  In this paper we study the generation of photon pairs through the process of
spontaneous four wave mixing (SFWM) in a $\chi^{(3)}$ cavity. Our key interest
is the generation of photon pairs in a guided-wave configuration - fiber or
waveguide - where at least one of the photons in a given pair is matched in
frequency and bandwidth to a particular atomic transition, as required for the
implementation of photon-atom interfaces. We present expressions, along with
plots, for the two-photon joint intensity both in the spectral and temporal
domains. We also present expressions for the absolute brightness, along with
numerical simulations, and show that the presence of the cavity can result in a
flux enhancement relative to an equivalent source without a cavity.
