Condensation of vanishing photon emission rates in random atomic clouds

TL;DR

This paper investigates a phase transition in the spectral properties of Euclidean random matrices describing collective photon emission in atomic clouds, revealing a new transition driven by cooperativeness rather than density.

Contribution

It uncovers a novel phase transition controlled by the cooperativeness parameter in the radiative dynamics of atomic clouds, expanding understanding of superradiance and subradiance phenomena.

Findings

Identification of a phase transition at a critical cooperativeness value.

Spectral spectrum lower edge vanishes at the transition point.

Consistent critical value obtained from different analytical approaches.

Abstract

In the collective photon emission from atomic clouds both the atomic transition frequency and the decay rate are modified compared to a single isolated atom, leading to the effects of superradiance and subradiance. In this article, we analyse the properties of the Euclidean random matrix associated to the radiative dynamics of a cold atomic cloud, previously investigated in the contexts of photon localization and Dicke super- and subradiance. We present evidence of a new type of phase transition, surprisingly controlled by the cooperativeness parameter, rather than the spatial density or the diagonal disorder. The numerical results corroborate the occurrence of such a phase transition at a critical value of the cooperativeness parameter, above which the lower edge of the spectrum vanishes exhibiting a macroscopic accumulation of eigenvalues. Independent evaluations based on the two phenomena provide the same value of the critical cooperativeness parameter.