Entanglement of nanomechanical oscillators and two-mode fields induced by atomic coherence

We propose a scheme for three-level cascade atoms to entangle two optomechanical oscillators as well as two-mode fields. We show that two movable mirrors and two-mode fields can be entangled even for bad cavity limits. We also study entanglement of the output of two-mode fields in the frequency domain. The results show that the frequency of the mirror oscillation and the injected atomic coherence affect the output entanglement of the two-mode fields.