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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 mean͒. We examine that the behavior of the single-atom device as ␤, the fraction of spontaneous emission into the lasing mode, is varied. Typical values considered for ␤ are 0.01Ͻ␤Ͻ1.0. We find that for large enough ␤, 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 ␤ 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 ␤ values in the range considered here. As ␤ 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. ͓S1050-2947͑99͒06510-5͔

We investigate the stochastic initiation of superradiant emission from a collection of excited two-state atoms coupled through a low-Q cavity mode. Noncollective emission into other modes of the electromagnetic field is included, allowing us to describe the transition from predominantly noncollective to collective behavior as the number of atoms is increased. We examine the dependence of the photon statistics on the number of atoms and the ratio of collective to noncollective decay rates. Numerical results for a few to 10 6 atoms are obtained using an approximation scheme developed within the framework of quantum trajectory theory. Results are compared with those for a pure collective emission process and an earlier treatment of noncollective effects.