Collapse-revivals and population trapping in the m-photon mazer

We present a study of collapse-revival patterns that appear in the changes of atomic populations induced by the interaction of ultracold two-level atoms with electromagnetic cavities in resonance with an $m$-photon transition of the atoms ($m$-photon mazer). In particular, sech$^2$ and gaussian cavity mode profiles are considered and differences in the collapse-revival patterns are reported. The quantum theory of the $m$-photon mazer is written in the framework of the dressed-state coordinate formalism. Simple expressions for the atomic populations, the cavity photon statistics, and the reflection and transmission probabilities are given for any initial state of the atom-field system. Evidence for the population trapping phenomenon which suppress the collapse-revivals in the $m$-photon mazer is given.