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Zonnios M, Levinsen J, Parish MM, Pollock FA, Modi K. Signatures of Quantum Chaos in an Out-of-Time-Order Tensor. PHYSICAL REVIEW LETTERS 2022; 128:150601. [PMID: 35499886 DOI: 10.1103/physrevlett.128.150601] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/05/2021] [Revised: 02/26/2022] [Accepted: 03/02/2022] [Indexed: 06/14/2023]
Abstract
Motivated by the famous ink-drop experiment, where ink droplets are used to determine the chaoticity of a fluid, we propose an experimentally implementable method for measuring the scrambling capacity of quantum processes. Here, a system of interest interacts with a small quantum probe whose dynamical properties identify the chaoticity of the system. Specifically, we propose a fully quantum version of the out-of-time-order correlator-which we term the out-of-time-order tensor-whose correlations offer clear information theoretic meanings about the chaoticity of a process. We illustrate the utility of the out-of-time-order tensor as a signature of chaos using random unitary processes as well as in the quantum kicked rotor, where the chaoticity is tunable.
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Affiliation(s)
- Magdalini Zonnios
- School of Physics and Astronomy, Monash University, Clayton, Victoria 3800, Australia
| | - Jesper Levinsen
- School of Physics and Astronomy, Monash University, Clayton, Victoria 3800, Australia
| | - Meera M Parish
- School of Physics and Astronomy, Monash University, Clayton, Victoria 3800, Australia
| | - Felix A Pollock
- School of Physics and Astronomy, Monash University, Clayton, Victoria 3800, Australia
| | - Kavan Modi
- School of Physics and Astronomy, Monash University, Clayton, Victoria 3800, Australia
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2
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Li M, Xiao Y, Tao Y, Gao Y, Tong P. Exploring the effects of phase modulation on the dynamics of the kicked rotor systems. Phys Rev E 2022; 105:014212. [PMID: 35193226 DOI: 10.1103/physreve.105.014212] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/14/2020] [Accepted: 01/05/2022] [Indexed: 06/14/2023]
Abstract
Inspired by the recent experimental progress in the time-driven phase transition in quantum chaos, we investigate comprehensively the energy diffusion of a kicked rotor in the presence of phase modulation. In the classical case, we found that there always exists anomalous diffusion as long as the phase is modulated periodically and changes by 0 or π from kick to kick. On the contrary, for quasiperiodic and random phase modulation, anomalous diffusion is suppressed. On the other hand, in the quantum case, there exist only ballistic energy diffusion and dynamical localization in the standard and periodically shifted cases, while random phase modulation destroys the quantum coherence and totally suppresses the dynamical localization. Furthermore, the quasiperiodic phase modulation is an intermediate phase between the standard case and the random one. In both the classical and quantum cases, quasiperiodic phase modulation is inequivalent to random phase modulation at large kicking times (>10^{3}), thus caution has to be taken when dealing with these two kinds of phase modulation in experiments.
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Affiliation(s)
- Mengyao Li
- Center for Quantum Transport and Thermal Energy Science, Jiangsu Key Lab on Opto-Electronic Technology, School of Physics and Technology, Nanjing Normal University, Nanjing 210023, China
| | - Yingying Xiao
- Center for Quantum Transport and Thermal Energy Science, Jiangsu Key Lab on Opto-Electronic Technology, School of Physics and Technology, Nanjing Normal University, Nanjing 210023, China
| | - Yongchun Tao
- Center for Quantum Transport and Thermal Energy Science, Jiangsu Key Lab on Opto-Electronic Technology, School of Physics and Technology, Nanjing Normal University, Nanjing 210023, China
| | - Yi Gao
- Center for Quantum Transport and Thermal Energy Science, Jiangsu Key Lab on Opto-Electronic Technology, School of Physics and Technology, Nanjing Normal University, Nanjing 210023, China
| | - Peiqing Tong
- School of Physics and Technology, Jiangsu Key Laboratory for Numerical Simulation of Large Scale Complex Systems, Nanjing Normal University, Nanjing 210023, China
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3
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Abstract
We analytically investigate the analogy between a standard continuous-time quantum walk in one dimension and the evolution of the quantum kicked rotor at quantum resonance conditions. We verify that the obtained probability distributions are equal for a suitable choice of the kick strength of the rotor. We further discuss how to engineer the evolution of the walk for dynamically preparing experimentally relevant states. These states are important for future applications of the atom-optics kicked rotor for the realization of ratchets and quantum search.
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4
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Impact of Lattice Vibrations on the Dynamics of a Spinor Atom-Optics Kicked Rotor. CONDENSED MATTER 2019. [DOI: 10.3390/condmat4010010] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
We investigate the effect of amplitude and phase noise on the dynamics of a discrete-time quantum walk and its related evolution. Our findings underline the robustness of the motion with respect to these noise sources, and can explain the stability of quantum walks that has recently been observed experimentally. This opens the road to measure topological properties of an atom-optics double kicked rotor with an additional internal spin degree of freedom.
