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Maurya SS, Kannan JB, Patel K, Dutta P, Biswas K, Mangaonkar J, Santhanam MS, Rapol UD. Interplay between quantum diffusion and localization in the atom-optics kicked rotor. Phys Rev E 2022; 106:034207. [PMID: 36266807 DOI: 10.1103/physreve.106.034207] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/19/2022] [Accepted: 08/04/2022] [Indexed: 06/16/2023]
Abstract
Atom-optics kicked rotor represents an experimentally reliable version of the paradigmatic quantum kicked rotor system. In this system, a periodic sequence of kicks are imparted to the cold atomic cloud. After a short initial diffusive phase the cloud settles down to a stationary state due to the onset of dynamical localization. In this paper, to explore the interplay between localized and diffusive phases, we experimentally implement a modification to this system in which the sign of the kick sequence is flipped after every M kicks. This is achieved in our experiment by allowing free evolution for half the Talbot time after every M kicks. Depending on the value of M, this modified system displays a combination of enhanced diffusion followed by asymptotic localization. This is explained as resulting from two competing processes-localization induced by standard kicked rotor type kicks, and diffusion induced by the half Talbot time evolution. The experimental and numerical simulations agree with one another. The evolving states display localized but nonexponential wave function profiles. This provides another route to quantum control in the kicked rotor class of systems.
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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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Wang WY, Zhao WL. Protected quantum coherence by gain and loss in a noisy quantum kicked rotor. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 34:025403. [PMID: 34587610 DOI: 10.1088/1361-648x/ac2b68] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/20/2021] [Accepted: 09/29/2021] [Indexed: 06/13/2023]
Abstract
We study the effects of non-Hermiticity on quantum coherence via a noisy quantum kicked rotor (NQKR). The random noise comes from the fluctuations in kick amplitude at each time. The non-Hermitian driving indicates the imaginary kicking potential, representing the environment-induced atom gain and loss. In the absence of gain and loss, the random noise destroys quantum coherence manifesting dynamical localization, which leads to classical diffusion. Interestingly, in the presence of non-Hermitian kicking potential, the occurrence of dynamical localization is highly sensitive to the gain and loss, manifesting the restoration of quantum coherence. Using the inverse participation ratio arguments, we numerically obtain a phase diagram of the classical diffusion and dynamical localization on the parameter plane of noise amplitude and non-Hermitian driving strength. With the help of analysis on the corresponding quasieigenstates, we achieve insight into dynamical localization, and uncover that the origin of the localization is interference between multiple quasi-eigenstates of the quantum kicked rotor. We further propose an experimental scheme to realize the NQKR in a dissipative cold atomic gas, which paves the way for future experimental investigation of an NQKR and its anomalous non-Hermitian properties.
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Affiliation(s)
- Wen-Yuan Wang
- Key Laboratory of Atomic and Molecular Physics & Functional Materials of Gansu Province, College of Physics and Electronic Engineering, Northwest Normal University, Lanzhou 730070, People's Republic of China
- Beijing Computational Science Research Center, Beijing 100193, People's Republic of China
| | - Wen-Lei Zhao
- School of Science, Jiangxi University of Science and Technology, Ganzhou 341000, People's Republic of China
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4
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Longhi S. Maryland model in optical waveguide lattices. OPTICS LETTERS 2021; 46:637-640. [PMID: 33528428 DOI: 10.1364/ol.414389] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/06/2020] [Accepted: 01/06/2021] [Indexed: 06/12/2023]
Abstract
The Maryland model was introduced more than 30 years ago as an integrable model of localization by aperiodic order. Even though it is quite popular and is rich with fascinating mathematical properties, this model has so far remained quite artificial, as compared to other models displaying dynamical localization like the periodically kicked quantum rotator or the Aubry-André model. Here we suggest that light propagation in a polygonal optical waveguide lattice provides a photonic realization of the Maryland model and enables us to observe a main prediction of this model, namely fragility of wave localization in the commensurate potential limit.
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Rylands C, Rozenbaum EB, Galitski V, Konik R. Many-Body Dynamical Localization in a Kicked Lieb-Liniger Gas. PHYSICAL REVIEW LETTERS 2020; 124:155302. [PMID: 32357048 DOI: 10.1103/physrevlett.124.155302] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/31/2019] [Accepted: 03/19/2020] [Indexed: 06/11/2023]
Abstract
The kicked rotor system is a textbook example of how classical and quantum dynamics can drastically differ. The energy of a classical particle confined to a ring and kicked periodically will increase linearly in time whereas in the quantum version the energy saturates after a finite number of kicks. The quantum system undergoes Anderson localization in angular-momentum space. Conventional wisdom says that in a many-particle system with short-range interactions the localization will be destroyed due to the coupling of widely separated momentum states. Here we provide evidence that for an interacting one-dimensional Bose gas, the Lieb-Liniger model, the dynamical localization can persist at least for an unexpectedly long time.
