this article ...

Indian Academy of Sciences (India)

CLASSROOM. Mitrajyoti Ghosh. 83, Mitrapara 2nd Lane, Harinavi,. Kolkata 700148, West Bengal,. India. Email: mijospeakingnow@gmail.com. The RC Circuit: An Approach with Fourier Transforms. In this article we shall mathematically analyse the Resistor-. Capacitor (RC) circuit with the help of Fourier transforms. (FT).

A prototype stationary Fourier transform spectrometer for near-infrared absorption spectroscopy.

Science.gov (United States)

Li, Jinyang; Lu, Dan-feng; Qi, Zhi-mei

2015-09-01

A prototype stationary Fourier transform spectrometer (FTS) was constructed with a fiber-coupled lithium niobate (LiNbO3) waveguide Mach-Zehnder interferometer (MZI) for the purpose of rapid on-site spectroscopy of biological and chemical measurands. The MZI contains push-pull electrodes for electro-optic modulation, and its interferogram as a plot of intensity against voltage was obtained by scanning the modulating voltage from -60 to +60 V in 50 ms. The power spectrum of input signal was retrieved by Fourier transform processing of the interferogram combined with the wavelength dispersion of half-wave voltage determined for the MZI used. The prototype FTS operates in the single-mode wavelength range from 1200 to 1700 nm and allows for reproducible spectroscopy. A linear concentration dependence of the absorbance at λmax = 1451 nm for water in ethanolic solution was obtained using the prototype FTS. The near-infrared spectroscopy of solid samples was also implemented, and the different spectra obtained with different materials evidenced the chemical recognition capability of the prototype FTS. To make this prototype FTS practically applicable, work on improving its spectral resolution by increasing the maximum optical path length difference is in progress.

Preliminary Tests of a Paul ion Trap as an Ion Source

Science.gov (United States)

Sadat Kiai, S. M.; Zirak, A. R.; Elahi, M.; Adlparvar, S.; Mortazavi, B. N.; Safarien, A.; Farhangi, S.; Sheibani, S.; Alhooie, S.; Khalaj, M. M. A.; Dabirzadeh, A. A.; Ruzbehani, M.; Zahedi, F.

2010-10-01

The paper reports on the design and construction of a Paul ion trap as an ion source by using an impact electron ionization technique. Ions are produced in the trap and confined for the specific time which is then extracted and detected by a Faraday cup. Especial electronic configurations are employed between the end caps, ring electrodes, electron gun and a negative voltage for the detector. This configuration allows a constant low level of pure ion source between the pulsed confined ion sources. The present experimental results are based on the production and confinement of Argon ions with good stability and repeatability, but in principle, the technique can be used for various Argon like ions.

External Second Gate, Fourier Transform Ion Mobility Spectrometry: Parametric Optimization for Detection of Weapons of Mass Destruction

Directory of Open Access Journals (Sweden)

Edward E. Tarver

2004-03-01

Full Text Available Abstract: Ion mobility spectrometry (IMS is recognized as one of the most sensitive and robust techniques for the detection of narcotics, explosives and chemical warfare agents. IMS is widely used in forensic, military and security applications. Increasing threat of terrorist attacks, the proliferation of narcotics, Chemical Weapons Convention (CWC treaty verification as well as humanitarian de-mining efforts have mandated that equal importance be placed on the time required to obtain results as well as the quality of the analytical data. [1] In this regard IMS is virtually unrivaled when both speed of response and sensitivity have to be considered. [2] The problem with conventional (signal averaging IMS systems is the fixed duty cycle of the entrance gate that restricts to less than 1%, the number of available ions contributing to the measured signal. Furthermore, the signal averaging process incorporates scan-to-scan variations that degrade the spectral resolution contributing to misidentifications and false positives. With external second gate, Fourier Transform ion mobility spectrometry (FT-IMS the entrance gate frequency is variable and can be altered in conjunction with other data acquisition parameters (scan time and sampling rate to increase the spectral resolution to reduce false alarms and improve the sensitivity for early warning and contamination avoidance. In addition, with FT-IMS the entrance gate operates with a 50% duty cycle and so affords a seven-fold increase in sensitivity. Recent data on high explosives are presented to demonstrate the parametric optimization in sensitivity and resolution of our system.

Fourier transform of delayed fluorescence as an indicator of herbicide concentration.

Science.gov (United States)

Guo, Ya; Tan, Jinglu

2014-12-21

It is well known that delayed fluorescence (DF) from Photosystem II (PSII) of plant leaves can be potentially used to sense herbicide pollution and evaluate the effect of herbicides on plant leaves. The research of using DF as a measure of herbicides in the literature was mainly conducted in time domain and qualitative correlation was often obtained. Fourier transform is often used to analyze signals. Viewing DF signal in frequency domain through Fourier transform may allow separation of signal components and provide a quantitative method for sensing herbicides. However, there is a lack of an attempt to use Fourier transform of DF as an indicator of herbicide. In this work, the relationship between the Fourier transform of DF and herbicide concentration was theoretically modelled and analyzed, which immediately yielded a quantitative method to measure herbicide concentration in frequency domain. Experiments were performed to validate the developed method. Copyright © 2014 Elsevier Ltd. All rights reserved.

Limitations on continuous variable quantum algorithms with Fourier transforms

International Nuclear Information System (INIS)

Adcock, Mark R A; Hoeyer, Peter; Sanders, Barry C

2009-01-01

We study quantum algorithms implemented within a single harmonic oscillator, or equivalently within a single mode of the electromagnetic field. Logical states correspond to functions of the canonical position, and the Fourier transform to canonical momentum serves as the analogue of the Hadamard transform for this implementation. This continuous variable version of quantum information processing has widespread appeal because of advanced quantum optics technology that can create, manipulate and read Gaussian states of light. We show that, contrary to a previous claim, this implementation of quantum information processing has limitations due to a position-momentum trade-off of the Fourier transform, analogous to the famous time-bandwidth theorem of signal processing.

HEART ABNORMALITY CLASSIFICATIONS USING FOURIER TRANSFORMS METHOD AND NEURAL NETWORKS

Directory of Open Access Journals (Sweden)

Endah Purwanti

2014-05-01

Full Text Available Health problems with cardiovascular system disorder are still ranked high globally. One way to detect abnormalities in the cardiovascular system especially in the heart is through the electrocardiogram (ECG reading. However, reading ECG recording needs experience and expertise, software-based neural networks has designed to help identify any abnormalities ofthe heart through electrocardiogram digital image. This image is processed using image processing methods to obtain ordinate chart which representing the heart’s electrical potential. Feature extraction using Fourier transforms which are divided into several numbers of coefficients. As the software input, Fourier transforms coefficient have been normalized. Output of this software is divided into three classes, namely heart with atrial fibrillation, coronary heart disease and normal. Maximum accuracy rate ofthis software is 95.45%, with the distribution of the Fourier transform coefficients 1/8 and number of nodes 5, while minimum accuracy rate of this software at least 68.18% by distribution of the Fourier transform coefficients 1/32 and the number of nodes 32. Overall result accuracy rate of this software has an average of86.05% and standard deviation of7.82.

Fourier transform spectra of quantum dots

Science.gov (United States)

Damian, V.; Ardelean, I.; Armăşelu, Anca; Apostol, D.

2010-05-01

Semiconductor quantum dots are nanometer-sized crystals with unique photochemical and photophysical properties that are not available from either isolated molecules or bulk solids. These nanocrystals absorb light over a very broad spectral range as compared to molecular fluorophores which have very narrow excitation spectra. High-quality QDs are proper to be use in different biological and medical applications (as fluorescent labels, the cancer treatment and the drug delivery). In this article, we discuss Fourier transform visible spectroscopy of commercial quantum dots. We reveal that QDs produced by Evident Technologies when are enlightened by laser or luminescent diode light provides a spectral shift of their fluorescence spectra correlated to exciting emission wavelengths, as shown by the ARCspectroNIR Fourier Transform Spectrometer. In the final part of this paper we show an important biological application of CdSe/ZnS core-shell ODs as microbial labeling both for pure cultures of cyanobacteria (Synechocystis PCC 6803) and for mixed cultures of phototrophic and heterotrophic microorganisms.

Space-charge effects in Penning ion traps

Czech Academy of Sciences Publication Activity Database

Porobic, T.; Beck, M.; Breitenfeldt, M.; Couratin, C.; Finlay, P.; Knecht, A.; Fabian, X.; Friedag, P.; Flechard, X.; Lienard, E.; Ban, G.; Zákoucký, Dalibor; Soti, G.; Van Gorp, S.; Weinheimer, C.; Wursten, E.; Severijns, N.