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5
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Zhao WL, Fu LB, Liu J. Nonlinearity effects on the directed momentum current. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:022907. [PMID: 25215799 DOI: 10.1103/physreve.90.022907] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/25/2013] [Indexed: 06/03/2023]
Abstract
We investigate the quantum transport dynamics governed by the nonlinear Schrödinger equation with a periodically-δ-kicking potential and discover the emergence of a directed current in momentum space. With the increase of nonlinearity, we find strikingly that the momentum current decreases, reverses, and finally vanishes, indicating that the quantum transport can be effectively manipulated through adjusting the nonlinearity. The underlying dynamic mechanism is uncovered and some important implications are addressed.
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Affiliation(s)
- Wen-Lei Zhao
- School of Science, Jiangxi University of Science and Technology, Ganzhou 341000, China and National Laboratory of Science and Technology on Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing 100088, China and HEDPS, Center for Applied Physics and Technology, Peking University, Beijing 100084, China
| | - Li-Bin Fu
- National Laboratory of Science and Technology on Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing 100088, China and HEDPS, Center for Applied Physics and Technology, Peking University, Beijing 100084, China
| | - Jie Liu
- National Laboratory of Science and Technology on Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing 100088, China and HEDPS, Center for Applied Physics and Technology, Peking University, Beijing 100084, China
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6
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Abb M, Guarneri I, Wimberger S. Pseudoclassical theory for fidelity of nearly resonant quantum rotors. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 80:035206. [PMID: 19905170 DOI: 10.1103/physreve.80.035206] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/03/2009] [Indexed: 05/28/2023]
Abstract
Using a semiclassical ansatz we analytically predict for the fidelity of delta-kicked rotors the occurrence of revivals and the disappearance of intermediate revival peaks arising from the breaking of a symmetry in the initial conditions. A numerical verification of the predicted effects is given and experimental ramifications are discussed.
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Affiliation(s)
- Martina Abb
- Institut für Theoretische Physik, Universität Heidelberg, Philosophenweg 19, 69120 Heidelberg, Germany
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7
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Lepers M, Zehnlé V, Garreau JC. Tracking quasiclassical chaos in ultracold boson gases. PHYSICAL REVIEW LETTERS 2008; 101:144103. [PMID: 18851533 DOI: 10.1103/physrevlett.101.144103] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/05/2008] [Indexed: 05/26/2023]
Abstract
We study the dynamics of an ultracold boson gas in a lattice submitted to a constant force. We track the route of the system towards chaos created by the many-body-induced nonlinearity and show that relevant information can be extracted from an experimentally accessible quantity, the gas mean position. The threshold nonlinearity for the appearance of chaotic behavior is deduced from Kolmogorov-Arnold-Moser arguments and agrees with the value obtained by calculating the associated Lyapunov exponent.
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Affiliation(s)
- Maxence Lepers
- Laboratoire de Physique des Lasers, Atomes et Molécules, Université des Sciences et Technologies de Lille, CNRS, F-59655 Villeneuve d'Ascq Cedex, France
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Sadgrove M, Wimberger S, Parkins S, Leonhardt R. Scaling law and stability for a noisy quantum system. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 78:025206. [PMID: 18850885 DOI: 10.1103/physreve.78.025206] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/16/2008] [Indexed: 05/26/2023]
Abstract
We show that a scaling law exists for the near-resonant dynamics of cold kicked atoms in the presence of a randomly fluctuating pulse amplitude. Analysis of a quasiclassical phase-space representation of the quantum system with noise allows a new scaling law to be deduced. The scaling law and associated stability are confirmed by comparison with quantum simulations and experimental data.
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Affiliation(s)
- Mark Sadgrove
- CREST, Japan Science and Technology Agency, Kawaguchi, Saitama 332-0012, Japan
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Kenfack A, Gong J, Pattanayak AK. Controlling the ratchet effect for cold atoms. PHYSICAL REVIEW LETTERS 2008; 100:044104. [PMID: 18352279 DOI: 10.1103/physrevlett.100.044104] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/05/2007] [Indexed: 05/26/2023]
Abstract
Low-order quantum resonances manifested by directed currents have been realized with cold atoms. Here we show that by increasing the strength of an experimentally achievable delta-kicking ratchet potential, quantum resonances of a very high order may naturally emerge and can induce larger ratchet currents than low-order resonances, with the underlying classical limit being fully chaotic. The results offer a means of controlling quantum transport of cold atoms.
