Anderson localization in optical lattices with speckle disorder

TL;DR

This paper investigates how speckle disorder affects wave localization in one-dimensional optical lattices, revealing that localization length becomes energy-independent under certain disorder correlation conditions.

Contribution

It introduces a decimation/renormalization method to estimate localization length in speckle-disordered lattices with correlated site energies.

Findings

Localization length becomes energy-independent at strong disorder.

Correlation width of speckle patterns influences localization properties.

Localization regime can be achieved with speckle grains smaller than four lattice sites.

Abstract

We study the localization properties of non-interacting waves propagating in a speckle-like potential superposed on a one-dimensional lattice. Using a decimation/renormalization procedure, we estimate the localization length for a tight-binding Hamiltonian where site-energies are square-sinc-correlated random variables. By decreasing the width of the correlation function, the disorder patterns approaches a $\delta$-correlated disorder, and the localization length becomes almost energy-independent in the strong disorder limit. We show that this regime can be reached for a size of the speckle grains of the order of (lower than) four lattice steps.