Nonlinear pumping induced multipartite entanglement in a hybrid magnon cavity QED system

We present a proposal to produce bipartite and tripartite entanglement in a hybrid magnon cavity QED system. Two macroscopic yttrium iron garnet (YIG) spheres are coupled to a single-mode microwave cavity, where the cavity photons are generated via a two-photon process induced by a strong pump field. Using mean-field theory, we show that nonlinear pumping can result in strong bipartite entanglement between the cavity photon and magnon under two conditions, i.e., delta(c)delta(m) = 2g(2) and delta(c) = -delta(m). For the latter one, we also show the possibility for producing bipartite entanglement between two magnon modes as well as tripartite entanglement among three modes. Combining these two conditions, we further derive a third condition, i.e., delta(2)(m) - phi(2) + 2g(2) = 0, where tripartite entanglement can be achieved when two magnon modes have different resonant frequencies.