Study of the optical response and coherence of a quadratically coupled optomechanical system

In this article, we theoretically investigate a quadratically coupled optomechanical system with a two-level atom. At steady-state, we examine the variation of transmission intensity with various parameters of the system as well as investigate the transmission in lower/upper sidebands. Moreover, taking into account the quantum fluctuations, we extend our investigation towards the study of quantum coherence for the optomechanical system. The result shows that the coherence inside the proposed cavity can be efficiently controlled by varying atom-to-photon coupling and modified optical detuning. We also discuss and provide a physical explanation of why the atomic coherence can surpass the optical and mechanical ones.