  We investigate the quantum fluctuations of a single atom in a weakly driven
cavity, where the center of mass motion of the atom is quantized in one
dimension. We present analytic results for the second order intensity
correlation function $g^{(2)}(\tau)$ and the intensity-field correlation
function $h_{\theta}(\tau)$, for both transmitted and fluorescent light for
weak driving fields. We find that the coupling of the center of mass motion to
the intracavity field mode can be deleterious to nonclassical effects in photon
statistics; less so for the intensity-field correlations.
