Quantum Effects in a Second-Order Coupled Electro-Optomechanical System with Kerr Medium

We propose a hybrid quantum-correlated tripartite system scheme involving an optical cavity with Kerr medium, a microwave cavity interacting via a mechanical resonator. Using a quantum Langevin equation (QLE) approach, we study the system’s steady state and stationary quantum fluctuations. The system features Kerr nonlinearity, second-order optomechanical coupling, and electro-optomechanical coupling. We examine how these nonlinearities impact normal mode splitting, entanglement, and the squeezing spectrum within the experimentally accessible parameter regime. Our results show that normal mode splitting occurs only when all nonlinearities in the system are present. We also found that these various nonlinearities influence entanglement between subsystems. Additionally, we discovered that only two specific nonlinearities-Kerr nonlinearity and second-order optomechanical coupling-affect the output field intensity and the squeezing spectrum of the light. The proposed scheme offers insight into the tripartite coherent interaction among the optical, mechanical and microwave modes, which helps to develop a quantum information processing unit.