Marie Piraud, Luca Pezzé, Laurent Sanchez-Palencia
The macroscopic transport properties in a disordered potential, namely diffusion and weak/strong localization, closely depend on the microscopic and statistical properties of the disorder itself. This dependence is rich of counter-intuitive consequences. It can be particularly exploited in matter wave experiments, where the disordered potential can be tailored and controlled, and anisotropies are naturally present. In this work, we apply a perturbative microscopic transport theory and the self consistent theory of Anderson localization to study the transport properties of ultracold atoms in anisotropic 2D and 3D speckle potentials. We show that structured correlations can induce rich effects, such as anisotropic suppression of the white-noise limit and inversion of the transport anisotropy. We also calculate a disorder-induced shift of the energy states and propose a method to include it, which amounts to renormalize energies in the standard on-shell approximation. We show that the renormalization of energies strongly affects the prediction for the 3D localization threshold (mobility edge). We illustrate the theoretical findings with examples which are revelant for current matter wave experiments, where the disorder is created with a laser speckle. This paper is a detailed version of [Europhys. Lett. 99, 50003 (2012)] and represents a guideline for future experiments aiming at the precise location of the 3D mobility edge and study of anisotropy diffusion and localization effects in 2D and 3D.
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http://arxiv.org/abs/1211.5872
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