Cooperative effects and photon localization in atomic gases: The two-dimensional case

TL;DR

This paper investigates how cooperative interactions influence photon escape rates in two-dimensional atomic gases, revealing a scaling behavior similar to three dimensions but distinct from one dimension.

Contribution

It introduces a spectral analysis of a random Euclidean matrix to understand photon localization and escape rates in 2D atomic gases, extending previous 3D results.

Findings

Photon escape rates exhibit a scaling behavior in 2D gases.

The spectral properties differ qualitatively from 1D systems.

Results align with 3D behavior, highlighting dimensional effects.

Abstract

We study photon escape rates from two-dimensional atomic gases while taking into account cooperative effects between the scatterers. Based on the spectrum of the random Euclidean matrix Uij = Jo(xij), where xij is the dimensionless random distance between any two atoms, a scaling behavior for the escape rates is obtained. This behavior is similar to the one obtained in the three-dimensional case, but qualitatively different from the result obtained in one dimension.