FROM SUB-POISSONIAN TO SUPER-POISSONIAN PUMPING IN THE MICROMASER - CORRECTIONS TO RESERVOIR THEORY

We present a quantum theory of the micromaser which allows for arbitra ry (sub- as well as super-Poissonian) fluctuations of the pumping beam . It handles the interaction with the active atoms (gain) and cavity d ecay (loss) on an equal footing. In conventional reservoir theory the rate of change of the cavity field is a sum of the changes due to sepa rate interactions with the individual reservoirs, i.e., the interactio ns are uncorrelated. In our approach, corrections to reservoir theory arise. They contain the commutator of the gain and loss operators. The magnitude of these additional terms is characterized by the quantity p/N-ex where p is a parameter describing pump-beam fluctuations. The p arameter is, in fact, the negative of the Mandel e parameter of the pu mp beam so that p = 1 corresponds to regular pumping, p = 0 to Poisson ian one and p < 0 to super-Poissonian pump beam fluctuations. N-ex is the number of excited atoms passing through the cavity during the life time of the intracavity field. Thus we recover the conventional reserv oir limit if p = 0 and/or N-ex is large. In all other cases the intera ctions with the gain and loss reservoirs are correlated. We exploit so me of the consequences of the additional terms, presenting analytical as well as numerical results for the steady-state photon statistics (m ean photon number and photon-number fluctuations, in particular) witho ut resorting to the p expansion.