Controllable optical bistability based on photons and phonons in a two-mode optomechanical system

We explore theoretically the bistable behavior of intracavity photon number in a two-mode cavity optomechanical system, where two cavity modes are coupled to a common mechanical resonator. When the two cavity modes are driven by two pump laser beams, respectively, we find that the optical bistability can be controlled by tuning the power and frequency of the pump beams. The common interaction to a mechanical mode enables one to control the bistable behavior in one cavity by adjusting the pump laser beam driving another cavity. We also show that both branches of optical bistability at photon numbers below unity can be observed in this two-mode optomechanical system. This phenomenon can find potential applications in controllable optical switch.