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Affiliation(s)
- Colin Rylands
- Joint Quantum Institute and Condensed Matter Theory Center, University of Maryland, College Park, Maryland 20742, USA
| | - Efim B Rozenbaum
- Joint Quantum Institute and Condensed Matter Theory Center, University of Maryland, College Park, Maryland 20742, USA
| | - Victor Galitski
- Joint Quantum Institute and Condensed Matter Theory Center, University of Maryland, College Park, Maryland 20742, USA
| | - Robert Konik
- Condensed Matter Physics & Materials Science Division, Brookhaven National Laboratory, Upton, New York 11973-5000, USA
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6
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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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7
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Notarnicola S, Iemini F, Rossini D, Fazio R, Silva A, Russomanno A. From localization to anomalous diffusion in the dynamics of coupled kicked rotors. Phys Rev E 2018; 97:022202. [PMID: 29548167 DOI: 10.1103/physreve.97.022202] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/26/2017] [Indexed: 06/08/2023]
Abstract
We study the effect of many-body quantum interference on the dynamics of coupled periodically kicked systems whose classical dynamics is chaotic and shows an unbounded energy increase. We specifically focus on an N-coupled kicked rotors model: We find that the interplay of quantumness and interactions dramatically modifies the system dynamics, inducing a transition between energy saturation and unbounded energy increase. We discuss this phenomenon both numerically and analytically through a mapping onto an N-dimensional Anderson model. The thermodynamic limit N→∞, in particular, always shows unbounded energy growth. This dynamical delocalization is genuinely quantum and very different from the classical one: Using a mean-field approximation, we see that the system self-organizes so that the energy per site increases in time as a power law with exponent smaller than 1. This wealth of phenomena is a genuine effect of quantum interference: The classical system for N≥2 always behaves ergodically with an energy per site linearly increasing in time. Our results show that quantum mechanics can deeply alter the regularity or ergodicity properties of a many-body-driven system.
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Affiliation(s)
| | - Fernando Iemini
- Abdus Salam ICTP, Strada Costiera 11, I-34151 Trieste, Italy
| | - Davide Rossini
- Dipartimento di Fisica, Università di Pisa and INFN, Largo Pontecorvo 3, I-56127 Pisa, Italy
| | - Rosario Fazio
- Abdus Salam ICTP, Strada Costiera 11, I-34151 Trieste, Italy
- NEST, Scuola Normale Superiore & Istituto Nanoscienze-CNR, I-56126 Pisa, Italy
| | | | - Angelo Russomanno
- Abdus Salam ICTP, Strada Costiera 11, I-34151 Trieste, Italy
- NEST, Scuola Normale Superiore & Istituto Nanoscienze-CNR, I-56126 Pisa, Italy
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8
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Bitter M, Milner V. Experimental Observation of Dynamical Localization in Laser-Kicked Molecular Rotors. PHYSICAL REVIEW LETTERS 2016; 117:144104. [PMID: 27740833 DOI: 10.1103/physrevlett.117.144104] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/17/2016] [Indexed: 06/06/2023]
Abstract
The periodically kicked rotor is a paradigm system for studying quantum effects on classically chaotic dynamics. The wave function of the quantum rotor localizes in angular momentum space, similarly to Anderson localization of the electronic wave function in disordered solids. Here, we observe dynamical localization in a system of true quantum rotors by subjecting nitrogen molecules to periodic sequences of femtosecond pulses. Exponential distribution of the molecular angular momentum-the hallmark of dynamical localization-is measured directly by means of coherent Raman scattering. We demonstrate the suppressed rotational energy growth with the number of laser kicks and study the dependence of the localization length on the kick strength. Because of its quantum coherent nature, both timing and amplitude noise are shown to destroy the localization and revive the diffusive growth of energy.
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Affiliation(s)
- M Bitter
- Department of Physics & Astronomy and The Laboratory for Advanced Spectroscopy and Imaging Research (LASIR), The University of British Columbia, V6T 1Z1 Vancouver, Canada
| | - V Milner
- Department of Physics & Astronomy and The Laboratory for Advanced Spectroscopy and Imaging Research (LASIR), The University of British Columbia, V6T 1Z1 Vancouver, Canada
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9
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Wimberger S. Applications of fidelity measures to complex quantum systems. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2016; 374:20150153. [PMID: 27140967 PMCID: PMC4855397 DOI: 10.1098/rsta.2015.0153] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 09/16/2015] [Indexed: 06/05/2023]
Abstract
We revisit fidelity as a measure for the stability and the complexity of the quantum motion of single-and many-body systems. Within the context of cold atoms, we present an overview of applications of two fidelities, which we call static and dynamical fidelity, respectively. The static fidelity applies to quantum problems which can be diagonalized since it is defined via the eigenfunctions. In particular, we show that the static fidelity is a highly effective practical detector of avoided crossings characterizing the complexity of the systems and their evolutions. The dynamical fidelity is defined via the time-dependent wave functions. Focusing on the quantum kicked rotor system, we highlight a few practical applications of fidelity measurements in order to better understand the large variety of dynamical regimes of this paradigm of a low-dimensional system with mixed regular-chaotic phase space.
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Affiliation(s)
- Sandro Wimberger
- Dipartimento di Fisica e Scienze della Terra, Università di Parma, Via G.P. Usberti 7/a, 43124 Parma, Italy INFN, Sezione di Milano Bicocca, Gruppo Collegato di Parma, Italy Institut für Theoretische Physik, Philosophenweg 12, Universität Heidelberg, 69120 Heidelberg, Germany
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10
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Chen Y, Tian C. Planck's quantum-driven integer quantum Hall effect in chaos. PHYSICAL REVIEW LETTERS 2014; 113:216802. [PMID: 25479514 DOI: 10.1103/physrevlett.113.216802] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/20/2014] [Indexed: 06/04/2023]
Abstract
We find in a canonical chaotic system, the kicked spin-1/2 rotor, a Planck's quantum(he)-driven phenomenon bearing a close analogy to the integer quantum Hall effect but of chaos origin. Specifically, the rotor's energy growth is unbounded ("metallic" phase) for a discrete set of critical values of he, but otherwise bounded ("insulating" phase). The latter phase is topological and characterized by a quantum number ("quantized Hall conductance"). The number jumps by unity whenever he passes through each critical value as it decreases. Our findings indicate that rich topological quantum phenomena can emerge from chaos.
