We consider a micromaser model to study the influence of Dicke superradiance in the context of the one-atom maser. The model involves a microwave cavity into which two-level Rydberg atoms are pumped in pairs. We consider a random pump mechanism which allows the presence of at most one pair of atoms in the cavity at any time. We analyze the differences between the present system, called the Dicke micromaser, and an equivalently pumped conventional one-atom micromaser. These differences are attributed to the Dicke cooperativity in the two-atom system. We also show that the two-atom Dicke micromaser is equivalent to a one-atom cascade two-photon micromaser. With the introduction of a one-photon detuning, the present theory further describes a true two-photon micromaser. We discuss in detail the role of one-photon detuning in the mechanism of a one-atom two-photon micromaser. This leads us to point out that the two-atom cavity dynamics can be verified by a proper scaling of the results from an equivalent one-atom two-photon micromaser.
We present a quantum theory of the micromaser which allows for arbitrary (sub- as well as super-Poissonian) fluctuations of the pumping beam. It handles the interaction with the active atoms (gain) and cavity decay (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 separate interactions with the individual reservoirs, i.e., the interactions 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/
Nex where p is a parameter describing pump-beam fluctuations. The parameter is, in fact, the negative of the Mandel Q parameter of the pump beam so that p=1 corresponds to regular pumping, p=0 to Poissonian one and p0 to super-Poissonian pump beam fluctuations.
Nex is the number of excited atoms passing through the cavity during the lifetime of the intracavity field. Thus we recover the conventional reservoir limit if p=0 and/or
Nex is large. In all other cases the interactions with the gain and loss reservoirs are correlated. We exploit some of the consequences of the additional terms, presenting analytical as well as numerical results for the steady-state photon statistics (mean photon number and photon-number fluctuations, in particular) without resorting to the p expansion.