Quantum light by atomic arrays in optical resonators

Light scattering by a periodic atomic array is studied when the atoms couple with the mode of a high-finesse optical resonator and are driven by a laser. When the von-Laue condition is not satified, there is no coherent emission into the cavity mode, and the latter is pumped via inelastic scattering processes. We consider this situation and identify conditions for which different non-linear optical processes can occur. We show that these processes can be controlled by suitably tuning the strength of laser and cavity coupling, the angle between laser and cavity axis, and the array periodicity. We characterize the coherence properties of the light when the system can either operate as degenerate parametric amplifier or as a source of antibunched-light. Our study permits us to identify the individual multi-photon components of the nonlinear optical response of the atomic array and the corresponding parameter regimes, thereby in principle allowing one for controlling the nonlinear optical response of the medium.