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Affiliation(s)
- Yu Chen
- Institute for Advanced Study, Tsinghua University, Beijing 100084, People's Republic of China
| | - Chushun Tian
- Institute for Advanced Study, Tsinghua University, Beijing 100084, People's Republic of China
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11
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Gadway B, Reeves J, Krinner L, Schneble D. Evidence for a quantum-to-classical transition in a pair of coupled quantum rotors. PHYSICAL REVIEW LETTERS 2013; 110:190401. [PMID: 23705694 DOI: 10.1103/physrevlett.110.190401] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/21/2012] [Revised: 11/08/2012] [Indexed: 06/02/2023]
Abstract
The understanding of how classical dynamics can emerge in closed quantum systems is a problem of fundamental importance. Remarkably, while classical behavior usually arises from coupling to thermal fluctuations or random spectral noise, it may also be an innate property of certain isolated, periodically driven quantum systems. Here, we experimentally realize the simplest such system, consisting of two coupled, kicked quantum rotors, by subjecting a coherent atomic matter wave to two periodically pulsed, incommensurate optical lattices. Momentum transport in this system is found to be radically different from that in a single kicked rotor, with a breakdown of dynamical localization and the emergence of classical diffusion. Our observation, which confirms a long-standing prediction for many-dimensional quantum-chaotic systems, sheds new light on the quantum-classical correspondence.
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Affiliation(s)
- Bryce Gadway
- Department of Physics and Astronomy, Stony Brook University, Stony Brook, New York 11794-3800, USA
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12
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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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13
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Wang J, García-García AM. Anderson transition in a three-dimensional kicked rotor. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 79:036206. [PMID: 19392034 DOI: 10.1103/physreve.79.036206] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/02/2008] [Indexed: 05/27/2023]
Abstract
We investigate Anderson localization in a three-dimensional (3D) kicked rotor. By a finite-size scaling analysis we identify a mobility edge for a certain value of the kicking strength k = k(c) . For k > k(c) dynamical localization does not occur, all eigenstates are delocalized and the spectral correlations are well described by Wigner-Dyson statistics. This can be understood by mapping the kicked rotor problem onto a 3D Anderson model (AM) where a band of metallic states exists for sufficiently weak disorder. Around the critical region k approximately k(c) we carry out a detailed study of the level statistics and quantum diffusion. In agreement with the predictions of the one parameter scaling theory (OPT) and with previous numerical simulations, the number variance is linear, level repulsion is still observed, and quantum diffusion is anomalous with <p(2)> proportional t(2/3) . We note that in the 3D kicked rotor the dynamics is not random but deterministic. In order to estimate the differences between these two situations we have studied a 3D kicked rotor in which the kinetic term of the associated evolution matrix is random. A detailed numerical comparison shows that the differences between the two cases are relatively small. However in the deterministic case only a small set of irrational periods was used. A qualitative analysis of a much larger set suggests that deviations between the random and the deterministic kicked rotor can be important for certain choices of periods. Heuristically it is expected that localization effects will be weaker in a nonrandom potential since destructive interference will be less effective to arrest quantum diffusion. However we have found that certain choices of irrational periods enhance Anderson localization effects.
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Affiliation(s)
- Jiao Wang
- Temasek Laboratories, National University of Singapore, 117542 Singapore
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14
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Carlo GG, Spina ME. Thermal effects on chaotic directed transport. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 79:026212. [PMID: 19391825 DOI: 10.1103/physreve.79.026212] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/03/2008] [Indexed: 05/27/2023]
Abstract
We study a chaotic ratchet system under the influence of a thermal environment. By direct integration of the Lindblad equation we are able to analyze its behavior for a wide range of couplings with the environment, and for different finite temperatures. We observe that the enhancement of the classical and quantum currents due to temperature depend strongly on the specific properties of the system. This makes it difficult to extract universal behaviors. We have also found that there is an analogy between the effects of the classical thermal noise and those of the finite h size. These results open many possibilities for their testing and implementation in kicked Bose-Einstein condensates and cold atoms experiments.
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Affiliation(s)
- Gabriel G Carlo
- Departamento de Física, CNEA, Libertador 8250, C1429BNP Buenos Aires, Argentina
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15
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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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16
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Weiss C, Teichmann N. Differences between mean-field dynamics and N-particle quantum dynamics as a signature of entanglement. PHYSICAL REVIEW LETTERS 2008; 100:140408. [PMID: 18518013 DOI: 10.1103/physrevlett.100.140408] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/27/2007] [Indexed: 05/26/2023]
Abstract
A Bose-Einstein condensate in a tilted double-well potential under the influence of time-periodic potential differences is investigated in the regime where the mean-field (Gross-Pitaevskii) dynamics become chaotic. For some parameters near stable regions, even averaging over several condensate oscillations does not remove the differences between mean-field and N-particle results. While introducing decoherence via piecewise deterministic processes reduces those differences, they are due to the emergence of mesoscopic entangled states in the chaotic regime.
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Affiliation(s)
- Christoph Weiss
- Laboratoire Kastler Brossel, Ecole Normale Supérieure, Université Pierre et Marie-Curie-Paris 6, 24 rue Lhomond, CNRS, F-75231 Paris Cedex 05, France
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17
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Kanem JF, Maneshi S, Partlow M, Spanner M, Steinberg AM. Observation of high-order quantum resonances in the kicked rotor. PHYSICAL REVIEW LETTERS 2007; 98:083004. [PMID: 17359095 DOI: 10.1103/physrevlett.98.083004] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/15/2006] [Indexed: 05/14/2023]
Abstract
Quantum resonances in the kicked rotor are characterized by a dramatically increased energy absorption rate, in stark contrast to the momentum localization generally observed. These resonances occur when the scaled Planck's constant Planck's [over ]=r/s 4pi, for any integers r and s. However, only the variant Planck's [over ]=r2pi resonances are easily observable. We have observed high-order quantum resonances (s>2) utilizing a sample of low energy, noncondensed atoms and a pulsed optical standing wave. Resonances are observed for variant Planck's [over ]=r/16 4pi for integers r=2-6. Quantum numerical simulations suggest that our observation of high-order resonances indicate a larger coherence length (i.e., coherence between different wells) than expected from an initially thermal atomic sample.