2015-01-01

Roč. 785, JUN (2015), s. 153-162 ISSN 0168-9002 R&D Projects: GA MŠk LA08015; GA MŠk(CZ) LG13031 Institutional support: RVO:61389005 Keywords : Penning trap * space-charge * magnetron motion * ion trapping * buffer gas cooling * ion cyclotron resonance Subject RIV: BG - Nuclear, Atomic and Molecular Physics, Colliders Impact factor: 1.200, year: 2015

Fourier-transform optical microsystems

Science.gov (United States)

Collins, S. D.; Smith, R. L.; Gonzalez, C.; Stewart, K. P.; Hagopian, J. G.; Sirota, J. M.

1999-01-01

The design, fabrication, and initial characterization of a miniature single-pass Fourier-transform spectrometer (FTS) that has an optical bench that measures 1 cm x 5 cm x 10 cm is presented. The FTS is predicated on the classic Michelson interferometer design with a moving mirror. Precision translation of the mirror is accomplished by microfabrication of dovetailed bearing surfaces along single-crystal planes in silicon. Although it is miniaturized, the FTS maintains a relatively high spectral resolution, 0.1 cm-1, with adequate optical throughput.

Properties of the Simpson discrete fourier transform | Singh ...

African Journals Online (AJOL)

The Simpson discrete Fourier transform (SDFT) and its inverse are transformations relating the time and frequency domains. In this paper we state and prove the important properties of shift, circular convolution, conjugation, time reversal and Plancherel's theorem. In addition, we provide an alternative representation of the ...

IDENTIFICATION OF MICROCYSTIN TOXINS FROM A STRAIN OF MICROCYSTIS AERUGINOSA BY LIQUID CHROMATOGRAPHY INTRODUCTION INTO A HYBRID LINEAR ION TRAP-FOURIER TRANSFORM ION CYCLOTRON RESONANCE MASS SPECTROMETER

Science.gov (United States)

The cyclic heptapeptide microcystin toxins produced by a strain of Microcystis aeruginosa that has not been investigated previously were separated by liquid chromatography and identified by high-accuracy m/z measurements of their [M + H]+ ions and the fragment i...

MATS and LaSpec: High-precision experiments using ion traps and lasers at FAIR

Science.gov (United States)

Rodríguez, D.; Blaum, K.; Nörtershäuser, W.; Ahammed, M.; Algora, A.; Audi, G.; Äystö, J.; Beck, D.; Bender, M.; Billowes, J.; Block, M.; Böhm, C.; Bollen, G.; Brodeur, M.; Brunner, T.; Bushaw, B. A.; Cakirli, R. B.; Campbell, P.; Cano-Ott, D.; Cortés, G.; Crespo López-Urrutia, J. R.; Das, P.; Dax, A.; de, A.; Delheij, P.; Dickel, T.; Dilling, J.; Eberhardt, K.; Eliseev, S.; Ettenauer, S.; Flanagan, K. T.; Ferrer, R.; García-Ramos, J.-E.; Gartzke, E.; Geissel, H.; George, S.; Geppert, C.; Gómez-Hornillos, M. B.; Gusev, Y.; Habs, D.; Heenen, P.-H.; Heinz, S.; Herfurth, F.; Herlert, A.; Hobein, M.; Huber, G.; Huyse, M.; Jesch, C.; Jokinen, A.; Kester, O.; Ketelaer, J.; Kolhinen, V.; Koudriavtsev, I.; Kowalska, M.; Krämer, J.; Kreim, S.; Krieger, A.; Kühl, T.; Lallena, A. M.; Lapierre, A.; Le Blanc, F.; Litvinov, Y. A.; Lunney, D.; Martínez, T.; Marx, G.; Matos, M.; Minaya-Ramirez, E.; Moore, I.; Nagy, S.; Naimi, S.; Neidherr, D.; Nesterenko, D.; Neyens, G.; Novikov, Y. N.; Petrick, M.; Plaß, W. R.; Popov, A.; Quint, W.; Ray, A.; Reinhard, P.-G.; Repp, J.; Roux, C.; Rubio, B.; Sánchez, R.; Schabinger, B.; Scheidenberger, C.; Schneider, D.; Schuch, R.; Schwarz, S.; Schweikhard, L.; Seliverstov, M.; Solders, A.; Suhonen, M.; Szerypo, J.; Taín, J. L.; Thirolf, P. G.; Ullrich, J.; van Duppen, P.; Vasiliev, A.; Vorobjev, G.; Weber, C.; Wendt, K.; Winkler, M.; Yordanov, D.; Ziegler, F.

2010-05-01

-destructive Fourier-Transform Ion-Cyclotron-Resonance (FT-ICR) detection technique on single stored ions. This accuracy limit is important for fundamental interaction tests, but also allows for the study of the fine structure of the nuclear mass surface with unprecedented accuracy, whenever required. The use of the FT-ICR technique provides true single ion sensitivity. This is essential to access isotopes that are produced with minimum rates which are very often the most interesting ones. Instead of pushing for highest accuracy, the high charge state of the ions can also be used to reduce the storage time of the ions, hence making measurements on even shorter-lived isotopes possible. Decay studies in ion traps will become possible with MATS. Novel spectroscopic tools for in-trap high-resolution conversion-electron and charged-particle spectroscopy from carrier-free sources will be developed, aiming e.g. at the measurements of quadrupole moments and E0 strengths. With the possibility of both high-accuracy mass measurements of the shortest-lived isotopes and decay studies, the high sensitivity and accuracy potential of MATS is ideally suited for the study of very exotic nuclides that will only be produced at the FAIR facility.Laser spectroscopy of radioactive isotopes and isomers is an efficient and model-independent approach for the determination of nuclear ground and isomeric state properties. Hyperfine structures and isotope shifts in electronic transitions exhibit readily accessible information on the nuclear spin, magnetic dipole and electric quadrupole moments as well as root-mean-square charge radii. The dependencies of the hyperfine splitting and isotope shift on the nuclear moments and mean square nuclear charge radii are well known and the theoretical framework for the extraction of nuclear parameters is well established. These extracted parameters provide fundamental information on the structure of nuclei at the limits of stability. Vital information on both bulk and valence

Linear ion-trap mass spectrometric characterization of human pituitary nitrotyrosine-containing proteins

Science.gov (United States)

Zhan, Xianquan; Desiderio, Dominic M.

2007-01-01

The nitric oxide-mediated Tyr-nitration of endogenous proteins is associated with several pathological and physiological processes. In order to investigate the presence - and potential roles - of Tyr-nitration in the human pituitary, a large-format two-dimensional gel separation plus a Western blot against a specific anti-3-nitrotyrosine antibody were used to separate and detect nitroproteins from a human pituitary proteome. The nitroproteins were subjected to in-gel trypsin digestion, and high-sensitivity vacuum matrix-assisted laser desorption/ionization (vMALDI) linear ion-trap tandem mass spectrometry was used to analyze the tryptic peptides. Those MS/MS data were used to determine the amino acid sequence and the specific nitration site of each tryptic nitropeptide, and were matched to corresponding proteins with Bioworks TuboSEQUEST software. Compared to our previous study, 16 new nitrotyrosine-immunoreactive positive Western blot spots were found within the area pI 3.0-10 and Mr 10-100 kDa. Four new nitroproteins were discovered: the stanniocalcin 1 precursor--involved in calcium and phosphate metabolism; mitochondrial co-chaperone protein HscB, which might act as a co-chaperone in iron-sulfur cluster assembly in mitochrondria; progestin and adipoQ receptor family member III--a seven-transmembrane receptor; proteasome subunit alpha type 2--involved in an ATP/ubiquitin-dependent non-lysosomal proteolytic pathway. Those data demonstrate that nitric oxide-mediated Tyr-nitration might participate in various biochemical, metabolic, and pathological processes in the human pituitary.

