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Conference on Lasers and Electro-Optics

Dimensional effects on dynamical localization with cold cesium atoms

Jean Ringot, P. Szrfitgiser, Jean Claude Garreau, Dominique Delande

Published Aug 29, 2005• 0 citations
Publisher

Abstract

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.

DOI
10.1109/iqec.2000.907952

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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 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.
We report a direct observation of dynamical localization. This effect is a quantum suppression of diffusion in a system that is classically chaotic. Our experiment measures the momentum transferred from a modulated standing wave of a near-resonant laser to a sample of ultracold atoms and is a realization of a periodically driven rotor. The conceptual simplicity and experimental control over the time dependent Hamiltonian make this system an ideal testing ground for the predictions of quantum chaos.
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.
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].
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.