Cavity QED with quantized center of mass motion

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)(τ) and the intensity-field correlation function hθ(τ), for transmitted light in the weak driving field limit. 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 and field-intensity correlations, and compare the use of trapped atoms in a cavity to atomic beams