Entanglement formation between magnon and center-of-mass motion of a levitated particle in a magnomechanical system

Entanglement formation between the magnons as the internal degrees of freedom and the center-of-mass motion (CM) as the external degrees of freedom of a levitated yttrium iron garnet (YIG) sphere in a cavitymagnomechanical system is studied. Here, we propose a scheme for generating magnon-CM entanglement independent from the mass and size of the sphere in the hybrid magnonic system by driving the magnon with the parametric amplification. First, we show that the power and frequency of the driving field significantly affect this entanglement, since the driving field increases effective magnon-CM coupling. But, by increasing the magnon damping rate, this entanglement considerably decreases. Moreover, in the next step, we demonstrate the manipulation and enhancement of this entanglement by driving the magnon into the squeezed state. Our results present an approach for preparing quantum states and may find promising applications in the quantum metrology and sensing.