We study the optical bistability and dynamics in a hybrid optomechanical system, where the cavity mode is coupled to the mechanical resonator via radiation pressure and to a two-level atom via the Jaynes-Cummings coupling. The nonlinearity due to optomechanical coupling and the addition of an atom leads to bistable behaviors of the steady-state intracavity photon number and atomic population inversion. We show that the optical bistability can be effectively controlled by the Rabi frequency of the atomic driving field, the cavity-atom coupling strength, and the amplitude and frequency of the cavity pump field. Moreover, the effects of different initial conditions of the cavity field and the amplitude of the cavity pump field on the dynamics of the system also have been discussed. (C) 2016 Optical Society of America
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