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Affiliation(s)
- J F Kanem
- Centre for Quantum Information & Quantum Control, University of Toronto, 60 St. George Street, Toronto, Ontario, Canada M5S 1A7
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18
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Sokolov VV, Benenti G, Casati G. Quantum dephasing and decay of classical correlation functions in chaotic systems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 75:026213. [PMID: 17358411 DOI: 10.1103/physreve.75.026213] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/19/2005] [Revised: 10/11/2006] [Indexed: 05/14/2023]
Abstract
We discuss the dephasing induced by internal classical chaotic motion in the absence of any external environment. To this end an extension of fidelity for mixed states is introduced, which we name allegiance. Such a quantity directly accounts for quantum interference and is measurable in a Ramsey interferometry experiment. We show that in the semiclassical limit the decay of the allegiance is exactly expressed, due to the dephasing, in terms of an appropriate classical correlation function. Our results are derived analytically for the case of a nonlinear driven oscillator and then numerically confirmed for the kicked rotor model.
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Affiliation(s)
- Valentin V Sokolov
- Center for Nonlinear and Complex Systems, Università degli Studi dell'Insubria, Via Valleggio 11, 22100 Como, Italy
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19
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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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20
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Boness T, Bose S, Monteiro TS. Entanglement and dynamics of spin chains in periodically pulsed magnetic fields: accelerator modes. PHYSICAL REVIEW LETTERS 2006; 96:187201. [PMID: 16712391 DOI: 10.1103/physrevlett.96.187201] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/23/2006] [Indexed: 05/09/2023]
Abstract
We study the dynamics of a single excitation in a Heisenberg spin-chain subjected to a sequence of periodic pulses from an external, parabolic, magnetic field. We show that, for experimentally reasonable parameters, a pair of counterpropagating coherent states is ejected from the center of the chain. We find an illuminating correspondence with the quantum time evolution of the well-known paradigm of quantum chaos, the quantum kicked rotor. From this we can analyze the entanglement production and interpret the ejected coherent states as a manifestation of the so-called "accelerator modes" of a classically chaotic system.
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Affiliation(s)
- T Boness
- Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom
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21
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Poletti D, Fu L, Liu J, Li B. Quantum resonance and antiresonance for a periodically kicked Bose-Einstein condensate in a one-dimensional box. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 73:056203. [PMID: 16803022 DOI: 10.1103/physreve.73.056203] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/19/2005] [Revised: 03/07/2006] [Indexed: 05/10/2023]
Abstract
We investigate the quantum dynamics of a periodically kicked Bose-Einstein condensate (BEC) confined in a one-dimensional (1D) box both numerically and theoretically, emphasizing on the phenomena of quantum resonance and antiresonance. The quantum resonant behavior of BEC is different from the single particle case but the antiresonance condition (Tau = 2pi and alpha = 0) is not affected by the atomic interaction. For the antiresonance case, the nonlinearity (atom interaction) causes the transition between oscillation and quantum beating. For the quantum resonance case, because of the coherence of BEC, the energy increase is oscillating and the rate is dramatically affected by the many-body interaction. We also discuss the relation between the quantum resonant behavior and the Kolmogorov-Arnold-Moser (KAM) or non-KAM property of the corresponding classical system.
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Affiliation(s)
- Dario Poletti
- Department of Physics and Center for Computational Science and Engineering, National University of Singapore, Republic of Singapore
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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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23
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Buchleitner A, d'Arcy MB, Fishman S, Gardiner SA, Guarneri I, Ma ZY, Rebuzzini L, Summy GS. Quantum accelerator modes from the Farey tree. PHYSICAL REVIEW LETTERS 2006; 96:164101. [PMID: 16712235 DOI: 10.1103/physrevlett.96.164101] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/21/2005] [Indexed: 05/09/2023]
Abstract
We show that mode locking finds a purely quantum nondissipative counterpart in atom-optical quantum accelerator modes. These modes are formed by exposing cold atoms to periodic kicks in the direction of the gravitational field. They are anchored to generalized Arnol'd tongues, parameter regions where driven nonlinear classical systems exhibit mode locking. A hierarchy for the rational numbers known as the Farey tree provides an ordering of the Arnol'd tongues and hence of experimentally observed accelerator modes.
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Affiliation(s)
- A Buchleitner
- Max-Planck-Institut für Physik komplexer Systeme, D-01187 Dresden, Germany
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24
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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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25
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Abstract
▪ Abstract Coherent control of atomic and molecular processes has been a rapidly developing field. Applications of coherent control to large and complex molecular systems are expected to encounter the effects of chaos in the underlying classical dynamics, i.e., quantum chaos. Hence, recent work has focused on examining control in model chaotic systems. This work is reviewed, with an emphasis on a variety of new quantum phenomena that are of interest to both areas of quantum chaos and coherent control.
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Affiliation(s)
- Jiangbin Gong
- Department of Chemistry and The James Franck Institute, The University of Chicago, Chicago, Illinois 60637, USA.
