Quantum entanglement between two magnon modes via Kerr nonlinearity driven far from equilibrium

We propose a scheme to entangle two magnon modes via the Kerr nonlinear effect when driving the systems far from equilibrium. We consider two macroscopic yttrium iron garnets interacting with a single-mode microcavity through the magnetic dipole coupling. The Kittel mode describing the collective excitations of a large number of spins is excited through the driving cavity with a strong microwave field. We demonstrate how Kerr nonlinearity creates the entangled quantum states between the two macroscopic ferromagnetic samples, when the microcavity is strongly driven by a blue-detuned microwave field. Such quantum entanglement survives at the steady state. Our work offers insights and guidance in designing experiments for observing entanglement in massive ferromagnetic materials. It can also find broad applications in macroscopic quantum effects and magnetic spintronics.