Theory of a two-mode micromaser simultaneously pumped by one- and two-photon atomic transitions

We formulate the theory of a micromaser operating simultaneously on a one- and a two-photon atomic transition. Departing from the complete microscopic Hamiltonian for this composite 'atom plus field' system, we derive the equations governing its behaviour in the semiclassical approximation and also the fully quantum mechanical master equation. Using parameters corresponding to existing realizations of the one- and two-photon micromaser, we obtain illustrative examples of some novel aspects of this system in the steady state as well as in dynamical evolution.