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26
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Carlo GG, Benenti G, Casati G, Shepelyansky DL. Quantum ratchets in dissipative chaotic systems. PHYSICAL REVIEW LETTERS 2005; 94:164101. [PMID: 15904228 DOI: 10.1103/physrevlett.94.164101] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/27/2004] [Revised: 01/19/2005] [Indexed: 05/02/2023]
Abstract
Using the method of quantum trajectories, we study a quantum chaotic dissipative ratchet appearing for particles in a pulsed asymmetric potential in the presence of a dissipative environment. The system is characterized by directed transport emerging from a quantum strange attractor. This model exhibits, in the limit of small effective Planck constant, a transition from quantum to classical behavior, in agreement with the correspondence principle. We also discuss parameter values suitable for the implementation of the quantum ratchet effect with cold atoms in optical lattices.
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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, Via Valleggio 11, 22100 Como, Italy
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27
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Rebuzzini L, Wimberger S, Artuso R. Delocalized and resonant quantum transport in nonlinear generalizations of the kicked rotor model. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 71:036220. [PMID: 15903559 DOI: 10.1103/physreve.71.036220] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/12/2004] [Indexed: 05/02/2023]
Abstract
We analyze the effects of a nonlinear cubic perturbation on the delta-kicked rotor. We consider two different models, in which the nonlinear term acts either in the position or in the momentum representation. We numerically investigate the modifications induced by the nonlinearity in the quantum transport in both localized and resonant regimes and a comparison between the results for the two models is presented. Analyzing the momentum distributions and the increase of the mean square momentum, we find that the quantum resonances asymptotically are very stable with respect to nonlinear perturbation of the rotor's phase evolution. For an intermittent time regime, the nonlinearity even enhances the resonant quantum transport, leading to superballistic motion.
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Affiliation(s)
- Laura Rebuzzini
- Center for Nonlinear and Complex Systems and Dipartimento di Fisica e Matematica, Università dell'Insubria, Via Valleggio 11, 22100 Como, Italy
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28
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Sadgrove M, Mullins T, Parkins S, Leonhardt R. Deviations from early-time quasilinear behavior for the atom-optics kicked rotor near the classical limit. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 71:027201. [PMID: 15783458 DOI: 10.1103/physreve.71.027201] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/03/2004] [Indexed: 05/24/2023]
Abstract
We present experimental measurements of the mean energy for the atom-optics kicked rotor after just two kicks. The energy is found to deviate from the quasilinear value for small kicking periods. The observed deviation is explained by recent theoretical results which include the effect of a nonuniform initial momentum distribution, previously applied only to systems using much colder atoms than ours.
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Affiliation(s)
- Mark Sadgrove
- Department of Physics, The University of Auckland, Private Bag 92019, Auckland, New Zealand
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29
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Jones PH, Stocklin MM, Hur G, Monteiro TS. Atoms in double-delta-kicked periodic potentials: chaos with long-range correlations. PHYSICAL REVIEW LETTERS 2004; 93:223002. [PMID: 15601086 DOI: 10.1103/physrevlett.93.223002] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/30/2004] [Indexed: 05/24/2023]
Abstract
We report an experimental and theoretical study of the dynamics of cold atoms subjected to pairs of closely spaced pulses in an optical lattice. For all previously studied delta-kicked systems, chaotic classical dynamics shows diffusion with short-time (2- or 3-kick) correlations; here, chaotic diffusion combines with new types of long-ranged global correlations, between all kick pairs, which control transport through trapping regions in phase space. Correlations are studied in the classical regime, but the diffusive behavior observed in experiment depends on the quantum dynamical localization.
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Affiliation(s)
- P H Jones
- Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom
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30
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Carvalho ARR, Buchleitner A. Web-assisted tunneling in the kicked harmonic oscillator. PHYSICAL REVIEW LETTERS 2004; 93:204101. [PMID: 15600927 DOI: 10.1103/physrevlett.93.204101] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/08/2004] [Indexed: 05/24/2023]
Abstract
We show that heating of harmonically trapped ions by periodic delta kicks is dramatically enhanced at isolated values of the Lamb-Dicke parameter. At these values, quasienergy eigenstates localized on island structures undergo avoided crossings with extended web states.
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Affiliation(s)
- André R R Carvalho
- Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Strasse 38, D-01187 Dresden, Germany
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31
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Duffy GJ, Parkins S, Müller T, Sadgrove M, Leonhardt R, Wilson AC. Experimental investigation of early-time diffusion in the quantum kicked rotor using a Bose-Einstein condensate. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 70:056206. [PMID: 15600727 DOI: 10.1103/physreve.70.056206] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/21/2004] [Revised: 06/01/2004] [Indexed: 05/24/2023]
Abstract
We report measurements of the early-time momentum diffusion for the atom-optical delta-kicked rotor. In this experiment a Bose-Einstein condensate provides a source of ultracold atoms with an ultranarrow initial momentum distribution, which is then subjected to periodic pulses (or "kicks") using an intense far-detuned optical standing wave. We characterize the effect of varying the effective Planck's constant for the system, while keeping all other parameters fixed. The observed behavior includes both quantum resonances (ballistic energy growth) and antiresonances (re-establishment of the initial state). Our experimental results are compared with theoretical predictions.
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Affiliation(s)
- G J Duffy
- Department of Physics, University of Otago, P.O. Box 56, Dunedin, New Zealand
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32
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Wójcik A, Łuczak T, Kurzyński P, Grudka A, Bednarska M. Quasiperiodic dynamics of a quantum walk on the line. PHYSICAL REVIEW LETTERS 2004; 93:180601. [PMID: 15525144 DOI: 10.1103/physrevlett.93.180601] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/16/2004] [Indexed: 05/24/2023]
Abstract
We study the dynamics of a generalization of a quantum coin walk on the line, which is a natural model for a diffusion modified by quantum or interference effects. In particular, our results provide surprisingly simple explanations for recurrence phenomena observed by Bouwmeester et al. [Phys. Rev. A 61, 13410 (1999)]] in their optical Galton board experiment, and a description of a stroboscopic quantum walk given by Buerschaper and Burnett [quant-ph/0406039] through numerical simulations. We also provide heuristic explanations for the behavior of our model which show, in particular, that its dynamics can be viewed as a discrete version of Bloch oscillations.
