We present a scheme to entangle the vibrational phonon modes of two massive ferromagnetic spheres in a dual-cavity magnomechanical system. In each cavity, a microwave cavity mode couples to a magnon mode (spin wave) via the magnetic dipole interaction, and the latter further couples to a deformation phonon mode of the ferromagnetic sphere via a nonlinear magnetostrictive interaction. We show that by directly driving the magnon mode with a red-detuned microwave field to activate the magnomechanical anti-Stokes process a cavity–magnon–phonon state-swap interaction can be realized. Therefore, if the two cavities are further driven by a two-mode squeezed vacuum field, the quantum correlation of the driving fields is successively transferred to the two magnon modes and subsequently to the two phonon modes, i.e., the two ferromagnetic spheres become remotely entangled. Our work demonstrates that cavity magnomechanical systems allow to prepare quantum entangled states at a more massive scale than currently possible with other schemes.

我们提出了一个方案，以在双腔机械系统中纠缠两个大铁磁球的振动声子模。在每个空腔中，微波空腔模式通过磁偶极子相互作用耦合到磁振子模式（自旋波），后者通过非线性磁致伸缩相互作用进一步耦合到铁磁球体的形变声子模子。我们表明，通过用红色失谐微波场直接驱动磁振子模式来激活反机械斯托克斯过程，可以实现腔-磁振子-声子状态-交换相互作用。因此，如果两个腔被双模式压缩真空场进一步驱动，则驱动场的量子相关性依次转移到两个磁振子模式，然后转移到两个声子模式，即，两个铁磁球变得遥远地纠缠在一起。我们的工作表明，腔体力学系统可以比目前其他方案更大规模地制备量子纠缠态。