Viviana Viggiano | Searcharxiv

arXiv2025

Condensation of vanishing photon emission rates in random atomic clouds

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.

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arXiv2023

Cooperative photon emission rates in random atomic clouds

We investigate the properties of the cooperative decay modes of a cold atomic cloud, characterized by a Gaussian distribution in three dimensions, initially excited by a laser in the linear regime. We study the properties of the decay rate matrix $S$, whose dimension coincides with the number of atoms in the cloud, in order to get a deeper insight into properties of cooperative photon emission. Since the atomic positions are random, $S$ is a Euclidean random matrix whose entries are function of the atom distances. We show that, in the limit of a large number of atoms in the cloud, the eigenvalue distribution of $S$ depends on a single parameter $b_0$, called the cooperativeness parameter, which can be viewed as a quantifier of the number of atoms that are coherently involved in an emission process. For very small values of $b_0$, we find that the limit eigenvalue density is approximately triangular. We also study the nearest-neighbour spacing distribution and the eigenvector statistics, finding that, although the decay rate matrices are Euclidean, the bulk of their spectra mostly behaves according to the expectations of classical random matrix theory. In particular, in the bulk there is level repulsion and the eigenvectors are delocalized, therefore exhibiting the universal behaviour of chaotic quantum systems.

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