The short time Fourier transform and local signals

Science.gov (United States)

Okumura, Shuhei

In this thesis, I examine the theoretical properties of the short time discrete Fourier transform (STFT). The STFT is obtained by applying the Fourier transform by a fixed-sized, moving window to input series. We move the window by one time point at a time, so we have overlapping windows. I present several theoretical properties of the STFT, applied to various types of complex-valued, univariate time series inputs, and their outputs in closed forms. In particular, just like the discrete Fourier transform, the STFT's modulus time series takes large positive values when the input is a periodic signal. One main point is that a white noise time series input results in the STFT output being a complex-valued stationary time series and we can derive the time and time-frequency dependency structure such as the cross-covariance functions. Our primary focus is the detection of local periodic signals. I present a method to detect local signals by computing the probability that the squared modulus STFT time series has consecutive large values exceeding some threshold after one exceeding observation following one observation less than the threshold. We discuss a method to reduce the computation of such probabilities by the Box-Cox transformation and the delta method, and show that it works well in comparison to the Monte Carlo simulation method.

Discrete Fourier Transform Analysis in a Complex Vector Space

Science.gov (United States)

Dean, Bruce H.

2009-01-01

Alternative computational strategies for the Discrete Fourier Transform (DFT) have been developed using analysis of geometric manifolds. This approach provides a general framework for performing DFT calculations, and suggests a more efficient implementation of the DFT for applications using iterative transform methods, particularly phase retrieval. The DFT can thus be implemented using fewer operations when compared to the usual DFT counterpart. The software decreases the run time of the DFT in certain applications such as phase retrieval that iteratively call the DFT function. The algorithm exploits a special computational approach based on analysis of the DFT as a transformation in a complex vector space. As such, this approach has the potential to realize a DFT computation that approaches N operations versus Nlog(N) operations for the equivalent Fast Fourier Transform (FFT) calculation.

Trapped-ion quantum logic gates based on oscillating magnetic fields

Science.gov (United States)

Ospelkaus, Christian; Langer, Christopher E.; Amini, Jason M.; Brown, Kenton R.; Leibfried, Dietrich; Wineland, David J.

2009-05-01

Oscillating magnetic fields and field gradients can be used to implement single-qubit rotations and entangling multiqubit quantum gates for trapped-ion quantum information processing. With fields generated by currents in microfabricated surface-electrode traps, it should be possible to achieve gate speeds that are comparable to those of optically induced gates for realistic distances between the ions and the electrode surface. Magnetic-field-mediated gates have the potential to significantly reduce the overhead in laser-beam control and motional-state initialization compared to current QIP experiments with trapped ions and will eliminate spontaneous scattering decoherence, a fundamental source of decoherence in laser-mediated gates. A potentially beneficial environment for the implementation of such schemes is a cryogenic ion trap, because small length scale traps with low motional heating rates can be realized. A cryogenic ion trap experiment is currently under construction at NIST.

Complex nonlinear Fourier transform and its inverse

International Nuclear Information System (INIS)

Saksida, Pavle

2015-01-01

We study the nonlinear Fourier transform associated to the integrable systems of AKNS-ZS type. Two versions of this transform appear in connection with the AKNS-ZS systems. These two versions can be considered as two real forms of a single complex transform F c . We construct an explicit algorithm for the calculation of the inverse transform (F c ) -1 (h) for an arbitrary argument h. The result is given in the form of a convergent series of functions in the domain space and the terms of this series can be computed explicitly by means of finitely many integrations. (paper)

Fourier transforms in spectroscopy

CERN Document Server

Kauppinen, Jyrki

2000-01-01

This modern approach to the subject is clearly and logically structured, and gives readers an understanding of the essence of Fourier transforms and their applications. All important aspects are included with respect to their use with optical spectroscopic data. Based on popular lectures, the authors provide the mathematical fundamentals and numerical applications which are essential in practical use. The main part of the book is dedicated to applications of FT in signal processing and spectroscopy, with IR and NIR, NMR and mass spectrometry dealt with both from a theoretical and practical poi

Decay of the Fourier transform analytic and geometric aspects

CERN Document Server

Iosevich, Alex

2014-01-01

The Plancherel formula says that the L2 norm of the function is equal to the L2 norm of its Fourier transform. This implies that at least on average, the Fourier transform of an L2 function decays at infinity. This book is dedicated to the study of the rate of this decay under various assumptions and circumstances, far beyond the original L2 setting. Analytic and geometric properties of the underlying functions interact in a seamless symbiosis which underlines the wide range influences and applications of the concepts under consideration.

Quantitative evaluation of temporal partial coherence using 3D Fourier transforms of through-focus TEM images

International Nuclear Information System (INIS)

Kimoto, Koji; Sawada, Hidetaka; Sasaki, Takeo; Sato, Yuta; Nagai, Takuro; Ohwada, Megumi; Suenaga, Kazu; Ishizuka, Kazuo

2013-01-01

We evaluate the temporal partial coherence of transmission electron microscopy (TEM) using the three-dimensional (3D) Fourier transform (FT) of through-focus images. Young's fringe method often indicates the unexpected high-frequency information due to non-linear imaging terms. We have already used the 3D FT of axial (non-tilted) through-focus images to reduce the effect of non-linear terms on the linear imaging term, and demonstrated the improvement of monochromated lower-voltage TEM performance [Kimoto et al., Ultramicroscopy 121 (2012) 31–39]. Here we apply the 3D FT method with intentionally tilted incidence to normalize various factors associated with a TEM specimen and an imaging device. The temporal partial coherence of two microscopes operated at 30, 60 and 80 kV is evaluated. Our method is applicable to such cases where the non-linear terms become more significant in lower acceleration voltage or aberration-corrected high spatial resolution TEM. - Highlights: • We assess the temporal partial coherence of TEM using a 3-dimensional (3D) Fourier transform (FT) of through-focus images. • We apply the 3D FT method with intentionally tilted incidence to normalize various factors associated with a TEM specimen and an imaging device. • The spatial frequency at which information transfer decreases to 1/e 2 (13.5%) is determined for two lower-voltage TEM systems

Scaling Trapped Ion Quantum Computers Using Fast Gates and Microtraps

Science.gov (United States)

Ratcliffe, Alexander K.; Taylor, Richard L.; Hope, Joseph J.; Carvalho, André R. R.

2018-06-01

Most attempts to produce a scalable quantum information processing platform based on ion traps have focused on the shuttling of ions in segmented traps. We show that an architecture based on an array of microtraps with fast gates will outperform architectures based on ion shuttling. This system requires higher power lasers but does not require the manipulation of potentials or shuttling of ions. This improves optical access, reduces the complexity of the trap, and reduces the number of conductive surfaces close to the ions. The use of fast gates also removes limitations on the gate time. Error rates of 10-5 are shown to be possible with 250 mW laser power and a trap separation of 100 μ m . The performance of the gates is shown to be robust to the limitations in the laser repetition rate and the presence of many ions in the trap array.

H∞ Robust Control of a Large-Piston MEMS Micromirror for Compact Fourier Transform Spectrometer Systems

Directory of Open Access Journals (Sweden)

Huipeng Chen

2018-02-01

Full Text Available Incorporating linear-scanning micro-electro-mechanical systems (MEMS micromirrors into Fourier transform spectral acquisition systems can greatly reduce the size of the spectrometer equipment, making portable Fourier transform spectrometers (FTS possible. How to minimize the tilting of the MEMS mirror plate during its large linear scan is a major problem in this application. In this work, an FTS system has been constructed based on a biaxial MEMS micromirror with a large-piston displacement of 180 μm, and a biaxial H∞ robust controller is designed. Compared with open-loop control and proportional-integral-derivative (PID closed-loop control, H∞ robust control has good stability and robustness. The experimental results show that the stable scanning displacement reaches 110.9 μm under the H∞ robust control, and the tilting angle of the MEMS mirror plate in that full scanning range falls within ±0.0014°. Without control, the FTS system cannot generate meaningful spectra. In contrast, the FTS yields a clean spectrum with a full width at half maximum (FWHM spectral linewidth of 96 cm−1 under the H∞ robust control. Moreover, the FTS system can maintain good stability and robustness under various driving conditions.

H∞ Robust Control of a Large-Piston MEMS Micromirror for Compact Fourier Transform Spectrometer Systems.

Science.gov (United States)

Chen, Huipeng; Li, Mengyuan; Zhang, Yi; Xie, Huikai; Chen, Chang; Peng, Zhangming; Su, Shaohui

2018-02-08

Incorporating linear-scanning micro-electro-mechanical systems (MEMS) micromirrors into Fourier transform spectral acquisition systems can greatly reduce the size of the spectrometer equipment, making portable Fourier transform spectrometers (FTS) possible. How to minimize the tilting of the MEMS mirror plate during its large linear scan is a major problem in this application. In this work, an FTS system has been constructed based on a biaxial MEMS micromirror with a large-piston displacement of 180 μm, and a biaxial H∞ robust controller is designed. Compared with open-loop control and proportional-integral-derivative (PID) closed-loop control, H∞ robust control has good stability and robustness. The experimental results show that the stable scanning displacement reaches 110.9 μm under the H∞ robust control, and the tilting angle of the MEMS mirror plate in that full scanning range falls within ±0.0014°. Without control, the FTS system cannot generate meaningful spectra. In contrast, the FTS yields a clean spectrum with a full width at half maximum (FWHM) spectral linewidth of 96 cm -1 under the H∞ robust control. Moreover, the FTS system can maintain good stability and robustness under various driving conditions.

