We present a theory of the micromaser including the effect of the arrival-time statistics of the active atoms in the theoretical treatments. Our starting point is an approach that explicitly incorporates the effect of pump statistics into the dynamical description of lasers and masers. We show that the application of standard laser theory to the micromaser is tantamount to the tacit assumption of Poissonian arrival-time statistics. Hence standard laser theory and the theory of the micromaser are, in general, not equivalent, but the latter contains the former, as a limiting case, for completely random arrival times. We show, as an application, that the steady-state value of the average photon number (first moment) is essentially unaffected by the pump statistics since it depends only on the flux of active atoms (average number of atoms entering the cavity per unit time) provided the flux is constant. The intensity fluctuations (second moment), however, exhibit a stronger dependence on the pump statistics. In particular, for sub-Poissonian pump statistics the sub-Poissonian character of the field is enhanced.
The model commonly used to describe non-Poissonian pumping of micrornasers refers to periodic pumping where the possible arrival times of the pump atoms are separated by constant time intervals.1 In contrast to this, we study a micromaser with strictly stationary pumping.2 We investigate the level-selective statistics of the atoms leaving the cavity as well as the photon statistics of the cavity field. Our method is based on treating the statistics of the arrival times of the individual pump atoms, which are in the upper state of the microwave transition, with the help of the theory of stochastic point processes.