Correlated photon-pair generation via single-atom cavity-assisted spontaneous four-wave mixing

We present a detailed study of the generation of photon pairs by spontaneous four-wave mixing in a bicavity system with a single atom inside. Cavity modes lead to larger coupling strength than that of the normally assumed thermal vacuum, and thus higher generation rates are expected. Unlike approaches that have emerged so far, this paper presents an approach based on the solution of the master equation. This method allows us to investigate the photon statistics more strictly, and we show that the choices of pumping detuning and leaking rate of the cavities significantly affect the degree of the autocorrelation, and a higher-purity heralded single photon source is possible. We also derive a concise expression for the output state and the generation rate for the extreme cases where the cavity leaking rate is much smaller or larger than the rate of spontaneous emission.