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Affiliation(s)
- Antoni Wójcik
- Faculty of Physics, Adam Mickiewicz University, Umultowska 85, 61-614 Poznań, Poland
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33
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Ma ZY, d'Arcy MB, Gardiner SA. Gravity-sensitive quantum dynamics in cold atoms. PHYSICAL REVIEW LETTERS 2004; 93:164101. [PMID: 15524992 DOI: 10.1103/physrevlett.93.164101] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/10/2003] [Revised: 06/24/2004] [Indexed: 05/24/2023]
Abstract
We subject a falling cloud of cold cesium atoms to periodic kicks from a sinusoidal potential created by a vertical standing wave of laser light. By controllably accelerating the potential, we show quantum accelerator mode dynamics to be highly sensitive to the effective gravitational acceleration when close to specific, resonant values. This quantum sensitivity to a control parameter is reminiscent of that associated with classical chaos and promises techniques for precision measurement.
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Affiliation(s)
- Z-Y Ma
- Clarendon Laboratory, Department of Physics, University of Oxford, Oxford OX1 3PU, United Kingdom
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34
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Sadgrove M, Hilliard A, Mullins T, Parkins S, Leonhardt R. Observation of robust quantum resonance peaks in an atom optics kicked rotor with amplitude noise. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 70:036217. [PMID: 15524622 DOI: 10.1103/physreve.70.036217] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/14/2004] [Revised: 06/18/2004] [Indexed: 05/24/2023]
Abstract
The effect of pulse train noise on the quantum resonance peaks of the atom optics kicked rotor is investigated experimentally. Quantum resonance peaks in the late time mean energy of the atoms are found to be surprisingly robust against all levels of noise applied to the kicking amplitude, while even small levels of noise on the kicking period lead to their destruction. The robustness to amplitude noise of the resonance peak and of the fall-off in mean energy to either side of this peak are explained in terms of the occurrence of stable, epsilon classical dynamics [Nonlinearity 16, 1381 (2003)]] around each quantum resonance.
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Affiliation(s)
- Mark Sadgrove
- Department of Physics, The University of Auckland, Private Bag 92019, Auckland, New Zealand
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35
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Gong J, Brumer P. Directed anomalous diffusion without a biased field: a ratchet accelerator. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 70:016202. [PMID: 15324147 DOI: 10.1103/physreve.70.016202] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/20/2004] [Indexed: 05/24/2023]
Abstract
Directed classical current that increases linearly with time without using a biased external field is obtained in a simple model Hamiltonian system derived from a modified kicked rotor model, by breaking the spatial symmetry of the transporting regular islands in the classical phase space. A parallel study of the corresponding quantum dynamics suggests that although quantum coherence effects suppress the directed current and can even induce a current reversal, directed quantum current that increases linearly with time can nonetheless be realized in a quantum system that is far from the classical limit.
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Affiliation(s)
- Jiangbin Gong
- Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Canada M5S 3H6
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36
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Wimberger S, Guarneri I, Fishman S. Classical scaling theory of quantum resonances. PHYSICAL REVIEW LETTERS 2004; 92:084102. [PMID: 14995777 DOI: 10.1103/physrevlett.92.084102] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/09/2003] [Indexed: 05/24/2023]
Abstract
The quantum resonances occurring with delta-kicked particles are studied with the help of a fictitious classical limit, establishing a direct correspondence between the nearly resonant quantum motion and the classical resonances of a related system. A scaling law which characterizes the structure of the resonant peaks is derived and numerically demonstrated.
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Affiliation(s)
- Sandro Wimberger
- Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Strasse 38, D-01187 Dresden, Germany
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37
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Zhang C, Liu J, Raizen MG, Niu Q. Transition to instability in a kicked bose-einstein condensate. PHYSICAL REVIEW LETTERS 2004; 92:054101. [PMID: 14995306 DOI: 10.1103/physrevlett.92.054101] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/30/2003] [Indexed: 05/24/2023]
Abstract
A periodically kicked ring of a Bose-Einstein condensate is considered as a nonlinear generalization of the quantum kicked rotor. For weak interactions between atoms, periodic motion (antiresonance) becomes quasiperiodic (quantum beating) but remains stable. There exists a critical strength of interactions beyond which quasiperiodic motion becomes chaotic, resulting in an instability of the condensate manifested by exponential growth in the number of noncondensed atoms. Similar behavior is observed for dynamically localized states (essentially quasiperiodic motions), where stability remains for weak interactions but is destroyed by strong interactions.
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Affiliation(s)
- Chuanwei Zhang
- Department of Physics, and Center for Nonlinear Dynamics, The University of Texas, Austin, Texas 78712-1081, USA
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38
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D'Arcy MB, Godun RM, Summy GS, Guarneri I, Wimberger S, Fishman S, Buchleitner A. Decoherence as a probe of coherent quantum dynamics. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 69:027201. [PMID: 14995591 DOI: 10.1103/physreve.69.027201] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/05/2003] [Indexed: 05/24/2023]
Abstract
The effect of decoherence, induced by spontaneous emission, on the dynamics of cold atoms periodically kicked by an optical lattice is experimentally and theoretically studied. Ideally, the mean energy growth is essentially unaffected by weak decoherence, but the resonant momentum distributions are fundamentally altered. It is shown that experiments are inevitably sensitive to certain nontrivial features of these distributions, in a way that explains the puzzle of the observed enhancement of resonances by decoherence [Phys. Rev. Lett. 87, 074102 (2001)]. This clarifies both the nature of the coherent evolution, and the way in which decoherence disrupts it.
