  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.
