Abstract
We study the quantum dynamics of an ultracold atomic gas trapped in an optical lattice within an optical high-$Q$ resonator. The atoms are coherently illuminated with the cavity resonance tuned to a blue vibrational sideband so that stimulated gain of the resonator mode is accompanied by vibrational cooling of the atoms. This system exhibits a threshold above which pairwise stimulated generation of a cavity photon and an atom in the lowest vibrational band dominates spontaneous scattering and we find a combination of optical lasing with a buildup of a macroscopic population in the lowest lattice band. Including output coupling of ground-state atoms and replenishing of hot atoms into the cavity volume leads to a coherent, quantum correlated atom-photon pair source very analogous to twin light beam generation in a nondegenerate optical parametric oscillator.
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