Accelerating the Non-equispaced Fast Fourier Transform on Commodity Graphics Hardware

DEFF Research Database (Denmark)

Sørensen, Thomas Sangild; Schaeffter, Tobias; Noe, Karsten Østergaard

2008-01-01

We present a fast parallel algorithm to compute the Non-equispaced fast Fourier transform on commodity graphics hardware (the GPU). We focus particularly on a novel implementation of the convolution step in the transform, which was previously its most time consuming part. We describe the performa......We present a fast parallel algorithm to compute the Non-equispaced fast Fourier transform on commodity graphics hardware (the GPU). We focus particularly on a novel implementation of the convolution step in the transform, which was previously its most time consuming part. We describe...

Potential of dynamically harmonized Fourier transform ion cyclotron resonance cell for high-throughput metabolomics fingerprinting: control of data quality.

Science.gov (United States)

Habchi, Baninia; Alves, Sandra; Jouan-Rimbaud Bouveresse, Delphine; Appenzeller, Brice; Paris, Alain; Rutledge, Douglas N; Rathahao-Paris, Estelle

2018-01-01

Due to the presence of pollutants in the environment and food, the assessment of human exposure is required. This necessitates high-throughput approaches enabling large-scale analysis and, as a consequence, the use of high-performance analytical instruments to obtain highly informative metabolomic profiles. In this study, direct introduction mass spectrometry (DIMS) was performed using a Fourier transform ion cyclotron resonance (FT-ICR) instrument equipped with a dynamically harmonized cell. Data quality was evaluated based on mass resolving power (RP), mass measurement accuracy, and ion intensity drifts from the repeated injections of quality control sample (QC) along the analytical process. The large DIMS data size entails the use of bioinformatic tools for the automatic selection of common ions found in all QC injections and for robustness assessment and correction of eventual technical drifts. RP values greater than 10 6 and mass measurement accuracy of lower than 1 ppm were obtained using broadband mode resulting in the detection of isotopic fine structure. Hence, a very accurate relative isotopic mass defect (RΔm) value was calculated. This reduces significantly the number of elemental composition (EC) candidates and greatly improves compound annotation. A very satisfactory estimate of repeatability of both peak intensity and mass measurement was demonstrated. Although, a non negligible ion intensity drift was observed for negative ion mode data, a normalization procedure was easily applied to correct this phenomenon. This study illustrates the performance and robustness of the dynamically harmonized FT-ICR cell to perform large-scale high-throughput metabolomic analyses in routine conditions. Graphical abstract Analytical performance of FT-ICR instrument equipped with a dynamically harmonized cell.

Functional differential equations for the q-Fourier transform of q-Gaussians

International Nuclear Information System (INIS)

Umarov, S; Queiros, S M Duarte

2010-01-01

In this paper the question 'is the q-Fourier transform of a q-Gaussian a q'-Gaussian (with some q') up to a constant factor?' is studied for the whole range of q in (- infty, 3). This question is connected with applicability of the q-Fourier transform in the study of limit processes in nonextensive statistical mechanics. Using the functional differential equation approach we prove that the answer is affirmative if and only if 1 ≤ q < 3, excluding two particular cases of q < 1, namely q=1/2 and q=2/3. Complementarily, we discuss some applications of the q-Fourier transform to nonlinear partial differential equations such as the porous medium equation.

Functional differential equations for the q-Fourier transform of q-Gaussians

Energy Technology Data Exchange (ETDEWEB)

Umarov, S [Department of Mathematics, Tufts University, Medford, MA (United States); Queiros, S M Duarte, E-mail: sdqueiro@gmail.co [Unilever R and D Port Sunlight, Quarry Road East, Wirral, CH63 3JW (United Kingdom)

2010-02-05

In this paper the question 'is the q-Fourier transform of a q-Gaussian a q'-Gaussian (with some q') up to a constant factor?' is studied for the whole range of q in (- infty, 3). This question is connected with applicability of the q-Fourier transform in the study of limit processes in nonextensive statistical mechanics. Using the functional differential equation approach we prove that the answer is affirmative if and only if 1 <= q < 3, excluding two particular cases of q < 1, namely q=1/2 and q=2/3. Complementarily, we discuss some applications of the q-Fourier transform to nonlinear partial differential equations such as the porous medium equation.

Detecting yocto (10-24) newton forces with trapped ions

CSIR Research Space (South Africa)

Uys, H

2010-09-01

Full Text Available This article reports on a calibrated measurement of 174 Yoctonewton using a cloud of 60 9 Be+ ion confined in a Penning ion trap. These measurements suggest that ion traps may form the basis of a new class of ultrasensitive deployable force sensors....

A linear radiofrequency quadrupole ion trap for the cooling and bunching of radioactive ion beams

CERN Document Server

Kellerbauer, A G; Dilling, J; Henry, S; Herfurth, F; Kluge, H J; Lamour, E; Moore, R B; Scheidenberger, C; Schwarz, S; Sikler, G; Szerypo, J

2002-01-01

A linear radiofrequency quadrupole ion guide and beam buncher has been installed at the ISOLTRAP mass spectrometry experiment at the ISOLDE facility at CERN. The apparatus is being used as a beam cooling, accumulation, and bunching system. It operates with a buffer gas that cools the injected ions and converts the quasicontinuous 60- keV beam from the ISOLDE facility to 2.5-keV beam pulses with improved normalized transverse emittance. Recent measurements suggest a capture efficiency of the ion guide of up to 40% and a cooling and bunching efficiency of at least 12% which is expected to still be increased. The improved ISOLTRAP setup has so far been used very successfully in three on-line experiments. (12 refs).

Cavity QED with single trapped Ca+-ions

International Nuclear Information System (INIS)

Mundt, A.B.

2003-02-01

This thesis reports on the design and setup of a vacuum apparatus allowing the investigation of cavity QED effects with single trapped 40 Ca + ions. The weak coupling of ion and cavity in the 'bad cavity limit' may serve to inter--convert stationary and flying qubits. The ion is confined in a miniaturized Paul trap and cooled via the Doppler effect to the Lamb--Dicke regime. The extent of the atomic wave function is less than 30 nm. The ion is enclosed by a high finesse optical cavity. The technically--involved apparatus allows movement of the trap relative to the cavity and the trapped ion can be placed at any position in the standing wave. By means of a transfer lock the cavity can be resonantly stabilized with the S 1/2 ↔ D 5/2 quadrupole transition at 729 nm (suitable as a qubit) without light at that wavelength being present in the cavity. The coupling of the cavity field to the S 1/2 ↔ D 5/2 quadrupole transition is investigated with various techniques in order to determine the spatial dependence as well as the temporal dynamics. The orthogonal coupling of carrier and first--order sideband transitions at field nodes and antinodes is explored. The coherent interaction of the ion and the cavity field is confirmed by exciting Rabi oscillations with short resonant pulses injected into the cavity. Finally, first experimental steps towards the observation of cavity enhanced spontaneous emission have been taken. (author)

MOMA and other next-generation ion trap mass spectrometers for planetary exploration

Science.gov (United States)

Arevalo, R. D., Jr.; Brinckerhoff, W. B.; Getty, S.; Mahaffy, P. R.; van Amerom, F. H. W.; Danell, R.; Pinnick, V. T.; Li, X.; Grubisic, A.; Southard, A. E.; Hovmand, L.; Cottin, H.; Makarov, A.

