Bistability-assisted Mechanical Squeezing and Entanglement

We propose a scheme to squeeze mechanical motion and to entangle optical field with mechanical motion in an optomechanical system containing a parametric amplification. The scheme is based on optical bistability which emerges in the system for a strong enough driving field. By considering the steady state's lower branch of the bistability, the system shows weak entanglement and almost no mechanical squeezing. When the steady state is on the upper branch of the bistable shape, both squeezing and entanglement are greatly enhanced. Specifically, the entanglement shows three degrees of magnitude enhancement. However, this giant entanglement is fragile against decoherence and thermal fluctuation. Regarding the mechanical squeezing, it reaches the standard quantum limit (SQL) in the upper branch of the bistability. Our proposal provides a way to improve quantum effects in optomechanical systems by taking advantage of nonlinearities. This scheme can be realized in similar systems such as superconducting microwave, and hybrid optomechanical systems.