Single Polariton Optomechanics

This paper investigates a novel hybrid cavity QED-optomechanics situation. We solve the Hamiltonian problem of a cavity coupled both to a two-level atom via a Jaynes-Cummings coupling and to a mechanical motion via radiation pressure coupling. The atom-cavity polariton number operator commutes with the total Hamiltonian leading to an exact analytical solution involving tripartite atom-cavity-mechanics polarons. Under optical pumping of polaronic transitions the system displays unusual atom-assisted cooling and amplification of mechanical motion. We demonstrate the possibility to obtain enhanced optomechanical cooling at the single polariton level, strong bunching of phonons, and describe the peculiar quantum noise statistics of mechanical motion in the single polariton amplification limit.