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Affiliation(s)
- Michael B D'Arcy
- Clarendon Laboratory, Department of Physics, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
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39
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Gong J, Wörner HJ, Brumer P. Control of dynamical localization. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003; 68:056202. [PMID: 14682866 DOI: 10.1103/physreve.68.056202] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/25/2003] [Indexed: 11/07/2022]
Abstract
Control over the quantum dynamics of chaotic kicked rotor systems is demonstrated. Specifically, control over a number of quantum coherent phenomena is achieved by a simple modification of the kicking field. These include the enhancement of the dynamical localization length, the introduction of classical anomalous diffusion assisted control for systems far from the semiclassical regime, and the observation of a variety of strongly nonexponential line shapes for dynamical localization. The results provide excellent examples of controlled quantum dynamics in a system that is classically chaotic and offer opportunities to explore quantum fluctuations and correlations in quantum chaos.
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Affiliation(s)
- Jiangbin Gong
- Chemical Physics Theory Group, Department of Chemistry, University of Toronto, 80 St. George Street, Toronto, Ontario, Canada M5S 3H6
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40
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Jonckheere T, Isherwood MR, Monteiro TS. Chaotic filtering of moving atoms in pulsed optical lattices by control of dynamical localization. PHYSICAL REVIEW LETTERS 2003; 91:253003. [PMID: 14754111 DOI: 10.1103/physrevlett.91.253003] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/17/2003] [Indexed: 05/24/2023]
Abstract
We propose a mechanism for a velocity-selective device which would allow packets of cold atoms traveling in one direction through a pulsed optical lattice to pass undisturbed, while dispersing atoms traveling in the opposite direction. The mechanism is generic and straightforward: for a simple quantum kicked rotor pulsed with unequal periods, the quantum suppression of momentum diffusion (dynamical localization) yields momentum localization lengths L which are no longer isotropic, as in the standard case, but vary smoothly and controllably with initial momentum.
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Affiliation(s)
- T Jonckheere
- Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom
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41
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Gong J, Wörner HJ, Brumer P. Coherent manipulation of quantum delta-kicked dynamics: faster-than-classical anomalous diffusion. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003; 68:026209. [PMID: 14525086 DOI: 10.1103/physreve.68.026209] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/25/2003] [Indexed: 11/07/2022]
Abstract
Large transporting regular islands are found in the classical phase space of a modified kicked rotor system in which the kicking potential is reversed after every two kicks. The corresponding quantum system, for a variety of system parameters and over long time scales, is shown to display energy absorption that is significantly faster than that associated with the underlying classical anomalous diffusion. The results are of interest to areas of both quantum chaos and quantum control.
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Affiliation(s)
- Jiangbin Gong
- Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Canada M5S 3H6
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42
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Schlunk S, D'Arcy MB, Gardiner SA, Summy GS. Experimental observation of high-order quantum accelerator modes. PHYSICAL REVIEW LETTERS 2003; 90:124102. [PMID: 12688874 DOI: 10.1103/physrevlett.90.124102] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/02/2002] [Indexed: 05/24/2023]
Abstract
Using a freely falling cloud of cold cesium atoms periodically kicked by pulses from a vertical standing wave of laser light, we present the first experimental observation of high-order quantum accelerator modes. This confirms the recent prediction by Fishman, Guarneri, and Rebuzzini [Phys. Rev. Lett. 89, 084101 (2002)]]. We also show how these accelerator modes can be identified with the stable regions of phase space in a classical-like chaotic system, despite their intrinsically quantum origin.
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Affiliation(s)
- S Schlunk
- Clarendon Laboratory, Department of Physics, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
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43
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Schlunk S, D'Arcy MB, Gardiner SA, Cassettari D, Godun RM, Summy GS. Signatures of quantum stability in a classically chaotic system. PHYSICAL REVIEW LETTERS 2003; 90:054101. [PMID: 12633358 DOI: 10.1103/physrevlett.90.054101] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/20/2002] [Indexed: 05/24/2023]
Abstract
We experimentally and numerically investigate the quantum accelerator mode dynamics of an atom optical realization of the quantum delta-kicked accelerator, whose classical dynamics are chaotic. Using a Ramsey-type experiment, we observe interference, demonstrating that quantum accelerator modes are formed coherently. We construct a link between the behavior of the evolution's fidelity and the phase space structure of a recently proposed pseudoclassical map, and thus account for the observed interference visibilities.
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Affiliation(s)
- S Schlunk
- Clarendon Laboratory, Department of Physics, University of Oxford, Parks Road, United Kingdom
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44
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Szriftgiser P, Ringot J, Delande D, Garreau JC. Observation of sub-Fourier resonances in a quantum-chaotic system. PHYSICAL REVIEW LETTERS 2002; 89:224101. [PMID: 12485069 DOI: 10.1103/physrevlett.89.224101] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/21/2002] [Indexed: 05/24/2023]
Abstract
We experimentally show that the response of a quantum-chaotic system can display resonance lines sharper than the inverse of the excitation duration. This allows us to discriminate two neighboring frequencies with a resolution nearly 40 times better than the limit set by the Fourier inequality. Furthermore, numerical studies indicate that there is no limit, but the loss of signal, to this resolution, opening ways for the development of sub-Fourier quantum-chaotic signal processing.
