Robust and macroscopic genuine tripartite entanglement of levitated magnomechanical systems based on a nonlinear optical medium

We present a scheme to generate robust and macroscopic genuine tripartite entanglement of a microwave cavity-magnomechanical system with a levitated yttrium iron garnet (YIG) sphere via a nonlinear optical medium. The center-of-mass motion (CM) of the YIG sphere (phonon) is trapped in a harmonic potential. The squeezing of the microwave cavity mode can enhance the coupling constant of the system and the noise of the squeezed cavity mode could be suppressed completely by introducing a broadband-squeezed vacuum environment when its phase is chosen appropriately. Particularly, there is genuine tripartite entanglement between the photon, magnon, and the CM of the YIG sphere which is robust against the thermal fluctuations and independent of the mass and size of the YIG sphere. The present work provides a method to produce robust and macroscopic tripartite entanglement in cavity magnomechanical systems in experiments.