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Affiliation(s)
- Anatole Kenfack
- Max-Planck-Institut für Physik Komplexer Systeme, Nöthnitzer Strasse 38, D-01187 Dresden, Germany
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10
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Wang J, Monteiro TS, Fishman S, Keating JP, Schubert R. Fractional variant Planck's over 2pi scaling for quantum kicked rotors without Cantori. PHYSICAL REVIEW LETTERS 2007; 99:234101. [PMID: 18233366 DOI: 10.1103/physrevlett.99.234101] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/20/2007] [Revised: 07/24/2007] [Indexed: 05/25/2023]
Abstract
Previous studies of quantum delta-kicked rotors have found momentum probability distributions with a typical width (localization length L) characterized by fractional variant Planck's over 2pi scaling; i.e., L approximately variant Planck's over 2pi;{2/3} in regimes and phase-space regions close to "golden-ratio" cantori. In contrast, in typical chaotic regimes, the scaling is integer, L approximately variant Planck's over 2pi;{-1}. Here we consider a generic variant of the kicked rotor, the random-pair-kicked particle, obtained by randomizing the phases every second kick; it has no Kol'mogorov-Arnol'd-Moser mixed-phase-space structures, such as golden-ratio cantori, at all. Our unexpected finding is that, over comparable phase-space regions, it also has fractional scaling, but L approximately variant Planck's over 2pi;{-2/3}. A semiclassical analysis indicates that the variant Planck's over 2pi;{2/3} scaling here is of quantum origin and is not a signature of classical cantori.
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Affiliation(s)
- J Wang
- Temasek Laboratories, National University of Singapore, 117542 Singapore
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11
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Behinaein G, Ramareddy V, Ahmadi P, Summy GS. Exploring the phase space of the quantum delta-kicked accelerator. PHYSICAL REVIEW LETTERS 2006; 97:244101. [PMID: 17280289 DOI: 10.1103/physrevlett.97.244101] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/15/2006] [Indexed: 05/13/2023]
Abstract
We experimentally explore the underlying pseudoclassical phase space structure of the quantum delta-kicked accelerator. This was achieved by exposing a Bose-Einstein condensate to the spatially corrugated potential created by pulses of an off-resonant standing light wave. For the first time quantum accelerator modes were realized in such a system. By utilizing the narrow momentum distribution of the condensate we were able to observe the discrete momentum state structure of a quantum accelerator mode and also to directly measure the size of the structures in the phase space.
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Affiliation(s)
- G Behinaein
- Department of Physics, Oklahoma State University, Stillwater, Oklahoma 74078-3072, USA
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12
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Stocklin MMA, Monteiro TS. Classical momentum diffusion in double-delta-kicked particles. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 74:026210. [PMID: 17025528 DOI: 10.1103/physreve.74.026210] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/11/2006] [Indexed: 05/12/2023]
Abstract
We investigate the classical chaotic diffusion of atoms subjected to pairs of closely spaced pulses ("kicks") from standing waves of light (the 2delta-KP ). Recent experimental studies with cold atoms implied an underlying classical diffusion of a type very different from the well-known paradigm of Hamiltonian chaos, the standard map. The kicks in each pair are separated by a small time interval E<<1, which together with the kick strength K, characterizes the transport. Phase space for the 2delta-KP is partitioned into momentum "cells" partially separated by momentum-trapping regions where diffusion is slow. We present here an analytical derivation of the classical diffusion for a 2delta-KP including all important correlations which were used to analyze the experimental data. We find an asymptotic (t-->infinity) regime of "hindered" diffusion: while for the standard map the diffusion rate, for K>>1 , D approximately K(2)/2[1-2J(2)(K)...] oscillates about the uncorrelated rate D(0)=K(2)/2, we find analytically, that the 2delta-KP can equal, but never diffuses faster than, a random walk rate. We argue this is due to the destruction of the important classical "accelerator modes" of the standard map. We analyze the experimental regime 0.1 less or approximately KE less or approximately 1 , where quantum localization lengths L approximately Planck's (-0.75) are affected by fractal cell boundaries. We find an approximate asymptotic diffusion rate D proportional to K(3)E, in correspondence to a D proportional to K(3) regime in the standard map associated with the "golden-ratio" cantori.
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Affiliation(s)
- M M A Stocklin
- Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom
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13
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Lundh E. Directed transport and Floquet analysis for a periodically kicked wave packet at a quantum resonance. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 74:016212. [PMID: 16907182 DOI: 10.1103/physreve.74.016212] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/09/2006] [Revised: 05/05/2006] [Indexed: 05/11/2023]
Abstract
The dynamics of a kicked quantum mechanical wave packet at a quantum resonance is studied in the framework of Floquet analysis. It is seen how a directed current can be created out of a homogeneous initial state at certain resonances in an asymmetric potential. The almost periodic parameter dependence of the current is found to be connected with level crossings in the Floquet spectrum.
