Entanglement between a Macroscopic Displacement and Microwave Fields from Levitated Macromagnet

Abstract This work is aimed at the quantum entanglement between cavity microwave and center-of-mass motion of a ferrimagnetic yttrium-iron-garnet (YIG) sphere levitated in two microwave cavities. In such a cavity magnomechanical (CMM) system, the magnons, i.e., quanta of collective spin-wave excitations in YIG sphere, are coupled to a center-of-mass displacement via intensive CMM coupling in a strongly driven cavity, and are simultaneously coupled to the other cavity via magnetic dipole interaction. We reveal that the detuning condition is necessary to improve the mediation effect of magnon for generating the macroscopic entanglement. Particularly, this center-of-mass motion can be adjusted by suitable levitation technology, unlike the mechanical deformation limited by the fixed construction of YIG sphere in standard CMM system. We also indicate that the entanglement via the unique CMM coupling is independent of size and mass of the YIG sphere, beneficial to explore the macroscopic entanglement effect in combination with size-independent cooling. These findings suggest that our scheme opens up an alternative and novel direction in the exploration and application of macroscopic quantum effect.