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

Dynamical localization of ultracold sodium atoms

C. F. Bharucha, J. C. Robinson, F. L. Moore, Bala Sundaram, Qian Niu, Mark G. Raizen

Published Oct 1, 1999• 65 citations
Publisher

Abstract

We report a study of atomic motion in time-dependent optical potentials. We measure momentum transfer in parameter regimes for which the classical dynamics are chaotic, and observe the quantum suppression of chaos by dynamical localization. The high degree of control over the experimental parameters enables detailed comparisons with theoretical predictions, and opens new avenues for investigating quantum chaos.

DOI
10.1103/physreve.60.3881

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We report a study of atomic motion in time-dependent optical potentials. We measure momentum transfer in parameter regimes for which the classical dynamics are chaotic, and observe the quantum suppression of chaos by dynamical localization. The high degree of control over the experimental parameters enables detailed comparisons with theoretical predictions, and opens new avenues for investigating quantum chaos.
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.
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We have identified ultracold atoms in magneto-optical double-well potentials as a very clean setting in which to study the quantum and classical dynamics of a nonlinear system with multiple degrees of freedom. In this system, entanglement at the quantum level and chaos at the classical level arise from nonseparable couplings between the atomic spin and its center of mass motion. The main features of the chaotic dynamics are analyzed using action-angle variables and Poincaré surfaces of section. We show that for the initial state prepared in current experiments [D. J. Haycock et al., Phys. Rev. Lett. 85, 3365 (2000)], classical and quantum expectation values diverge after a finite time, and the observed experimental dynamics is consistent with quantum-mechanical predictions. Furthermore, the motion corresponds to tunneling through a dynamical potential barrier. The coupling between the spin and the motional subsystems, which are very different in nature from one another, leads to interesting questions regarding the transition from regular quantum dynamics to chaotic classical motion.
We report an experimental and theoretical study of momentum transfer from a modulated standing wave of light to a sample of ultracold atoms. This system is a quantum realization of the periodically driven rotor where the underlying classical phase space goes from stable to chaotic as a control parameter is varied. Our experimental results are in good absolute agreement with a quantum Floquet analysis and with a quantum simulation. We relate the quantum evolution to the underlying classical dynamics in this mixed phase space regime.