Tunable optical response in a hybrid quadratic optomechanical system coupled with single semiconductor quantum well

Quantum optomechanical system serves as an interface for coupling between photons and phonons via radiation pressure. We theoretically investigate the optical response of a hybrid optomechanical system that contains a single undoped semiconductor quantum well inside a cavity as well as a thin dielectric movable membrane in the middle, quadratically coupled to the cavity photons. We find that in the presence of both quadratic optomechanical coupling and exciton-cavity field coupling, two additional absorption dips appear in the output field spectrum of the probe field as compared to a standard quadratic optomechanical system which gives only two-phonon optomechanical induced transparency and optomechanical induced absorption phenomena with probe field detuning. This is due to the formation of the dressed state mediated by the single-photon state and the exciton mode. Furthermore, we have shown that the optical transmission of the probe field at these two absorption dips can be controlled by a number of parameters present in the system like exciton-cavity field coupling strength, decay rate of exciton as well as the mean number of thermal phonons- in the environment. We also explore the possibility of slow light in this absorption regime due to exciton-photon coupling. Our study shall provide a method to control the propagation of light in quadratic hybrid optomechanical system containing semiconductor nanostructures.