Photon statistics of the light transmitted and reflected by a two-dimensional atomic array

Abstract: This work proposes to investigate the photon statistics of the light transmitted and reflected by a two-dimensional array of interacting atoms. The reflected beam is characterized by photon antibunching. On the other hand, in the transmitted beam the indistinguishability between the driving laser photons and the photons re-emitted by the atoms results in photon bunching. The overlap between the driving and scattered fields is enhanced by the cooperative optical response of the atomic array. In the examples used in this paper, up to 25\% of the transmitted photons are grouped in pairs. The simulations are carried out using the stochastic method of quantum trajectories.