Our recent paper reports the experimental realization of a one-atom laser in a regime of strong coupling (Ref. [1]). Here we provide the supporting theoretical analysis relevant to the operating regime of our experiment. By way of a simplified four-state model, we investigate the passage from the domain of conventional laser theory into the regime of strong coupling for a single intracavity atom pumped by coherent external fields. The four-state model is also employed to exhibit the vacuum-Rabi splitting and to calculate the optical spectrum. We next extend this model to incorporate the relevant Zeeman hyperfine states as well as a simple description of the pumping processes in the presence of polarization gradients and atomic motion. This extended model is employed to make quantitative comparisons with the measurements of Ref. [1] for the intracavity photon number versus pump strength and for the photon statistics as expressed by the intensity correlation function g2(tau).
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