Controllable optical multistability in hybrid optomechanical system assisted by parametric interactions

We theoretically investigate the multistable behavior of a hybrid optomechanical system, in which a charged mechanical resonator is coupled via Coulomb interaction to an optomechanical cavity containing an optical parametric amplifier (OPA). It is shown that the multistable behavior of the mean intracavity photon number can be controlled flexibly by adjusting the nonlinear gain parameter of the OPA, the phase of the field pumping the OPA, the power and frequency of the field driving the cavity, and the Coulomb coupling strength between the two charged mechanical resonators. In particular, the increase of the nonlinear gain parameter can result in a transition from bistability to tristability. Moreover, the effect of the Coulomb coupling strength on the bistable behavior of the steady-state positions of the two mechanical resonators is discussed.