Photon localization and Dicke superradiance in atomic gases

TL;DR

This paper investigates how photon escape rates in atomic gases are affected by disorder and system size, revealing the role of cooperative effects and drawing parallels with small world network statistics.

Contribution

It introduces a random matrix model for photon escape rates in atomic gases, highlighting the impact of cooperative effects on photon localization.

Findings

Scaling behavior of photon escape rates with disorder and size

Microscopic and stochastic models explain cooperative effects

Relation between photon localization and small world network properties

Abstract

Photon propagation in a gas of N atoms is studied using an effective Hamiltonian describing photon mediated atomic dipolar interactions. The density P(\Gamma) of photon escape rates is determined from the spectrum of the N x N random matrix \Gamma_{ij} = \sin (x_{ij}) / x_{ij}, where x_{ij} is the dimensionless random distance between any two atoms. Varying disorder and system size, a scaling behavior is observed for the escape rates. It is explained using microscopic calculations and a stochastic model which emphasizes the role of cooperative effects in photon localization and provides an interesting relation with statistical properties of "small world networks".