Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review Letters

Experimental Study of Quantum Dynamics in a Regime of Classical Anomalous Diffusion

Bruce G. Klappauf, Windell H. Oskay, D. Steck, Mark G. Raizen

Published Nov 9, 1998• 72 citations
Publisher

Abstract

We measure the momentum of cold cesium atoms in a periodically pulsed standing wave of light. This system is an experimental realization of the quantum kicked rotor. The momentum diffusion in the (chaotic) classical analog of this system is typically suppressed by quantum localization. We find, however, that for certain pulse amplitudes where the classical system exhibits anomalous diffusion, our momentum distributions are not exponentially localized. We observe a predicted correspondence between the classical and quantum energy growth as a function of pulse amplitude and period.

DOI
10.1103/physrevlett.81.4044

Related papers

An experimental realization of the quantum -kicked rotor

Mark G. Raizen, F L Moore, J C Robinson +2 more

We study experimentally quantum effects in atomic motion for a classically chaotic regime. A standing wave is pulsed on periodically in time, and the resulting atomic momentum is measured. Momentum grows diffusively until the quantum break time, after which dynamical localization is observed. Quantum resonances are observed for certain pulse durations.

Quantum and Semiclassical Optics Journal of the European Optical Society Part B•Jun 1, 1996•12 citations

Dimensional effects on dynamical localization with cold cesium atoms

Jean Ringot, P. Szrfitgiser, Jean Claude Garreau +1 more

Summary form only given. Dynamical localization is one of the signatures of quantum chaos most intensely studied in recent years. These studies rely on the experimental realization of a kicked rotor by placing cold atoms in a far detuned, periodically driven, stationary wave. For a set of parameters such that the classical limit of such a system shows a chaotic diffusive motion in the momentum space, quantum interferences have been shown to suppress the chaotic diffusion in the quantum case. The momentum distribution then presents a characteristic double exponential form. We have performed an experiment in which dynamical localization is studied in the presence of a stationary wave driven by two series of pulses that can have commensurable or incommensurable frequencies, which can be shown to be formally equivalent to perform the experiment in two dimensions. We have thus shown that localization is still observed when the two frequencies are commensurable, but that the classical diffusion in momentum space persists for a much longer time if the frequencies are incommensurable.

Conference on Lasers and Electro-Optics•Aug 29, 2005•0 citations

Quantitative study of amplitude noise effects on dynamical localization

D. Steck, Valery Milner, Windell H. Oskay +1 more

We study the motion of cold atoms in a pulsed standing wave of light, which constitutes an experimental realization of the quantum kicked rotor. This system exhibits dynamical localization, where quantum effects suppress classical momentum diffusion. As we introduce amplitude noise, the coherences that lead to localization are destroyed, resulting in restored diffusion. For high levels of noise, we find that the experiment is well described by a classical model, suggesting that classical behavior has been restored. We present a detailed experimental study of this noise-induced transition from quantum to classical behavior.

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics•Sep 1, 2000•71 citations

Quantum Signatures of Anomalous Diffusion in Atom Optics

Bruce G. Klappauf, Windell H. Oskay, D. Steck +1 more

It is well established that classical chaotic motion is suppressed by quantum mechanics. The paradigm theoretical system has been the ?-kicked rotor, where the suppression manifests itself as dynamical localization. This effect is saturation of momentum growth after the quantum break time, with a resulting exponentially localized distribution. Classical analyses of this system have also identified regimes of anomalous diffusion, characterized by “Levy-type” flights in phase space [1]. This behavior is considerably more complex than simple diffusion and has attracted much interest in recent years. The quantum system was predicted to exhibit an increase in localization length near regions of anomalous diffusion [2], and recent theoretical work predicts very large growth of energy in this case, even for systems that are far from the semiclassical limit [3].

•May 3, 1998•0 citations

Quantum scaling laws in the onset of dynamical delocalization

Julien Chabé, Hans Lignier, Hugo L. D. de S. Cavalcante +3 more

By submitting a cloud of cold caesium atoms to a periodically pulsed standing wave, we experimentally realized a quantum system presenting a dynamic that is chaotic in the classical limit called the Kicked Rotor. Such a system presents a phenomenon called dynamical localization (DL). DL is the suppression of the classical chaotic energy growth by quantum interferences due to long range coherence in momentum space. After a breaktime, the quantum momentum distribution is frozen to a steady state and the energy is stuck to an asymptotic value.

Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)•Jun 1, 2007•2 citations

Quantum dynamics of matter waves in a pulsed disordered lattice

Bryce Gadway, Jeremy B. Reeves, Ludwig Krinner +1 more

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.

•Mar 14, 2012•0 citations
We measure the momentum of cold cesium atoms in a periodically pulsed standing wave of light. This system is an experimental realization of the quantum kicked rotor. The momentum diffusion in the (chaotic) classical analog of this system is typically suppressed by quantum localization. We find, however, that for certain pulse amplitudes where the classical system exhibits anomalous diffusion, our momentum distributions are not exponentially localized. We observe a predicted correspondence between the classical and quantum energy growth as a function of pulse amplitude and period.
Summary form only given. Dynamical localization is one of the signatures of quantum chaos most intensely studied in recent years. These studies rely on the experimental realization of a kicked rotor by placing cold atoms in a far detuned, periodically driven, stationary wave. For a set of parameters such that the classical limit of such a system shows a chaotic diffusive motion in the momentum space, quantum interferences have been shown to suppress the chaotic diffusion in the quantum case. The momentum distribution then presents a characteristic double exponential form. We have performed an experiment in which dynamical localization is studied in the presence of a stationary wave driven by two series of pulses that can have commensurable or incommensurable frequencies, which can be shown to be formally equivalent to perform the experiment in two dimensions. We have thus shown that localization is still observed when the two frequencies are commensurable, but that the classical diffusion in momentum space persists for a much longer time if the frequencies are incommensurable.
We study the motion of cold atoms in a pulsed standing wave of light, which constitutes an experimental realization of the quantum kicked rotor. This system exhibits dynamical localization, where quantum effects suppress classical momentum diffusion. As we introduce amplitude noise, the coherences that lead to localization are destroyed, resulting in restored diffusion. For high levels of noise, we find that the experiment is well described by a classical model, suggesting that classical behavior has been restored. We present a detailed experimental study of this noise-induced transition from quantum to classical behavior.
It is well established that classical chaotic motion is suppressed by quantum mechanics. The paradigm theoretical system has been the ?-kicked rotor, where the suppression manifests itself as dynamical localization. This effect is saturation of momentum growth after the quantum break time, with a resulting exponentially localized distribution. Classical analyses of this system have also identified regimes of anomalous diffusion, characterized by “Levy-type” flights in phase space [1]. This behavior is considerably more complex than simple diffusion and has attracted much interest in recent years. The quantum system was predicted to exhibit an increase in localization length near regions of anomalous diffusion [2], and recent theoretical work predicts very large growth of energy in this case, even for systems that are far from the semiclassical limit [3].
By submitting a cloud of cold caesium atoms to a periodically pulsed standing wave, we experimentally realized a quantum system presenting a dynamic that is chaotic in the classical limit called the Kicked Rotor. Such a system presents a phenomenon called dynamical localization (DL). DL is the suppression of the classical chaotic energy growth by quantum interferences due to long range coherence in momentum space. After a breaktime, the quantum momentum distribution is frozen to a steady state and the energy is stuck to an asymptotic value.
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.