Universal, environmentally-induced entangling transition in an optomechanical system

Optomechanical systems subjected to environmental noise give rise to rich physical phenomena. We investigate the entanglement between a mechanical oscillator and an outgoing coherent optical field in a general, not necessarily Markovian environment. For the ingoing optical field, we consider general, stationary Gaussian states, incorporating arbitrary frequency-dependent squeezing. Assuming linearized interactions, we demonstrate that when the ingoing light field is the vacuum state, optomechanical entanglement is destroyed after a threshold that depends only on the environmental noises—independent from the coherent coupling between the oscillator and the optical field. In this way, we have found a universal entangling-disentangling transition. We also show that for an initially separable system, entanglement cannot be generated by incorporating frequency-dependent squeezing in the optical field.