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Affiliation(s)
- Pascal Szriftgiser
- Laboratoire de Physique des Lasers, Atomes et Molécules, UMR CNRS 8523, Centre d'Etudes et de Recherches Laser et Applications, Université des Sciences et Technologies de Lille, F-59655 Villeneuve d'Ascq Cedex, France
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45
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Monteiro TS, Dando PA, Hutchings NAC, Isherwood MR. Proposal for a chaotic ratchet using cold atoms in optical lattices. PHYSICAL REVIEW LETTERS 2002; 89:194102. [PMID: 12443118 DOI: 10.1103/physrevlett.89.194102] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/05/2002] [Indexed: 05/24/2023]
Abstract
We investigate a new type of quantum ratchet which may be realized by cold atoms in a double-well optical lattice, pulsed with unequal periods. The classical dynamics is chaotic and we find the classical diffusion rate D is asymmetric in momentum up to a finite time t(r). The quantum behavior produces a corresponding asymmetry in the momentum distribution which is "frozen-in" by dynamical localization provided the break time t(*)>or=t(r). We conclude that the cold atom ratchets require Db/ variant Planck's over 2pi approximately 1, where b is a small deviation from period-one pulses.
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Affiliation(s)
- T S Monteiro
- Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom
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46
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Daley AJ, Parkins AS. Early time diffusion for the quantum kicked rotor with narrow initial momentum distributions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2002; 66:056210. [PMID: 12513589 DOI: 10.1103/physreve.66.056210] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/27/2002] [Indexed: 05/24/2023]
Abstract
We investigate analytically and numerically early-time momentum diffusion rates for the delta-kicked rotor across the quantum to classical transition, i.e., as increased total system action produces more macroscopic dynamics. For sufficiently narrow initial momentum distributions we find a rich structure of resonances in these diffusion rates as a function of the effective Planck's constant. Our study is set in the physical context of the atom optics kicked rotor, and numerical simulations confirm that the resonances persist with kicks of finite duration and with other typical experimental imperfections, such as spontaneous emission noise. Our results should be testable in experiments where narrow initial momentum distributions are prepared using, for example, velocity selective Raman transitions or Bose-Einstein condensates.
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Affiliation(s)
- A J Daley
- Department of Physics, University of Auckland, Private Bag 92019, Auckland, New Zealand.
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47
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Fishman S, Guarneri I, Rebuzzini L. Stable quantum resonances in atom optics. PHYSICAL REVIEW LETTERS 2002; 89:084101. [PMID: 12190467 DOI: 10.1103/physrevlett.89.084101] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/10/2002] [Indexed: 05/23/2023]
Abstract
A theory for stabilization of quantum resonances by a mechanism similar to one leading to classical resonances in nonlinear systems is presented. It explains recent surprising experimental results, obtained for cold cesium atoms when driven in the presence of gravity, and leads to further predictions. The theory makes use of invariance properties of the system allowing for separation into independent kicked rotor problems. The analysis relies on a fictitious classical limit where the small parameter is not Planck's constant, but rather the detuning from the frequency that is resonant in the absence of gravity.
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Bienert M, Haug F, Schleich WP, Raizen MG. State reconstruction of the kicked rotor. PHYSICAL REVIEW LETTERS 2002; 89:050403. [PMID: 12144430 DOI: 10.1103/physrevlett.89.050403] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/08/2002] [Indexed: 05/23/2023]
Abstract
We propose two experimentally feasible methods based on atom interferometry to measure the quantum state of the kicked rotor.
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Affiliation(s)
- M Bienert
- Abteilung für Quantenphysik, Universität Ulm, Albert-Einstein-Allee 11, D-89069 Ulm, Germany
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Gong J, Brumer P. Phase control of nonadiabaticity-induced quantum chaos in an optical lattice. PHYSICAL REVIEW LETTERS 2002; 88:203001. [PMID: 12005561 DOI: 10.1103/physrevlett.88.203001] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/27/2001] [Indexed: 05/23/2023]
Abstract
The qualitative nature (i.e., integrable vs chaotic) of the translational dynamics of a three-level atom in an optical lattice is shown to be controllable by varying the relative laser phase of two standing-wave lasers. Control is explained in terms of the nonadiabatic transition between optical potentials and the corresponding regular-to-chaotic transition in mixed classical-quantum dynamics. The results are of interest to both areas of coherent control and quantum chaos.
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Affiliation(s)
- Jiangbin Gong
- Chemical Physics Theory Group, University of Toronto, Toronto, Canada M5S 3H6
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d'Arcy MB, Godun RM, Oberthaler MK, Summy GS, Burnett K, Gardiner SA. Approaching classicality in quantum accelerator modes through decoherence. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2001; 64:056233. [PMID: 11736080 DOI: 10.1103/physreve.64.056233] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/23/2000] [Revised: 08/07/2001] [Indexed: 05/23/2023]
Abstract
We describe measurements of the mean energy of an ensemble of laser-cooled atoms in an atom optical system in which the cold atoms, falling freely under gravity, receive approximate delta-kicks from a pulsed standing wave of laser light. We call this system a "delta-kicked accelerator." Additionally, we can counteract the effect of gravity by appropriate shifting of the position of the standing wave, which restores the dynamics of the standard delta-kicked rotor. The presence of gravity (delta-kicked accelerator) yields quantum phenomena, quantum accelerator modes, which are markedly different from those in the case for which gravity is absent (delta-kicked rotor). Quantum accelerator modes result in a much higher rate of increase in the mean energy of the system than is found in its classical analog. When gravity is counteracted, the system exhibits the suppression of the momentum diffusion characteristic of dynamical localization. The effect of noise is examined and a comparison is made with simulations of both quantum-mechanical and classical versions of the system. We find that the introduction of noise results in the restoration of several signatures of classical behavior, although significant quantum features remain.
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Affiliation(s)
- M B d'Arcy
- Clarendon Laboratory, Department of Physics, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
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