We examine nonclassical correlations and entanglement for an atom in a driven cavity (Cavity QED) with an external potential. The external potential introduces new degrees of freedom that require treatment of the center of mass motion including tunneling. We find a very sensitive dependence of quantum correlation functions on center of mass motion. We obtain analytic results in the case of a harmonic potential , or that of a lattice potential that has half the wavelength of the driving field. It may be possible to use the sensitivity of these correlation functions to yield information about atomic motion, such as Levy flights. We find that two cross correlations between transmitted and fluorescent light yield information about the entanglement in the system. Also, we discuss inequalities between intensity-intensity and intensity-field correlations in this system, and find nonclassical behavior of a new type. Figure 1 shows a schematic of the cavity QED system.
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