Controllable double optical bistability via photon and phonon interaction in a hybrid optomechanical system

Optical bistability has been studied theoretically in a multi-mode optomechanical system with two mechanical oscillators independently coupled to two cavities in addition to direct tunnel coupling between cavities. It is shown that the bistable behavior of the mean intracavity photon number in the right cavity can be tuned by adjusting the strength of the pump laser beam driving the left cavity. In addition, the mean intracavity photon number is relatively larger in the red sideband regime than that in the blue sideband regime. Moreover, we show that the double optical bistability of the intracavity photon in the right cavity and the two steady-state positions of the mechanical resonators can be observed when the control field power is increased to a critical value. In addition, the critical values for the observation of bistability and double bistability can be tuned by adjusting the coupling coefficient between the two cavities and the coupling rates between cavity mode and mechanical mode.