Quantum theory of the micromaser with ultra-cold cascade three-level atoms

We derive the dressed states for the interaction of a cascade three-level a tom with a quantum cavity field, suggest using ultra-cold cascade three-lev el atoms in micromasers, put forward the idea of the two-photon mazer, esta blish its general quantum theory and study its emission probability and pho ton statistics. We examine the effects of the atomic centre-of-mass momentu m, the atom-field detuning, the photon number in thermal equilibrium, the r atio of the atomic injection rate to the cavity decay rate and the interact ion length on the emission probability and the photon statistics.