Enhancement of entanglement in distant micromechanical mirrors using parametric interactions

We theoretically investigate the stability of a two cascaded cavity optomechanical system with optical parametric amplifiers (OPAs) inside the two coupled cavities, and study the steady-state entanglement between two distant mechanical resonators. We show that the parameter regime where the system is unstable without OPAs, such as relatively high laser intensity and blue detuning, can be exploited to build the steady-state mechanical entanglement by modulating the parametric gain. The application of OPAs is helpful to preserve the mechanical entanglement suffered from the dissipation at some finite temperature. The scheme provides an alternative way for improving and engineering the quantum entanglement of two distant mechanical oscillators.