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

Abstract

The correspondence between a quantum system and the underlying classical dynamics is a topic of fundamental importance. The paradigm system for the study of this correspondence is the kicked rotor, because of the simplicity of its equations of motion and the wealth of knowledge available on the classical system. One particularly interesting aspect of the kicked rotor is the existence of accelerator modes, which lead to Levy flights in generic phase-space trajectories [1,2]. These Levy flights can have a strong influence on the global transport properties of a system, and have been recently employed in the understanding of a subrecoil laser cooling scheme for atoms [3] and the motion of particles in a nonuniform fluid flow [4]. In the classical kicked rotor, the effects of the accelerator modes become most important in the long-time limit, because they account for a relatively small area in phase space. However, recent theoretical work has shown that these structures can have a dramatic effect in the quantum case, because of the nonlocal nature of the wave functions [5]. In this Letter, we study an experimental realization of the quantum kicked rotor, where cold cesium atoms are “kicked” by a periodically pulsed standing wave of fardetuned light. Previous work with sodium atoms has established this system as an excellent setting for the study of quantum chaos [6,7]. In this previous work, we observed dynamical localization, which is the quantum suppression of the classical chaotic momentum diffusion; the hallmark of this effect is a localized momentum distribution with an exponential profile. Here, we report the experimental study of the atomic momenta as a function of the pulse amplitude and period. We observe the oscillations in the momentum distribution widths that are expected from theory. We also observe that for certain kick amplitudes where accelerator modes are present in the classical phase space, the momentum distributions do not have the expected exponential form over the time scale of our experiment [8]. These results, which form the main focus of this Letter, suggest a correlation between classical anomalous diffusion and the observed quantum dynamics.