Anderson localization in optical lattices with correlated disorder

TL;DR

This paper investigates Anderson localization in optical lattices with correlated disorder, identifying mobility edges and critical filling factors through theoretical models and analyzing the impact of disorder correlations, with relevance to experimental atomic gases.

Contribution

It provides a detailed analysis of mobility edges in correlated disordered optical lattices using continuous and simplified models, advancing understanding of localization phenomena.

Findings

Determined mobility edges as a function of disorder strength.

Identified the universal ratio of level spacings at the mobility edge.

Compared theoretical results with experimental data on atomic Fermi gases.

Abstract

We study the Anderson localization of atomic gases exposed to simple-cubic optical lattices with a superimposed disordered speckle pattern. The two mobility edges in the first band and the corresponding critical filling factors are determined as a function of the disorder strength, ranging from vanishing disorder up to the critical disorder intensity where the two mobility edges merge and the whole band becomes localized. Our theoretical analysis is based both on continuous-space models which take into account the details of the spatial correlation of the speckle pattern, and also on a simplified tight-binding model with an uncorrelated distribution of the on-site energies. The mobility edges are computed via the analysis of the energy-level statistics, and we determine the universal value of the ratio between consecutive level spacings at the mobility edge. We analyze the role of the spatial correlation of the disorder, and we also discuss a qualitative comparison with available experimental data for interacting atomic Fermi gases measured in the moderate interaction regime.