Einstein-Podolsky-Rosen entanglement and asymmetric steering between distant macroscopic mechanical and magnonic systems

We propose a deterministic scheme for establishing hybrid Einstein-Podolsky-Rosen (EPR) entanglement channel between macroscopic mechanical oscillator and magnon mode in distant yttrium-iron-garnet (YIG) sphere across about ten gigahertz of frequency difference. The system consists driven electromechanical cavity which is unidirectionally coupled to electromagnonical inside YIG placed. find that far beyond the sideband-resolved regime subsystem, stationary phonon-magnon EPR can be achieved. This realized by utilizing output field being an intermediary distributes magnons, thus remote entanglement. strong enough such quantum steering attainable asymmetric manner. long-distance enable potential applications not only fundamental tests mechanics at macro scale, but also networking one-sided device-independent cryptography based on magnonics electromechanics.