ANOMALOUS DIFFUSION AND LEVY WALKS IN OPTICAL LATTICES

We study theoretically the spatial diffusion (transport) of two-level atoms in one- and two-dimensional optical molasses derived from counte rpropagating laser beams. We use both quantum Monte Carlo and semiclas sical methods to study the microscopic characteristics of the atomic m otion and their effect on the macroscopic behavior of the spatial dist ribution. We find that there exists a certain critical depth of the op tical potential below which the atomic trajectories show Levy flights in space that last on a definite time scale (Levy walks). This behavio r leads to a transition from Gaussian spatial diffusion to anomalous d iffusion while crossing this critical potential depth. We show that on ly atoms with very high momentum are responsible for these Levy walks. This observation allows us to predict the critical parameters via a s emiclassical Fokker-Planck equation approach.