  We study the interaction of an atom with a quantum guided field in a weakly
driven fiber-Bragg-grating (FBG) cavity. We present an effective Hamiltonian
and derive the density-matrix equations for the combined atom-cavity system. We
calculate the mean photon number, the second-order photon correlation function,
and the atomic excited-state population. We show that, due to the confinement
of the guided cavity field in the fiber cross-section plane and in the space
between the FBG mirrors, the presence of the atom in the FBG cavity can
significantly affect the mean photon number and the photon statistics even
though the cavity finesse is moderate, the cavity is long, and the probe field
is weak.
