An atom-photon pair laser

We study the quantum dynamics of an ultracold atomic gas in a deep 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 photon scattering to 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.