Optomechanically induced transparency associated with steady-state entanglement

We theoretically investigate a two-cavity optomechanical system in which a cavity (cavity a) couples to a mechanical resonator via radiation pressure and to another cavity (cavity c) via a common waveguide. In the excitation of a strong pump filed to cavity a, the steady-state entanglement between cavity a and c, as a quantum channel, can be generated, which provides an indirect optical pathway to excite cavity c by means of the pump filed. Quantum interference between the direct and indirect optical pathways gives rise to an optomechanically induced transparency appearing in the probe transmission of cavity c. Unlike in a typical optomechanically induced transparency effect, the electromagnetical control of the transmission is implemented by resorting to the quantum channel. Furthermore, the coupling strength of the two cavities is an important factor of the quantum channel, which can influence the width of the transparency window and the bistable behavior of the mean photon number in cavity a. We also illustrate that the electromagnetical control via quantum channel can be exploited to implement the optical switch and the slow light.