Abstract
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 in 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 two-dimensional (2D) and three-dimensional (3D) speckle potentials. In particular, we discuss the anisotropy of single-scattering, diffusion and localization. We also calculate disorder-induced shift of the energy states and propose a method to include it, which amounts to renormalizing 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 relevant for current matter wave experiments, where the disorder is created with laser speckle. This paper provides a guideline for future experiments aiming at the precise location of the 3D mobility edge and study of anisotropic diffusion and localization effects in 2D and 3D.
Highlights
The regular part contributes to the finite time and finite distance propagation of the density, which we disregard here
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 exploited in matter wave experiments, where the disordered potential can be tailored and controlled, and anisotropies are naturally present
We show that the renormalization of energies strongly affects the prediction for the 3D localization threshold
Summary
The regular part contributes to the finite time and finite distance propagation of the density, which we disregard here. To cite this version: Marie Piraud, Luca Pezzé, Laurent Sanchez-Palencia. Quantum transport of atomic matterwaves in anisotropic 2D and 3D disorder.
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