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Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics

Quantitative study of amplitude noise effects on dynamical localization

D. Steck, Valery Milner, Windell H. Oskay, Mark G. Raizen

Published Sep 1, 2000• 71 citations
Publisher

Abstract

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.

DOI
10.1103/physreve.62.3461

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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.
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.
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.
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.
We present detailed observations of the quantum delta-kicked rotor in the vicinity of a quantum resonance. Our experiment consists of an ensemble of cold cesium atoms subject to a pulsed off-resonant standing wave of light. We measure the mean energy and show clearly that at the quantum resonance it is a local maximum. We also examine the effect of noise on the system and find that the greatest sensitivity to this occurs at the resonances. This makes these regions ideal for examining quantum-classical correspondence. A picture based on diffraction is developed which allows the experiments to be readily understood.
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