  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, we present a
new mechanism to prepare microwave-optics entanglement based on a hybrid system
of two coupled opto- and magnomechanical microspheres, i.e., a 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. We show 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. Our
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.
