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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)

Quantum scaling laws in the onset of dynamical delocalization

Julien Chabé, Hans Lignier, Hugo L. D. de S. Cavalcante, Dominique Delande, Pascal Szriftgiser, Jean Claude Garreau

Published Jun 1, 2007• 2 citations
Publisher

Abstract

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.

DOI
10.1109/cleoe-iqec.2007.4386712

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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.
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.
This paper presents the first experimental evidence of the transition from dynamical localization to delocalization under the influence of a quasiperiodic driving on a quantum system. A quantum kicked rotator is realized by placing cold atoms in a pulsed, far-detuned, standing wave. If the standing wave is periodically pulsed, one observes the suppression of the classical chaotic diffusion, i.e., dynamical localization. If the standing wave is pulsed quasiperiodically, dynamical localization is observed or not, depending on the driving frequencies being commensurable or incommensurable. One can thus study the transition from the localized to the delocalized case as a function of the effective dimensionality of the system.
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.
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].
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.