Effects of cross-Kerr coupling and parametric nonlinearity on normal mode splitting, cooling, and entanglement in optomechanical systems

We study the influence of cross-Kerr (CK) coupling and optical parametric amplifier (OPA) on the effective frequency, damping, normal mode splitting, ground state cooling, and steady state entanglement of an optomechanical system formed by one fixed mirror and one movable mirror. The CK coupling could increase the damping of the movable mirror. The normal mode splitting of the output field is observed due to the CK coupling. The combination of the CK coupling and OPA decreases the minimum attainable phonon number and the effective temperature of the movable mirror. The amount of stationary entanglement between the mechanical and cavity modes can be enhanced by the weak CK coupling. In particular, we find the stationary entanglement becomes more robust against thermal fluctuations of the movable mirror in the presence of the weak CK coupling.