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In the paper a model of a single-atom laser with incoherent pumping istheoretically investigated. In the stationary case, a linear homogeneousdifferential equation for the phase-averaged Hussimi Q-function is derived fromthe equation for the density operator of the system. In the regime when thecoupling of the field with an atom is many times stronger than the coupling ofthe field with the reservoir providing its decay, an asymptotic solution ofthis equation is found. This solution makes it possible to describe somestatistical features of a single-atom laser, in particular the weaksub-Poissonian photon statistics.

Quasi-probability Q for a single-atom laser generating in the 'semi-classical' regime