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Affiliation(s)
- Emil Lundh
- Department of Physics, Royal Institute of Technology, AlbaNova, SE-106 91 Stockholm, Sweden
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14
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Ryu C, Andersen MF, Vaziri A, d'Arcy MB, Grossman JM, Helmerson K, Phillips WD. High-order quantum resonances observed in a periodically kicked Bose-Einstein condensate. PHYSICAL REVIEW LETTERS 2006; 96:160403. [PMID: 16712208 DOI: 10.1103/physrevlett.96.160403] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/10/2006] [Indexed: 05/09/2023]
Abstract
We have observed high-order quantum resonances in a realization of the quantum delta-kicked rotor, using Bose-condensed Na atoms subjected to a pulsed standing wave of laser light. These resonances occur for pulse intervals that are rational fractions of the Talbot time, and are characterized by ballistic momentum transfer to the atoms. The condensate's narrow momentum distribution not only permits the observation of the quantum resonances at 3/4 and 1/3 of the Talbot time, but also allows us to study scaling laws for the resonance width in quasimomentum and pulse interval.
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Affiliation(s)
- C Ryu
- Atomic Physics Division, National Institute of Science and Technology, Gaithersburg, Maryland 20899-8424, USA
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15
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Carlo GG, Benenti G, Shepelyansky DL. Dissipative quantum chaos: transition from wave packet collapse to explosion. PHYSICAL REVIEW LETTERS 2005; 95:164101. [PMID: 16241802 DOI: 10.1103/physrevlett.95.164101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/08/2005] [Indexed: 05/05/2023]
Abstract
Using the quantum trajectories approach, we study the quantum dynamics of a dissipative chaotic system described by the Zaslavsky map. For strong dissipation the quantum wave function in the phase space collapses onto a compact packet which follows classical chaotic dynamics and whose area is proportional to the Planck constant. At weak dissipation the exponential instability of quantum dynamics on the Ehrenfest time scale dominates and leads to wave packet explosion. The transition from collapse to explosion takes place when the dissipation time scale exceeds the Ehrenfest time. For integrable nonlinear dynamics the explosion practically disappears leaving place to collapse.
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Affiliation(s)
- Gabriel G Carlo
- Center for Nonlinear and Complex Systems, Università degli Studi dell'Insubria and Istituto Nazionale per la Fisica della Materia, Unità di Como, Italy
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Sadgrove M, Wimberger S, Parkins S, Leonhardt R. Ballistic and localized transport for the atom optics kicked rotor in the limit of a vanishing kicking period. PHYSICAL REVIEW LETTERS 2005; 94:174103. [PMID: 15904296 DOI: 10.1103/physrevlett.94.174103] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/08/2004] [Indexed: 05/02/2023]
Abstract
We present mean energy measurements for the atom optics kicked rotor as the kicking period tends to zero. A narrow resonance is observed marked by quadratic energy growth, in parallel with a complete freezing of the energy absorption away from the resonance peak. Both phenomena are explained by classical means, taking proper account of the atoms' initial momentum distribution.
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Affiliation(s)
- Mark Sadgrove
- Department of Physics, University of Auckland, Private Bag 92019, Auckland, New Zealand
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Wimberger S, Mannella R, Morsch O, Arimondo E. Resonant nonlinear quantum transport for a periodically kicked bose condensate. PHYSICAL REVIEW LETTERS 2005; 94:130404. [PMID: 15903976 DOI: 10.1103/physrevlett.94.130404] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/13/2004] [Indexed: 05/02/2023]
Abstract
Our realistic numerical results show that the fundamental and higher-order quantum resonances of the delta-kicked rotor are observable in state-of-the-art experiments with a Bose condensate in a shallow harmonic trap, kicked by a spatially periodic optical lattice. For stronger confinement, interaction-induced destruction of the resonant motion of the kicked harmonic oscillator is predicted.
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Affiliation(s)
- Sandro Wimberger
- INFM, Dipartimento di Fisica E. Fermi, Unversità di Pisa, Largo Pontecorvo 3, 56127 Pisa, Italy
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Lundh E, Wallin M. Ratchet effect for cold atoms in an optical lattice. PHYSICAL REVIEW LETTERS 2005; 94:110603. [PMID: 15903839 DOI: 10.1103/physrevlett.94.110603] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/07/2004] [Indexed: 05/02/2023]
Abstract
The possibility of realizing a directed current for a quantum particle in a flashing asymmetric potential is investigated. It is found that quantum resonances, where the value of the effective Planck constant is equal to an integer or half-integer multiple of pi, give rise to a directed current. The effect should be readily observable in experiments.
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Affiliation(s)
- Emil Lundh
- Department of Physics, Royal Institute of Technology, AlbaNova, SE-106 91 Stockholm, Sweden
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