Generation of optical-photon-and-magnon entanglement in an optomagnonics-mechanical system

We present a scheme to implement a steady optical-photon-and-magnon entanglement in a hybrid optomagnonics-mechanical system by adiabatical elimination of the auxiliary microwave (MW) cavity and effective laser cooling of a delocalized Bogoliubov mode. The system consists of a magnon, an optical and a MW cavities, and a mechanical vibrator. To achieve a direct entangling interaction between the magnon and the optical photon, we drive the optical cavity and magnon at the red and blue sideband associated with the mechanical resonator, respectively. In particular, by eliminating the MW cavity and optimizing the relative ratio of effect couplings, rather than merely increasing their magnitudes, we achieve a strong entanglement between optical photons and magnons.