2016-12-01

Since the 1970's, quadrupole mass spectrometer (QMS) systems have served as low-risk, cost-efficient means to explore the inner and outer reaches of the solar system. These legacy instruments have interrogated the compositions of the lunar exosphere (LADEE), surface materials on Mars (MSL), and the atmospheres of Venus (Pioneer Venus), Mars (MAVEN) and outer planets (Galileo and Cassini-Huygens). However, the in situ detection of organic compounds on Mars and Titan, coupled with ground-based measurements of amino acids in meteorites and a variety of organics in comets, has underlined the importance of molecular disambiguation in the characterization of high-priority planetary environments. The Mars Organic Molecule Analyzer (MOMA) flight instrument, centered on a linear ion trap, enables the in situ detection of volatile and non-volatile organics, but also the characterization of molecular structures through SWIFT ion isolation/excitation and tandem mass spectrometry (MSn). Like the SAM instrument on MSL, the MOMA investigation also includes a gas chromatograph (GC), thereby enabling the chemical separation of potential isobaric interferences based on retention times. The Linear Ion Trap Mass Spectrometer (LITMS; PI: William Brinckerhoff), developed to TRL 6 via the ROSES MatISSE Program, augments the core MOMA design and adds: expanded mass range (from 20 - 2000 Da); high-temperature evolved gas analysis (up to 1300°C); and, dual polarity detector assemblies (supporting the measurement of negative ions). The LITMS instrument will be tested in the field in 2017 through the Atacama Rover Astrobiology Drilling Studies (ARADS; PI: Brian Glass) ROSES PSTAR award. Following on these advancements, the Advanced Resolution Organic Molecule Analyzer (AROMA; PI: Ricardo Arevalo Jr.), supported through the ROSES PICASSO Program, combines a highly capable MOMA/LITMS-like linear ion trap and the ultrahigh resolution CosmOrbitrap mass analyzer developed by a consortium of five

Studies of Interactions of Positive Helium Ions with Small Neutrals at Temperatures Below 50K

Science.gov (United States)

Schauer, Martin Michael

1990-01-01

Interactions of He^+ ions with small neutrals are important because of their fundamental nature and applicability to other areas of research. In the past, very little work has been done on such systems at very low temperatures (T Boehringer and Arnold (1986) and Johnsen, Chen, and Biondi (1980). A new method of detecting the ions in the trap was also developed and implemented. The Fourier Transform Ion Z-resonance (FTIZR) technique took advantage of an induced coherence in the oscillations of the ions in the trap. This method allowed for measurement of faster ion -neutral reactions. This method was demonstrated by studying the non -resonant charge transfer process ^3He ^+{+}^4He{toatop >=ts}^3He{+}^4He^+. These measurements confirmed that the forward reaction is endothermic by about 1.1 meV.

Optical movie encryption based on a discrete multiple-parameter fractional Fourier transform

International Nuclear Information System (INIS)

Zhong, Zhi; Zhang, Yujie; Shan, Mingguang; Wang, Ying; Zhang, Yabin; Xie, Hong

2014-01-01

A movie encryption scheme is proposed using a discrete multiple-parameter fractional Fourier transform and theta modulation. After being modulated by sinusoidal amplitude grating, each frame of the movie is transformed by a filtering procedure and then multiplexed into a complex signal. The complex signal is multiplied by a pixel scrambling operation and random phase mask, and then encrypted by a discrete multiple-parameter fractional Fourier transform. The movie can be retrieved by using the correct keys, such as a random phase mask, a pixel scrambling operation, the parameters in a discrete multiple-parameter fractional Fourier transform and a time sequence. Numerical simulations have been performed to demonstrate the validity and the security of the proposed method. (paper)

Sympathetic Wigner-function tomography of a dark trapped ion

DEFF Research Database (Denmark)

Mirkhalaf, Safoura; Mølmer, Klaus

2012-01-01

A protocol is provided to reconstruct the Wigner function for the motional state of a trapped ion via fluorescence detection on another ion in the same trap. This “sympathetic tomography” of a dark ion without optical transitions suitable for state measurements is based on the mapping of its...

Two-dimensional fourier transform spectrometer

Science.gov (United States)

DeFlores, Lauren; Tokmakoff, Andrei

2013-09-03

The present invention relates to a system and methods for acquiring two-dimensional Fourier transform (2D FT) spectra. Overlap of a collinear pulse pair and probe induce a molecular response which is collected by spectral dispersion of the signal modulated probe beam. Simultaneous collection of the molecular response, pulse timing and characteristics permit real time phasing and rapid acquisition of spectra. Full spectra are acquired as a function of pulse pair timings and numerically transformed to achieve the full frequency-frequency spectrum. This method demonstrates the ability to acquire information on molecular dynamics, couplings and structure in a simple apparatus. Multi-dimensional methods can be used for diagnostic and analytical measurements in the biological, biomedical, and chemical fields.

Atomic physics of highly charged ions in an electron beam ion trap

International Nuclear Information System (INIS)

Marrs, R.E.

1990-07-01

Two electron beam ion traps are in use at LLNL for the purpose of studying the properties of very highly charged ions and their interactions with electrons. This paper reviews the operation of the traps and discusses recent experiments in three areas: precision transition energy measurements in the limit of very high ion charge, dielectronic recombination measurements for the He-like isoelectronic sequence, and measurements of x-ray polarization. 22 refs., 11 figs., 1 tab

HITRAP: A Facility for Experiments with Trapped Highly Charged Ions

International Nuclear Information System (INIS)

Quint, W.; Dilling, J.; Djekic, S.; Haeffner, H.; Hermanspahn, N.; Kluge, H.-J.; Marx, G.; Moore, R.; Rodriguez, D.; Schoenfelder, J.; Sikler, G.; Valenzuela, T.; Verdu, J.; Weber, C.; Werth, G.

2001-01-01

HITRAP is a planned ion trap facility for capturing and cooling of highly charged ions produced at GSI in the heavy-ion complex of the UNILAC-SIS accelerators and the ESR storage ring. In this facility heavy highly charged ions up to uranium will be available as bare nuclei, hydrogen-like ions or few-electron systems at low temperatures. The trap for receiving and studying these ions is designed for operation at extremely high vacuum by cooling to cryogenic temperatures. The stored highly charged ions can be investigated in the trap itself or can be extracted from the trap at energies up to about 10 keV/q. The proposed physics experiments are collision studies with highly charged ions at well-defined low energies (eV/u), high-accuracy measurements to determine the g-factor of the electron bound in a hydrogen-like heavy ion and the atomic binding energies of few-electron systems, laser spectroscopy of HFS transitions and X-ray spectroscopy

The Fourier transform of tubular densities

International Nuclear Information System (INIS)

Prior, C B; Goriely, A

2012-01-01

We consider the Fourier transform of tubular volume densities, with arbitrary axial geometry and (possibly) twisted internal structure. This density can be used to represent, among others, magnetic flux or the electron density of biopolymer molecules. We consider tubes of both finite radii and unrestricted radius. When there is overlap of the tube structure the net density is calculated using the super-position principle. The Fourier transform of this density is composed of two expressions, one for which the radius of the tube is less than the curvature of the axis and one for which the radius is greater (which must have density overlap). This expression can accommodate an asymmetric density distribution and a tube structure which has non-uniform twisting. In addition we give several simpler expressions for isotropic densities, densities of finite radius, densities which decay at a rate sufficient to minimize local overlap and finally individual surfaces of the tube manifold. These simplified cases can often be expressed as arclength integrals and can be evaluated using a system of first-order ODEs. (paper)

The Fourier transform of tubular densities

KAUST Repository

Prior, C B

2012-05-18

We consider the Fourier transform of tubular volume densities, with arbitrary axial geometry and (possibly) twisted internal structure. This density can be used to represent, among others, magnetic flux or the electron density of biopolymer molecules. We consider tubes of both finite radii and unrestricted radius. When there is overlap of the tube structure the net density is calculated using the super-position principle. The Fourier transform of this density is composed of two expressions, one for which the radius of the tube is less than the curvature of the axis and one for which the radius is greater (which must have density overlap). This expression can accommodate an asymmetric density distribution and a tube structure which has non-uniform twisting. In addition we give several simpler expressions for isotropic densities, densities of finite radius, densities which decay at a rate sufficient to minimize local overlap and finally individual surfaces of the tube manifold. These simplified cases can often be expressed as arclength integrals and can be evaluated using a system of first-order ODEs. © 2012 IOP Publishing Ltd.

On the moments of the Wigner distribution and the fractional Fourier transform

NARCIS (Netherlands)

Alieva, T.; Bastiaans, M.J.; Veen, J.P.

2000-01-01

A Fourier transformation maps a one-dimensional time signal into a one-dimensional frequency function, the signal spectrum. Although the Fourier transform provides the signal's spectral content, it fails to indicate the time location of the spectral components, which is important, for example, when

Screening and identification of steroidal saponins from Anemarrhena asphodeloides employing UPLC tandem triple quadrupole linear ion trap mass spectrometry.

