Nonreciprocal entanglement in cavity magnomechanics exploiting chiral cavity-magnon coupling

We show how to achieve nonreciprocal quantum entanglement in a cavity magnomechanical system by exploiting the chiral cavity-magnon coupling. The system consists of a magnon mode, a mechanical vibration mode, and two degenerate counter-propagating microwave cavity modes in a torus-shaped cavity. We show that nonreciprocal stationary microwave-magnon and -phonon bipartite entanglements and photon-magnon-phonon tripartite entanglement can be achieved by respectively driving different circulating cavity modes that hold a chiral coupling to the magnon mode. The nonreciprocal entanglements are shown to be robust against various experimental imperfections. The work may find promising applications of the cavity magnomechanical systems in nonreciprocal electromechanical quantum teleportation and chiral magnonic quantum networks.