Anomalous diffusion and Lévy walks in optical lattices

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Abstract
We study theoretically the spatial diffusion (transport) of two-level atoms in one- and two-dimensional optical molasses derived from counterpropagating laser beams. We use both quantum Monte Carlo and semiclassical methods to study the microscopic characteristics of the atomic motion and their effect on the macroscopic behavior of the spatial distribution. We find that there exists a certain critical depth of the optical potential below which the atomic trajectories show Lévy flights in space that last on a definite time scale (Lévy walks). This behavior leads to a transition from Gaussian spatial diffusion to anomalous diffusion while crossing this critical potential depth. We show that only atoms with very high momentum are responsible for these Lévy walks. This observation allows us to predict the critical parameters via a semiclassical Fokker-Planck equation approach. © 1996 The American Physical Society.