Effective scheme for enhancing entanglement in distant optomechanical system by injecting the atomic medium

In this paper, we propose a method to enhance the steady-state entanglement between cavity fields and mechanical modes by injecting atomic media into the cavities. The atomic medium interaction with the cavities can change the effective decay rate of the photons and the radiation pressure of the cavity fields on the two mirrors. Thus it provides us with a way to enhance the quantum entanglement in the optomechanical system.