Quantum transport of atomic matterwaves in anisotropic 2D and 3D disorder

TL;DR

This paper investigates how anisotropic disorder affects the transport, diffusion, and localization of ultracold atoms in 2D and 3D speckle potentials, providing theoretical insights relevant for current matter wave experiments.

Contribution

It applies a microscopic transport theory and self-consistent localization theory to analyze anisotropic disorder effects and introduces a method to include disorder-induced energy shifts affecting localization thresholds.

Findings

Disorder-induced energy shifts significantly influence the 3D localization threshold.

Anisotropy affects single-scattering, diffusion, and localization properties.

Theoretical results guide future experiments on mobility edges and anisotropic localization.

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 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. In particular, we discuss the anisotropy of single-scattering, diffusion and localization. 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 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.