Co-operative atomic interactions in one- and two-photon micromasers

We have developed a quantum theory of the micromaser for a pair of two-leve l atoms for the case of one- and two-photon transition coupling. We have st udied the effect of co-operativity on the photon statistics for these syste ms for different coupling constant ratios. It is found that for equal coupl ing, our system of a two-atom, one-photon micromaser behaves like a double one-photon cascade micromaser. Similarly, for equal coupling, the photon st atistics of the two-atom, two-photon micromaser reduces to that of a three- level, four-photon cascade micromaser.