Photon Localization and Dicke Superradiance in Atomic Gases

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 NxN random matrix Gammaᵢⱼ=sin(xᵢⱼ)/xᵢⱼ, where xᵢⱼ 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."