Nonreciprocal mechanical entanglement in a spinning optomechanical system

Quantum entanglement between distant massive mechanical oscillators is an important resource in sensitive measurements and quantum information processing. We achieve the nonreciprocal mechanical entanglement in a compound optomechanical device consisting of two mechanical oscillators and a spinning whispering-gallery mode (WGM) optical microresonator. It is found that obvious nonreciprocal mechanical entanglement emerges in this system in the presence of the Sagnac effect which is induced by the rotation of the WGM resonator, and the nonreciprocal region can be controlled by tuning the angular velocity of the rotation. The nonreciprocity originates from the breaking of the time-reversal symmetry of this multimode system due to the presence of the Sagnac effect. The optomechanical coupling and the mechanical interaction provide cooling channels for the first and second mechanical oscillators, respectively. Two mechanical oscillators can be cooled simultaneously. The simultaneous cooling and the mechanical coupling of two mechanical oscillators ensure the generation of mechanical entanglement. Furthermore, an optimal mechanical entanglement can be achieved when the moderate optical frequency detuning and the driving power are chosen. The thermal noise of the mechanical environment has a negative effect on mechanical entanglement. Our scheme provides promising opportunities for research of quantum information processing based on phonons and sensitive measurements.