Entanglement generation between different center-of-mass motions in double levitated micromagnet system

We theoretically propose a scheme to realize quantum entanglement between two center-of-mass motion (CM) as the external degrees of freedom of two separated levitated yttrium iron garnet spheres. The microwave cavity field is introduced to bridge the interaction between the two separated micromagnet spheres. The optimal condition for getting entanglement between the two CM modes with and without effective cavity-magnon interaction cases are investigated. It is found that the entanglement between two CM modes could be obtained by choosing the appropriate magnon detunings for each case. The effect of the coupling strength and the thermal occupation on the entanglement are also discussed. To realize the entanglement between to CM modes, it is necessary to balance the related parametric interaction and beam splitter interaction. The results show that the CM-CM entanglement is robust against the thermal noise. This scheme would be valuable for quantum network generation and quantum information processing.