Optical bistability in coupled optomechanical cavities in the presence of Kerr effect

We theoretically investigate optical bistability for a hybrid optomechanical system, where two cavities (an optomechanical cavity and a traditional one) are coupled together. A Kerr medium is inserted in the optomechanical cavity and there is an ultra-cold atomic gas inside the other. Dynamics of the system is described by Heisenberg-Langevin equations of motion in the steady-state regime. Bistability is observed in intracavity intensity for the optomechanical cavity, and the response of this phenomenon to optical parameters of the system is investigated. It is observed that the atomic medium has a deep effect on bistable behavior of intracavity intensity for the optomechanical cavity. Also, we determine a critical value for the Kerr coefficient of the Kerr medium to observe bistability in intracavity intensity for the optomechanical cavity.