Enhancing the Steady-State Entanglement between a Laguerre-Gaussian-Cavity Mode and a Rotating Mirror via Cross-Kerr Nonlinearity

Quantum entanglement will play an important role in future quantum technologies. Here, we theoretically study the steady-state entanglement between a cavity field and a macroscopic rotating mirror in a Laguerre-Gaussian-(LG)-cavity optomechanical system with cross-Kerr nonlinearity. Logarithmic negativity is used to quantify the steady-state entanglement between the cavity and mechanical modes. We analyze the impacts of the cross-Kerr coupling strength, the cavity detuning, the input laser power, the topological charge of the LG-cavity mode, and the temperature of the environment on the steady-state optomechanical entanglement. We find that cross-Kerr nonlinearity can significantly enhance steady-state optomechanical entanglement and make steady-state optomechanical entanglement more robust against the temperature of the thermal environment.