Photon statistics of a single atom laser

We consider a laser model consisting of a single four-level or three-level atom, an optical cavity, and an incoherent pump. Results for photon statistics for varying pump levels are obtained using a quantum trajectory algorithm. In particular, we calculate the mean photon number, Fano factor (which is the variance over the mean). We examine that the behavior of the single-atom device as beta, the fraction of spontaneous emission into the lasing mode, is varied. Typical values considered for beta are 0.01<beta<1.0. We find that for large enough beta, lasing action, with properties similar to those predicted by semiclassical theories that factorize atom-field correlations and use a small-noise approximation, can occur. Squeezing can occur as beta is increased. There is no evidence of a sharp phase transition from weakly excited thermal light to coherent light at a particular pump power. This is consistent with work on many-atom lasers with beta values in the range considered here. As beta is increased, the output goes from quasithermal light to coherent and finally to squeezed light, progressing into a fully quantum-mechanical regime. We also consider the effects of cavity damping and spontaneous emission rates on these results. [S1050-2947(99)06510-5].