Figure 1

(a)-(b) Hybrid atom-optomagnomechanical system. An optical mode driven by a laser at frequency \(\omega _{L}\) in a spinning resonator couples to an ensemble of two-level atoms (a) and a magnon mode (m) in a YIG micro-bridge by the mediation of a phonon mode (b) induced by magnetostriction. The YIG micro-bridge is driven by a strong microwave field at frequency \(\omega _{0}\), and simultaneously is in a uniform bias magnetic field along the z direction. (c) Frequencies and linewidths of the system. When the magnon is resonant with the blue sideband (anti-Stokes) of the driven field at frequencies \(\omega _{0}+\omega _{b}\) and the optical photon and atom modes are scatted by the phonon onto two sidebands, the genuine atom-magnon-phonon entanglement is generated at the steady state. (d) By fixing the CW rotation of the resonator, we have the frequency \(\omega _{c}-\Delta _{s}\) (\(\omega _{c}+\Delta _{s}\)) for the optical CW (CCW) mode when the light is driven from the right-hand (left-hand)