Science.gov (United States)

Xia, Yong-Gang; Guo, Xin-Dong; Liang, Jun; Yang, Bing-You; Kuang, Hai-Xue

2017-09-01

This study presents a practical and valid strategy for the screening and structural characterization of Anemarrhena asphodeloides Bge steroidal saponins (SSs) using ultra-high performance liquid chromatography coupled with triple quadrupole linear ion trap mass spectrometry. The whole analytical protocols integrate four-step procedures in the positive mode: (1) rational deduction of mass fragmentation pathways of A. asphodeloides SSs; (2) untargeted screening of potential A. asphodeloides SSs by multiple-ion monitoring-information-dependent-acquiring-enhanced product ion (MIM-IDA-EPI) scan through reverse phase liquid chromatography; (3) comprehensive construction of an ammoniated precursor ion database by combining untargeted MIM-IDA-EPI scans and data literature; and (4) structural interpretation of targeted A. asphodeloides SSs using MIM-IDA-EPI and multiple reaction monitoring (MRM)-IDA-EPI with an energy-resolved technique. The protocols were used to analyze SSs in A. asphodeloides; of the 87 detected SSs that were unambiguously characterized or tentatively identified, 19 compounds were the first to be reported from A. asphodeloides and 13 ones were characterized as potential new compounds. Accuracy of the analytical procedure was demonstrated by structural identification of three SSs by NMR spectroscopy. The proposed schemes hold an excellent promise in the structural prediction and interpretation of complex SSs from plant medicines by mass spectrometry. Copyright © 2017 Elsevier Inc. All rights reserved.

Technical developments for an upgrade of the LEBIT Penning trap mass spectrometry facility for rare isotopes

Science.gov (United States)

Redshaw, M.; Barquest, B. R.; Bollen, G.; Bustabad, S. E.; Campbell, C. M.; Ferrer, R.; Gehring, A.; Kwiatkowski, A. A.; Lincoln, D. L.; Morrissey, D. J.; Pang, G. K.; Ringle, R.; Schwarz, S.

2011-07-01

The LEBIT (Low Energy Beam and Ion Trap) facility is the only Penning trap mass spectrometry (PTMS) facility to utilize rare isotopes produced via fast-beam fragmentation. This technique allows access to practically all elements lighter than uranium, and in particular enables the production of isotopes that are not available or that are difficult to obtain at isotope separation on-line facilities. The preparation of the high-energy rare-isotope beam produced by projectile fragmentation for low-energy PTMS experiments is achieved by gas stopping to slow down and thermalize the fast-beam ions, along with an rf quadrupole cooler and buncher and rf quadrupole ion guides to deliver the beam to the Penning trap. During its first phase of operation LEBIT has been very successful, and new developments are now underway to access rare isotopes even farther from stability, which requires dealing with extremely short lifetimes and low production rates. These developments aim at increasing delivery efficiency, minimizing delivery and measurement time, and maximizing use of available beam time. They include an upgrade to the gas-stopping station, active magnetic field monitoring and stabilization by employing a miniature Penning trap as a magnetometer, the use of stored waveform inverse Fourier transform (SWIFT) to most effectively remove unwanted ions, and charge breeding.

Technical developments for an upgrade of the LEBIT Penning trap mass spectrometry facility for rare isotopes

International Nuclear Information System (INIS)

Redshaw, M.; Barquest, B. R.; Bollen, G.; Bustabad, S. E.; Campbell, C. M.; Ferrer, R.; Gehring, A.; Kwiatkowski, A. A.; Lincoln, D. L.; Morrissey, D. J.; Pang, G. K.; Ringle, R.; Schwarz, S.

2011-01-01

The LEBIT (Low Energy Beam and Ion Trap) facility is the only Penning trap mass spectrometry (PTMS) facility to utilize rare isotopes produced via fast-beam fragmentation. This technique allows access to practically all elements lighter than uranium, and in particular enables the production of isotopes that are not available or that are difficult to obtain at isotope separation on-line facilities. The preparation of the high-energy rare-isotope beam produced by projectile fragmentation for low-energy PTMS experiments is achieved by gas stopping to slow down and thermalize the fast-beam ions, along with an rf quadrupole cooler and buncher and rf quadrupole ion guides to deliver the beam to the Penning trap. During its first phase of operation LEBIT has been very successful, and new developments are now underway to access rare isotopes even farther from stability, which requires dealing with extremely short lifetimes and low production rates. These developments aim at increasing delivery efficiency, minimizing delivery and measurement time, and maximizing use of available beam time. They include an upgrade to the gas-stopping station, active magnetic field monitoring and stabilization by employing a miniature Penning trap as a magnetometer, the use of stored waveform inverse Fourier transform (SWIFT) to most effectively remove unwanted ions, and charge breeding.

Comparing Laser Desorption Ionization and Atmospheric Pressure Photoionization Coupled to Fourier Transform Ion Cyclotron Resonance Mass Spectrometry To Characterize Shale Oils at the Molecular Level

Science.gov (United States)

Cho, Yunjo; Jin, Jang Mi; Witt, Matthias; Birdwell, Justin E.; Na, Jeong-Geol; Roh, Nam-Sun; Kim, Sunghwan

2013-01-01

Laser desorption ionization (LDI) coupled to Fourier transform ion cyclotron resonance mass spectrometry (FT-ICR MS) was used to analyze shale oils. Previous work showed that LDI is a sensitive ionization technique for assessing aromatic nitrogen compounds, and oils generated from Green River Formation oil shales are well-documented as being rich in nitrogen. The data presented here demonstrate that LDI is effective in ionizing high-double-bond-equivalent (DBE) compounds and, therefore, is a suitable method for characterizing compounds with condensed structures. Additionally, LDI generates radical cations and protonated ions concurrently, the distribution of which depends upon the molecular structures and elemental compositions, and the basicity of compounds is closely related to the generation of protonated ions. This study demonstrates that LDI FT-ICR MS is an effective ionization technique for use in the study of shale oils at the molecular level. To the best of our knowledge, this is the first time that LDI FT-ICR MS has been applied to shale oils.

TMS320C25 Digital Signal Processor For 2-Dimensional Fast Fourier Transform Computation

International Nuclear Information System (INIS)

Ardisasmita, M. Syamsa

1996-01-01

The Fourier transform is one of the most important mathematical tool in signal processing and analysis, which converts information from the time/spatial domain into the frequency domain. Even with implementation of the Fast Fourier Transform algorithms in imaging data, the discrete Fourier transform execution consume a lot of time. Digital signal processors are designed specifically to perform computation intensive digital signal processing algorithms. By taking advantage of the advanced architecture. parallel processing, and dedicated digital signal processing (DSP) instruction sets. This device can execute million of DSP operations per second. The device architecture, characteristics and feature suitable for fast Fourier transform application and speed-up are discussed

The use of Fourier eigen transform to the boundary element method for transient elastodynamic problems

International Nuclear Information System (INIS)

Ji, X.; Chen, Y.M.

1989-01-01

The boundary element method (BEM) is developed from the boundary integral equation method and the discretization techniques. Compared with other numerical method, BEM has been shown to be a versatile and efficient method for a wide variety of engineering problems, including the wave propagation in elastic media. The first formulation and solution of the transient elastodynamic problem by combining BEM and Laplace transform is due to Cruse. Further improvement was achieved by introducing Durbin's method instead of Papoulis method of numerical Laplace inverse transform. However, a great deal of computer time is still needed for the inverse transformation. The alternative integral transform approach is BEM combining with Fourier transform. The numerical Fourier inverse transformation is also computer time consuming, even if the fast Fourier transform is used. In the present paper, the authors use BEM combining with Fourier transform and Fourier eigen transform (FET). The new approach is very attractive in saving on computer time. This paper illustrates the application of FET to BEM of 2-dimensional transient elastodynamic problem. The example of a half plane subjected to a discontinuous boundary load is solved on ELXSI 6400 computer. The CPU time is less than one minute. If Laplace or Fourier transform is adopted, the CPU time will be more than 10 minutes

METHOD AND APPARATUS FOR TRAPPING IONS IN A MAGNETIC FIELD

Science.gov (United States)

Luce, J.S.

