Spatial dependence of moving atoms with a two-photon process

We propose an alternative treatment to describe the spatial-dependence of the non-resonant two-photon mazer. Previous work presented a treatment for studying the cold atom micromaser (mazer) but under certain restrictive conditions. We now extend those results to a general case taking into account the spatial dependence, off-resonant interaction and Stark-shift. In a mesa mode profile, we obtain an exactly analytic solution of the model, by means of which we analyze the analytical form of the emission probability. We demonstrate that, when the spatial dependence effects are taken into consideration, the feature of the emission probability is influenced significantly.