Anderson localization of ultracold atoms: Where is the mobility edge?

TL;DR

This paper investigates the location of the mobility edge in Anderson localization of ultracold atoms, using numerical simulations to assess the impact of anisotropy and clarify experimental discrepancies.

Contribution

The study demonstrates that anisotropy alone does not account for the experimental overestimation of the mobility edge, highlighting the need for alternative explanations.

Findings

Anisotropy has minimal effect on the mobility edge for moderate levels.

Disorder configurations are similar to isotropic cases after energy rescaling.

Experimental discrepancies are unlikely due to anisotropy effects.

Abstract

Recent experiments on non-interacting ultra-cold atoms in correlated disorder have yielded conflicting results regarding the so-called mobility edge, i.e. the energy threshold separating Anderson localized from diffusive states. At the same time, there are theoretical indications that the experimental data overestimate the position of this critical energy, sometimes by a large amount. The non-trivial effect of anisotropy in the spatial correlations of experimental speckle potentials have been put forward as a possible cause for such discrepancy. Using extensive numerical simulations we show that the effect of anisotropy alone is not sufficient to explain the experimental data. In particular, we find that, for not-too-strong anisotropy, realistic disorder configurations are essentially identical to the isotropic case, modulo a simple rescaling of the energies.