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Macroscopic entanglement of two magnon modes via quantum correlated microwave fields

We present a scheme to entangle two magnon modes in two macroscopic yttrium-iron-garnet spheres. The two spheres are placed inside two microwave cavities, which are driven by a two-mode squeezed microwave field. By using the linear state-swap interaction between the cavity and the magnon mode in each cavity, the quantum correlation of the two driving fields is with high efficiency transferred to the two magnon modes. Considerable entanglement could be achieved under experimentally achievable conditions $g \gg κ_a \gg κ_m$, where $g$ is the cavity-magnon coupling rate and $κ_a$, $κ_m$ are the decay rates of the cavity and magnon modes, respectively. The entanglement is in the steady state and robust against temperature, surviving up to hundreds of milliKelvin with experimentally accessible two-mode squeezed source.