Cooperative effects in atom-photon interactions

We investigate cooperative photon emission by a random cold atomic cloud described by a Gaussian distribution in three dimensions. We formulate the problem in terms of Euclidean random matrices (ERMs), whose entries are a function of the atomic distances. After formulating and physically motivating the model, we present a detailed analysis of the Euclidean random matrix S, related to the dissipative dynamics of the atomic cloud, induced by photon-mediated interaction. We first focus on the bulk spectral properties of this matrix, characterizing the microscopic spectral statistics, the level spacing and the eigenvectors corresponding to the central part of the spectrum. We then analyze the extremely subradiant part of the spectrum of S, finding evidence of a phase transition, controlled by the cooperativeness parameter b, related to the number of atoms that coherently cooperate in photon emission. Finally, we present ongoing research activity on a different, non-Hermitian Euclidean random matrix, describing both the Hamiltonian and the dissipative photon-mediated dynamics of the cloud, and shed light on the connections between these two ERMs and a more general open system approach.