Cavity optomechanical coupling assisted by an atomic gas

We theoretically study a cavity filled with atoms, which provides the optical-mechanical interaction between the modified cavity photonic field and a oscillating mirror at one end. We show that the cavity field ``dresses'' these atoms, producing two types of polaritons, effectively enhancing the radiation pressure of the cavity field upon the oscillating mirror, as well as establishing an additional squeezing mode of the oscillating mirror. This squeezing produces an adiabatic entanglement, which is absent in usual vacuum cavities, between the oscillating mirror and the rest of the system. We analyze the entanglement and quantify it using the Loschmidt echo and fidelity.