THE THEORY OF THE 2-PHOTON MICROMASER

We develop the theory of the degenerate and non-degenerate two-photon micromaser using the full, three-level Hamiltonian under conditions of overall two-photon resonance. Subject to this condition, our results are valid for arbitrary one-photon detunings, but we consider in particular the large detuning and zero detuning limits, where some simplification is possible. For the case of zero detuning, we obtain semianalytic solutions, and find that, depending upon the interaction time, the system lases as either a single-mode or a two-mode system. We have compared our results with the degenerate two-photon micromaser, and find qualitative differences. Our results are valid for arbitrary one-photon detunings, provided the interaction times are not too long. The solution to the Fokker-Planck equation is found using a detailed balance, linearization procedure, and the photon statistics is investigated. Markedly sub-Poissonian behaviour is possible under certain conditions. We find that the behaviour in the zero detuning, non-degenerate situation is quite distinct to that of all other cases.