Entanglement of Optical and Mechanical Modes Enhanced in Distant Optomechanical Systems by Atomic Coherence

We present a scheme for three-level cascade atoms to entangle various optical and mechanical modes of two coupled cavity optomechanical system. With the existence of atomic mediums, our study shows that the larger stationary macroscopic entanglement of distant optomechanical systems can be obtained and reaches the maximum at the same effective detuning. Furthermore, we find that it is insensitive to the cavity decay rate for the entanglement between the two distant movable mirrors, and between the mirror and the adjacent or the distant cavity mode, which compensates for the effects of the cavity dissipation.