Normal-mode splitting in an optomechanical system enhanced by an optical parametric amplifier and coherent feedback

Abstract

Normal-mode splitting (NMS) is an evident signature of strong coupling interactions for observing quantum phenomena, such as optomechanical squeezing and entanglement. In the previous literature, optical parametric amplifier (OPA) and coherent feedback are independently proposed to enhance the NMS. Here, we combine OPA and coherent feedback into a single optomechanical system to enhance the NMS. Controllable parameters, such as input optical power, OPA gain and phase, coherent feedback strength, are varied to observe NMS variations. In particular, we consider positive and negative feedback in terms of the amplitude reflectivity of the beam splitter for coherent feedback. The NMS appears mostly with the positive coherent feedback rather than the negative. Furthermore, the largest mode separation occurs at an OPA phase of approximately rather than zero because the effective cavity detuning changes the effective intracavity round-trip phase, and therefore changes the OPA amplification/deamplification condition. The results indicate that the interplay between OPA and coherent feedback can enhance the NMS with more controllable parameter freedoms. This scheme provides a promising way to increase the optomechanical coupling strength, thereby having potential applications in the ground state cooling of a mechanical oscillator, the preparation of optomechanical quantum states, and the sensitive detection of a weak force.