Optical tristability in a hybrid optomechanical system

In this paper, we investigate a hybrid optomechanical system consisting of two cavities, which one of them is an optomechanical cavity that includes an optical parametric amplifier (OPA) and the other is a traditional cavity which contains an atomic medium. Hamiltonian of the system is written in a rotating frame with a rotation frequency of the frequency of input field to the system. Using Heisenberg-Langevin equations of motion, the dynamics of the system is described. Applying the steady-state conditions leads to a system of equations of the mean values of the operators of the system. The stability condition of the system is satisfied numerically and behavior of optomechanical cavity is investigated in different situations to find the effect of changing of the parameters of the system on the type of its stability. We show proposed system has the capability of tristable behavior, where, the gain coefficient of OPA acts as a switch in changing the bistability of the system to a tristable manner. The building block of the tristability in this system can be figured out as the enhanced nonlinearity of the system due to the presence of OPA.