Barnett effect boosted nonreciprocal entanglement and EPR-steering in magnomechanics in the presence of coherent feedback loop

We propose an experimental scheme for enhancing entanglement, achieving asymmetric Einstein-Podolsky-Rosen (EPR) steering, and creating nonreciprocal quantum correlations within a hybrid system. This system integrates a yttrium iron garnet (YIG) sphere, which exhibits magnon-phonon coupling via magnetostriction, with a silica sphere featuring optomechanical whispering-gallery modes. By tuning the Barnett effect through the magnetic field direction, our system enables controllable asymmetric EPR steering and nonreciprocal entanglement between both directly and indirectly coupled modes. We demonstrate that adjusting the reflectivity of a beam splitter can boost stationary quantum steering and entanglement, effectively countering thermal noise. This approach allows for the generation of multipartite entanglement and both one-way and two-way steering. The proposed system is experimentally feasible and holds significant promise for various quantum information applications.