Abstract
We theoretically calculate normal-mode splitting (NMS) in a linear and quadratic optomechanical system (OMS) with an ensemble of two-level atoms, where the interaction between the mechanical membrane and the optical cavity includes linear optomechanical coupling and quadratic optomechanical coupling (QOC). In the presence of atomic ensemble, a negative QOC strength is instrumental for generating NMS, while the positive QOC restricts NMS, and eventually it disappears. Further, for the hybrid OMS assisted with the atomic ensemble, the displacement spectrum of the mechanical resonator displays three peaks, where the middle peak results from the effective coupling strength between the cavity field and the atomic ensemble. Here the negative QOC strength and the effective ensemble-field coupling can provide an efficient control of the amplitude and position of the three peaks. (C) 2019 Optical Society of America