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 statist ics for varying pump levels are obtained using a quantum trajectory algorit hm. 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 m ode, is varied. Typical values considered for beta are 0.01<beta<1.0. We fi nd that for large enough beta, lasing action, with properties similar to th ose predicted by semiclassical theories that factorize atom-field correlati ons 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 we akly excited thermal light to coherent light at a particular pump power. Th is is consistent with work on many-atom lasers with beta values in the rang e considered here. As beta is increased, the output goes from quasithermal light to coherent and finally to squeezed light, progressing into a fully q uantum-mechanical regime. We also consider the effects of cavity damping an d spontaneous emission rates on these results. [S1050-2947(99)06510-5].