Quantum fluctuations for two-level atoms in a high-Q cavity with a spatially varying field mode

An extension of the quantum theory of the atom-field interaction within a high-finesse resonator is made to include spatial variations of the field mode in the limit of small cavity decay rate. The two particular examples of a Gaussian mode field in a ring cavity and a plane-wave field in a standing-wave interferometer are presented to illustrate the method. Analytic expressions are obtained for the incoherent intensity and photon correlations of the transmitted field. In qualitative terms, effects such as sub-Poissonian photon statistics predicted by the plane-wave theory in a ring cavity are preserved. In either the weak-field or dispersive limit the results of the plane-wave theory in a ring cavity are recovered independent of the form of the spatial dependence of the cavity mode.