Normal-mode splitting in the optomechanical system with an optical parametric amplifier and coherent feedback

Strong coupling in optomechanical systems is the basic condition for observing many quantum phenomena such as optomechanical squeezing and entanglement. Normal-mode splitting (NMS) is the most evident signature of strong coupling systems. Here we show the NMS in the spectra of the movable mirror and the output field in an optomechanical system can be flexibly engineered by a combination of optical parametric amplifier (OPA) and coherent feedback (CF). Moreover, the NMS could be enhanced by optimizing the parameters such as input optical power, OPA gain and phase, CF strength in terms of amplitude reflectivity of beam splitter.