SUB-POISSONIAN PHOTON STATISTICS IN THE MICROMASER

We present a tutorial review of the quantum theory of the micromaser w hich allows for arbitrary (sub- as well as super-Poissonian) fluctuati ons of the pumping beam. In conventional reservoir theory the rate of change of the cavity field is a sum of the changes due to separate int eraction with the individual reservoirs, i.e. the interactions are unc orrelated. In our approach, which is based on discrete mapping rather than a master equation, corrections to reservoir theory arise due to c orrelations between these interactions. The magnitude of these terms i s characterized by the quantity p/N-ex. Here p, the parameter describi ng pump beam fluctuations, is the negative of the Mandel Q parameter o f the pump beam so that p = 1 corresponds to regular pumping, p = 0 to Poissonian one and p < 0 to super-Poissonian pump beam fluctuations. N-ex is the number of atoms passing through the cavity during the life time of the intracavity field. The conventional reservoir limit (stand ard laser theory) is recovered if p = 0 and/or N-ex is large. In ail o ther cases the interactions with the gain and loss reservoirs are corr elated. We present analytical results to demonstrate the effect of pum p regularity on steady-state problems (photon statistics, mean number of photons and photon number variance) as well as on transient phenome na (correlation function and spectrum). In particular, it is shown tha t the approach to equilibrium can have non-Markovian character.