One-dimensional Anderson localization in certain correlated random potentials

TL;DR

This paper investigates Anderson localization of ultracold atoms in one-dimensional speckle potentials, revealing sharp crossovers in localization length and dependence on potential sign, supported by perturbation theory and numerical validation.

Contribution

It introduces a perturbative approach beyond Born approximation to identify effective mobility edges in correlated random potentials for ultracold atoms.

Findings

Existence of sharp crossovers in localization lengths

Localization length depends on the sign of the potential

Results align with numerical simulations in experimental regimes

Abstract

We study Anderson localization of ultracold atoms in weak, one-dimensional speckle potentials, using perturbation theory beyond Born approximation. We show the existence of a series of sharp crossovers (effective mobility edges) between energy regions where localization lengths differ by orders of magnitude. We also point out that the correction to the Born term explicitly depends on the sign of the potential. Our results are in agreement with numerical calculations in a regime relevant for experiments. Finally, we analyze our findings in the light of a diagrammatic approach.