EFFECTS OF COUPLING BETWEEN CENTER OF MASS MOTION OF AN ATOM AND A CAVITY MODE: PHOTON STATISTICS AND WAVE-PARTICLE CORRELATIONS

by Mumba, Mambwe

We examine a system comprised of a single two-level atom inside a driven optical cavity. We allow for cavity decay and atomic spontaneous emission out the side of the cavity. There is a spatial dependent coupling between the atom and the cavity mode,which we take into account, using explicit trapping potentials for the atom. Previous work has revolved around a harmonic oscillator potential, we also find here a solution for a realistic optical lattice potential when the lattice wavelength is half the driving laser wavelength. Atomic and cavity detunings are included, as well as effective Franck-Condon factors. Analytic results are obtained for various intensity-intensity and field-intensity correlation functions, using quantum trajectory theory in the weak driving field limit. Nonclassical effects are obtained, and we investigate the effect of a nonstationary atom on these effects. These result from violation of inequalities that must be satisfied if there is an underlying classical stochastic field; violations imply that there is no well defined electric field at all times, with some underlying positive definite probability distribution. The center of mass wave function is specified either by a list of probability amplitudes, or these amplitudes are calculated from an explicit wave function(typically a Gaussian). The correlation functions are quite sensitive to the center of mass wave function, and perhaps correlation functions can be used as probes of atomic motion. We also examine a new inequality between intensity-intensity and field intensity correlation functions, that is violated here.