Entangling two magnon modes via magnetostrictive interaction

We present a scheme to entangle two magnon modes in a cavity magnomechanical system. The two magnon modes are embodied by collective motions of a large number of spins in two macroscopic ferrimagnets, and couple to a single microwave cavity mode via magnetic dipole interaction. We show that by activating the nonlinear magnetostrictive interaction in one ferrimagnet, realized by driving the magnon mode with a strong red-detuned microwave field, the two magnon modes can be prepared in an entangled state. The entanglement is achieved by exploiting the nonlinear magnon-phonon coupling and the linear magnon-cavity coupling, and is in the steady state and robust against temperature. The entangled magnon modes in two massive ferrimagnets represent genuinely macroscopic quantum states, and may find applications in the study of macroscopic quantum mechanics and quantum information processing based on magnonics. (paper)