Microwave-optics entanglement plays a crucial role in building hybrid quantum networks with quantum nodes working in the microwave and optical frequency bands. However, there are limited efficient ways to produce such entanglement due to the large frequency mismatch between the two regimes. Here, a new mechanism is presented to prepare microwave-optics entanglement based on a hybrid system of two coupled opto- and magnomechanical microspheres, i.e., an yttrium-iron-garnet (YIG) sphere and a silica sphere. The YIG sphere holds a magnon mode and a vibration mode induced by magnetostriction, while the silica sphere supports an optical whispering-gallery mode and a mechanical mode coupled via an optomechanical interaction. The two mechanical modes are close in frequency and directly coupled via physical contact of the two microspheres. It is shown that by simultaneously activating the magnomechanical (optomechanical) Stokes (anti-Stokes) scattering, stationary entanglement can be established between the magnon and optical modes via mechanics-mechanics coupling. This leads to stationary microwave-optics entanglement by further coupling the YIG sphere to a microwave cavity and utilizing the magnon-microwave state swapping. The protocol is within reach of current technology and may become a promising new approach for preparing microwave-optics entanglement, which finds unique applications in hybrid quantum networks and quantum information processing with hybrid quantum systems.

Microwave-optics entanglement is a vital component for building hybrid quantum networks. Here, a new mechanism for preparing stationary entanglement between microwave and optical cavity fields in a cavity optomagnomechanical system is proposed. It consists of a magnon mode in a ferrimagnetic crystal that couples directly to a microwave cavity mode via the magnetic dipole interaction and indirectly to an optical cavity through the deformation displacement of the crystal. The mechanical displacement is induced by the magnetostrictive force and coupled to the optical cavity via radiation pressure. Both the opto- and magnomechanical couplings are dispersive. Magnon–phonon entanglement is created via magnomechanical parametric down-conversion, which is further distributed to optical and microwave photons via simultaneous optomechanical beamsplitter interaction and electromagnonic state-swap interaction, yielding stationary microwave-optics entanglement. The microwave-optics entanglement is robust against thermal noise, which will find broad potential applications in quantum networks and quantum information processing with hybrid quantum systems.