1962-04-17

A method and apparatus are described for trapping ions within an evacuated container and within a magnetic field utilizing dissociation and/or ionization of molecular ions to form atomic ions and energetic neutral particles. The atomic ions are magnetically trapped as a result of a change of charge-to- mass ratio. The molecular ions are injected into the container and into the path of an energetic carbon arc discharge which dissociates and/or ionizes a portion of the molecular ions into atomic ions and energetic neutrals. The resulting atomic ions are trapped by the magnetic field to form a circulating beam of atomic ions, and the energetic neutrals pass out of the system and may be utilized in a particle accelerator. (AEC)

Reduction and coding of synthetic aperture radar data with Fourier transforms

Science.gov (United States)

Tilley, David G.

1995-01-01

Recently, aboard the Space Radar Laboratory (SRL), the two roles of Fourier Transforms for ocean image synthesis and surface wave analysis have been implemented with a dedicated radar processor to significantly reduce Synthetic Aperture Radar (SAR) ocean data before transmission to the ground. The object was to archive the SAR image spectrum, rather than the SAR image itself, to reduce data volume and capture the essential descriptors of the surface wave field. SAR signal data are usually sampled and coded in the time domain for transmission to the ground where Fourier Transforms are applied both to individual radar pulses and to long sequences of radar pulses to form two-dimensional images. High resolution images of the ocean often contain no striking features and subtle image modulations by wind generated surface waves are only apparent when large ocean regions are studied, with Fourier transforms, to reveal periodic patterns created by wind stress over the surface wave field. Major ocean currents and atmospheric instability in coastal environments are apparent as large scale modulations of SAR imagery. This paper explores the possibility of computing complex Fourier spectrum codes representing SAR images, transmitting the coded spectra to Earth for data archives and creating scenes of surface wave signatures and air-sea interactions via inverse Fourier transformations with ground station processors.

Trapping behaviour of deuterium ions implanted into tungsten simultaneously with carbon ions

International Nuclear Information System (INIS)

Kobayashi, Makoto; Suzuki, Sachiko; Wang, Wanjing; Kurata, Rie; Kida, Katsuya; Oya, Yasuhisa; Okuno, Kenji; Ashikawa, Naoko; Sagara, Akio; Yoshida, Naoaki

2009-01-01

The trapping behaviour of deuterium ions implanted into tungsten simultaneously with carbon ions was investigated by thermal desorption spectroscopy (TDS) and x-ray photoelectron spectroscopy (XPS). The D 2 TDS spectrum consisted of three desorption stages, namely desorption of deuterium trapped by intrinsic defects, ion-induced defects and carbon with the formation of the C-D bond. Although the deuterium retention trapped by intrinsic defects was almost constant, that by ion-induced defects increased as the ion fluence increased. The retention of deuterium with the formation of the C-D bond was saturated at an ion fluence of 0.5x10 22 D + m -2 , where the major process was changed from the sputtering of tungsten with the formation of a W-C mixture to the formation of a C-C layer, and deuterium retention as the C-D bond decreased. It was concluded that the C-C layer would enhance the chemical sputtering of carbon with deuterium with the formation of CD x and the chemical state of carbon would control the deuterium retention in tungsten under C + -D 2 + implantation.

Imaging properties of the mesooptical Fourier transform microscope for nuclear research emulsion

International Nuclear Information System (INIS)

Bencze, Gy.L.; Soroko, L.M.

1987-01-01

The optical signal transformation in the Mesooptical Fourier Transform Microscope (MFTM) for nuclear emulsion is treated in terms of Fourier Optics. A continuous conversion of the traditional optical microscope into the MFTM is followed. The images of dot-like and straight line objects given by the MFTM are discussed

CrossRef Space-charge effects in Penning ion traps

CERN Document Server

Porobić, T; Breitenfeldt, M; Couratin, C; Finlay, P; Knecht, A; Fabian, X; Friedag, P; Fléchard, X; Liénard, E; Ban, G; Zákoucký, D; Soti, G; Van Gorp, S; Weinheimer, Ch; Wursten, E; Severijns, N

2015-01-01

The influence of space-charge on ion cyclotron resonances and magnetron eigenfrequency in a gas-filled Penning ion trap has been investigated. Off-line measurements with View the MathML source using the cooling trap of the WITCH retardation spectrometer-based setup at ISOLDE/CERN were performed. Experimental ion cyclotron resonances were compared with ab initio Coulomb simulations and found to be in agreement. As an important systematic effect of the WITCH experiment, the magnetron eigenfrequency of the ion cloud was studied under increasing space-charge conditions. Finally, the helium buffer gas pressure in the Penning trap was determined by comparing experimental cooling rates with simulations.

Application of Fourier transforms for microwave radiometric inversions

Science.gov (United States)

Holmes, J. J.; Balanis, C. A.; Truman, W. M.

1975-01-01

Existing microwave radiometer technology now provides a suitable method for remote determination of the ocean surface's absolute brightness temperature. To extract the brightness temperature of the water from the antenna temperature, an unstable Fredholm integral equation of the first kind is solved. Fourier transform techniques are used to invert the integral after it is placed into a cross correlation form. Application and verification of the methods to a two-dimensional modeling of a laboratory wave tank system are included. The instability of the ill-posed Fredholm equation is examined and a restoration procedure is included which smooths the resulting oscillations. With the recent availability and advances of fast Fourier transform (FFT) techniques, the method presented becomes very attractive in the evaluation of large quantities of data.

MSM, an Efficient Workflow for Metabolite Identification Using Hybrid Linear Ion Trap Orbitrap Mass Spectrometer

Science.gov (United States)

Cho, Robert; Huang, Yingying; Schwartz, Jae C.; Chen, Yan; Carlson, Timothy J.; Ma, Ji

2012-05-01

Identification of drug metabolites can often yield important information regarding clearance mechanism, pharmacologic activity, or toxicity for drug candidate molecules. Additionally, the identification of metabolites can provide beneficial structure-activity insight to help guide lead optimization efforts towards molecules with optimal metabolic profiles. There are challenges associated with detecting and identifying metabolites in the presence of complex biological matrices, and new LC-MS technologies have been developed to meet these challenges. In this report, we describe the development of an experimental approach that applies unique features of the hybrid linear ion trap Orbitrap mass spectrometer to streamline in vitro and in vivo metabolite identification experiments. The approach, referred to as MSM, utilizes multiple collision cells, dissociation methods, mass analyzers, and detectors. With multiple scan types and different dissociation modes built into one experimental method, along with flexible post-acquisition analysis options, the MSM workflow offers an attractive option to fast and reliable identification of metabolites in different kinds of in vitro and in vivo samples. The MSM workflow was successfully applied to metabolite identification analysis of verapamil in both in vitro rat hepatocyte incubations and in vivo rat bile samples.

Realization of quantum Fourier transform over ZN

International Nuclear Information System (INIS)

Fu Xiang-Qun; Bao Wan-Su; Li Fa-Da; Zhang Yu-Chao

2014-01-01

Since the difficulty in preparing the equal superposition state of amplitude is 1/√N, we construct a quantile transform of quantum Fourier transform (QFT) over Z N based on the elementary transforms, such as Hadamard transform and Pauli transform. The QFT over Z N can then be realized by the quantile transform, and used to further design its quantum circuit and analyze the requirements for the quantum register and quantum gates. However, the transform needs considerable quantum computational resources and it is difficult to construct a high-dimensional quantum register. Hence, we investigate the design of t-bit quantile transform, and introduce the definition of t-bit semiclassical QFT over Z N . According to probability amplitude, we prove that the transform can be used to realize QFT over Z N and further design its quantum circuit. For this transform, the requirements for the quantum register, the one-qubit gate, and two-qubit gate reduce obviously when compared with those for the QFT over Z N . (general)

Rectangular-to-quincunx Gabor lattice conversion via fractional Fourier transformation

NARCIS (Netherlands)

Bastiaans, M.J.; Leest, van A.J.

1998-01-01

Transformations of Gabor lattices are associated with operations on the window functions that arise in Gabor theory. In particular it is shown that transformation from a rectangular to a quincunx lattice can be associated with fractional Fourier transformation. Since a Gaussian function, which plays

Reconstruction of on-axis lensless Fourier transform digital hologram with the screen division method

Science.gov (United States)

Jiang, Hongzhen; Liu, Xu; Liu, Yong; Li, Dong; Chen, Zhu; Zheng, Fanglan; Yu, Deqiang

2017-10-01

An effective approach for reconstructing on-axis lensless Fourier Transform digital hologram by using the screen division method is proposed. Firstly, the on-axis Fourier Transform digital hologram is divided into sub-holograms. Then the reconstruction result of every sub-hologram is obtained according to the position of corresponding sub-hologram in the hologram reconstruction plane with Fourier transform operation. Finally, the reconstruction image of on-axis Fourier Transform digital hologram can be acquired by the superposition of the reconstruction result of sub-holograms. Compared with the traditional reconstruction method with the phase shifting technology, in which multiple digital holograms are required to record for obtaining the reconstruction image, this method can obtain the reconstruction image with only one digital hologram and therefore greatly simplify the recording and reconstruction process of on-axis lensless Fourier Transform digital holography. The effectiveness of the proposed method is well proved with the experimental results and it will have potential application foreground in the holographic measurement and display field.

