Quantum Diffusion of Matter Waves in 2D Speckle Potentials

TL;DR

This paper explores quantum diffusion and localization of matter waves in 2D speckle potentials, providing theoretical expressions and criteria for observing localization in Bose-Einstein condensates.

Contribution

It introduces comprehensive theoretical models for quantum diffusion, including interference effects and localization criteria, in 2D speckle potentials for matter waves.

Findings

Derived expressions for diffusion constant and probability density distribution.

Analyzed effects of dephasing and finite system size.

Provided criteria for observing localization experimentally.

Abstract

This paper investigates quantum diffusion of matter waves in two-dimensional random potentials, focussing on expanding Bose-Einstein condensates in spatially correlated optical speckle potentials. Special care is taken to describe the effect of dephasing, finite system size, and an initial momentum distribution. We derive general expressions for the interference-renormalized diffusion constant, the disorder-averaged probability density distribution, the variance of the expanding atomic cloud, and the localized fraction of atoms. These quantities are studied in detail for the special case of an inverted-parabola momentum distribution as obtained from an expanding condensate in the Thomas-Fermi regime. Lastly, we derive quantitative criteria for the unambiguous observation of localization effects in a possible 2D experiment.