Regimes of classical transport of cold gases in a two-dimensional anisotropic disorder

We numerically study the dynamics of cold atoms in a two-dimensional disordered potential. We consider an anisotropic speckle potential and focus on the classical dynamics, which is relevant to some recent experiments. Firstly, we study the behavior of particles with a fixed energy and identify different transport regimes. At low energy, the particles are classically localized due to the absence of a percolating cluster. At high energy, the particles undergo normal diffusion, and we show that the diffusion coefficients scale algebraically with the particle energy, with an anisotropy factor that is significantly different from that of the disordered potential. At intermediate energy, we find a transient sub-diffusive regime, which is relevant to the time scale of typical experiments. Secondly, we study the behavior of a cold atomic gas with an arbitrary energy distribution, using the above results as the groundwork. We show that the density profile of the atomic cloud in the diffusion regime is strongly peaked and, in particular, that it is not Gaussian. Its behavior at large distances allows us to extract the energy-dependent diffusion coefficients from experimental density distributions. For a thermal cloud released into the disordered potential, we show that our numerical predictions are in agreement with experimental findings. Not only does this paper give insights into recent experimental results, but it may also help in the interpretation of future experiments searching for deviation from classical diffusion and traces of Anderson localization.