Optical Response and Drift Matrix of Quadratic Optomechanical System

Nonlinear interactions in optomechanical systems play a crucial role in many emerging number of interesting studies and phenomena such as existence of optomechanical chaos introduced by F. Monifi et al. [Nature Photonics 10, 399405 (2016)] and optomechanical symmetry breaking proposed by Zhong-Peng Liu et al. [Phys. Rev. Lett.117, 110802 (2016)]. In this article we have theoretically examined quadratically coupled optomechanical system containing two atomic levels. We have first studied the solution of various modes of the system at steady state and later we have observed the variation of Transmission Intensity (T) with several parameters of the system. Further we have extended our analyzation to find Drift matrix of the quadratic optomechanical system and stability conditions by adiabetically eliminating atomic degree of freedom.