Atomic and nuclear physics with stored particles in ion traps

CERN Document Server

Kluge, H J; Herfurth, F; Quint, W

2002-01-01

Trapping and cooling techniques play an increasingly important role in many areas of science. This review concentrates on recent applications of ion traps installed at accelerator facilities to atomic and nuclear physics such as mass spectrometry of radioactive isotopes, weak interaction studies, symmetry tests, determination of fundamental constants, laser spectroscopy, and spectroscopy of highly-charged ions. In addition, ion traps are proven to be extremely efficient devices for (radioactive) ion beam manipulation as, for example, retardation, accumulation, cooling, beam cleaning, charge-breeding, and bunching.

Reducing Motional Decoherence in Ion Traps with Surface Science Methods

Science.gov (United States)

Haeffner, Hartmut

2014-03-01

Many trapped ions experiments ask for low motional heating rates while trapping the ions close to trapping electrodes. However, in practice small ion-electrode distances lead to unexpected high heating rates. While the mechanisms for the heating is still unclear, it is now evident that surface contamination of the metallic electrodes is at least partially responsible for the elevated heating rates. I will discuss heating rate measurements in a microfabricated surface trap complemented with basic surface science studies. We monitor the elemental surface composition of the Cu-Al alloy trap with an Auger spectrometer. After bake-out, we find a strong Carbon and Oxygen contamination and heating rates of 200 quanta/s at 1 MHz trap frequency. After removing most of the Carbon and Oxygen with Ar-Ion sputtering, the heating rates drop to 4 quanta/s. Interestingly, we still measure the decreased heating rate even after the surface oxidized from the background gas throughout a 40-day waiting time in UHV.

Surface-Induced Dissociation of Protein Complexes in a Hybrid Fourier Transform Ion Cyclotron Resonance Mass Spectrometer

Energy Technology Data Exchange (ETDEWEB)

Yan, Jing; Zhou, Mowei; Gilbert, Joshua D.; Wolff, Jeremy J.; Somogyi, Árpád; Pedder, Randall E.; Quintyn, Royston S.; Morrison, Lindsay J.; Easterling, Michael L.; Paša-Tolić, Ljiljana; Wysocki, Vicki H.

2017-01-03

Mass spectrometry continues to develop as a valuable tool in the analysis of proteins and protein complexes. In protein complex mass spectrometry studies, surface-induced dissociation (SID) has been successfully applied in quadrupole time-of-flight (Q-TOF) instruments. SID provides structural information on non-covalent protein complexes that is complementary to other techniques. However, the mass resolution of Q-TOF instruments can limit the information that can be obtained for protein complexes by SID. Fourier transform ion cyclotron resonance mass spectrometry (FT-ICR MS) provides ultrahigh resolution and ultrahigh mass accuracy measurements. In this study, an SID device was designed and successfully installed in a hybrid FT-ICR instrument in place of the standard gas collision cell. The SID-FT-ICR platform has been tested with several protein complex systems (homooligomers, a heterooligomer, and a protein-ligand complex, ranging from 53 kDa to 85 kDa), and the results are consistent with data previously acquired on Q-TOF platforms, matching predictions from known protein interface information. SID fragments with the same m/z but different charge states are well-resolved based on distinct spacing between adjacent isotope peaks, and the addition of metal cations and ligands can also be isotopically resolved with the ultrahigh mass resolution available in FT-ICR.

Pipeline Analyzer using the Fractional Fourier Transform for Engine Control and Satellites Data

Directory of Open Access Journals (Sweden)

Darian M. Onchiș

2011-09-01

Full Text Available The aim of this paper is to present an algorithm for computing the fractional Fourier transform integrated into the pipeline of processing multi-variate and distributed data recorded by the engine control unit (ECU of a car and its satellites. The role of this transform is vital in establishing a time-variant filter and therefore it must be computed in a fast way. But for large scale time series, the application of the discrete fractional Fourier transform involves the computations of a large number of Hermite polynomials of increasingly order. The parallel algorithm presented will optimally compute the discrete Fourier-type transform for any given angle.

Missing texture reconstruction method based on error reduction algorithm using Fourier transform magnitude estimation scheme.

Science.gov (United States)

Ogawa, Takahiro; Haseyama, Miki

2013-03-01

A missing texture reconstruction method based on an error reduction (ER) algorithm, including a novel estimation scheme of Fourier transform magnitudes is presented in this brief. In our method, Fourier transform magnitude is estimated for a target patch including missing areas, and the missing intensities are estimated by retrieving its phase based on the ER algorithm. Specifically, by monitoring errors converged in the ER algorithm, known patches whose Fourier transform magnitudes are similar to that of the target patch are selected from the target image. In the second approach, the Fourier transform magnitude of the target patch is estimated from those of the selected known patches and their corresponding errors. Consequently, by using the ER algorithm, we can estimate both the Fourier transform magnitudes and phases to reconstruct the missing areas.

Parallel Transport Quantum Logic Gates with Trapped Ions.

Science.gov (United States)

de Clercq, Ludwig E; Lo, Hsiang-Yu; Marinelli, Matteo; Nadlinger, David; Oswald, Robin; Negnevitsky, Vlad; Kienzler, Daniel; Keitch, Ben; Home, Jonathan P

2016-02-26

We demonstrate single-qubit operations by transporting a beryllium ion with a controlled velocity through a stationary laser beam. We use these to perform coherent sequences of quantum operations, and to perform parallel quantum logic gates on two ions in different processing zones of a multiplexed ion trap chip using a single recycled laser beam. For the latter, we demonstrate individually addressed single-qubit gates by local control of the speed of each ion. The fidelities we observe are consistent with operations performed using standard methods involving static ions and pulsed laser fields. This work therefore provides a path to scalable ion trap quantum computing with reduced requirements on the optical control complexity.

Self-Fourier functions and coherent laser combination

International Nuclear Information System (INIS)

Corcoran, C J; Pasch, K A

2004-01-01

The Gaussian and Comb functions are generally quoted as being the two basic functions that are their own Fourier transforms. In 1991, Caola presented a recipe for generating functions that are their own Fourier transforms by symmetrizing any transformable function and then adding its own Fourier transform to it. In this letter, we present a new method for generating a set of functions that are exactly their own Fourier transforms, and which have direct application to laser cavity design for a wide variety of applications. The generated set includes the Gaussian and Comb functions as special cases and forms a continuous bridge of functions between them. The new generating method uses the Gaussian and Comb functions as bases and does not rely on the Fourier operator itself. This self-Fourier function promises to be particularly useful in high-power laser design through coherent laser beam combination. Although these results are presented in a single dimension as with a linear array, the results are equally valid in two dimensions. (letter to the editor)

New focus on Fourier optics techniques

NARCIS (Netherlands)

Calvo, M.L.; Alieva, T.; Bastiaans, M.J.; Rodrigo Martín-Romo, J.A.; Rodríguez Merlo, D.; Vlad, V.I.

2004-01-01

We present a short overview on the application of fractional cyclic and linear canonical transformations to optical signal processing and dedicate some of the discussions to the particular features found in the fractional Fourier transform domain.

Nonlinear Fourier transforms for the sine-Gordon equation in the quarter plane

Science.gov (United States)

Huang, Lin; Lenells, Jonatan

2018-03-01

Using the Unified Transform, also known as the Fokas method, the solution of the sine-Gordon equation in the quarter plane can be expressed in terms of the solution of a matrix Riemann-Hilbert problem whose definition involves four spectral functions a , b , A , B. The functions a (k) and b (k) are defined via a nonlinear Fourier transform of the initial data, whereas A (k) and B (k) are defined via a nonlinear Fourier transform of the boundary values. In this paper, we provide an extensive study of these nonlinear Fourier transforms and the associated eigenfunctions under weak regularity and decay assumptions on the initial and boundary values. The results can be used to determine the long-time asymptotics of the sine-Gordon quarter-plane solution via nonlinear steepest descent techniques.