Localization of light in a three-dimensional disordered crystal of atoms

TL;DR

This study shows that weak positional disorder in a 3D atomic lattice causes localized optical modes near band edges, with a transition to extended modes as disorder increases, revealing mobility edges and critical behavior.

Contribution

It provides the first demonstration of light localization in a 3D atomic crystal with controlled disorder, identifying mobility edges and estimating the critical exponent.

Findings

Localized modes appear near band edges due to weak disorder.

Two mobility edges are identified through finite-size scaling.

Localized modes vanish with strong disorder, leading to extended modes.

Abstract

We demonstrate that a weak disorder in atomic positions introduces spatially localized optical modes in a dense three-dimensional ensemble of immobile two-level atoms arranged in a diamond lattice and coupled by the electromagnetic field. The frequencies of the localized modes concentrate near band edges of the unperturbed lattice. Finite-size scaling analysis of the percentiles of Thouless conductance reveals two mobility edges and yields an estimation $\nu = 0.8$--1.1 for the critical exponent of the localization length. The localized modes disappear when the disorder becomes too strong and the system starts to resemble a fully disordered one where all modes are extended.