Magnetostrictively induced stationary entanglement between two microwave fields

We present a scheme to entangle two microwave fields by using the nonlinear magnetostrictive interaction in a ferrimagnet. The magnetostrictive interaction enables the coupling between a magnon mode (spin wave) and a mechanical mode in the ferrimagnet, and the magnon mode simultaneously couples to two microwave cavity fields via the magnetic dipole interaction. The magnon-phonon coupling is enhanced by directly driving the ferrimagnet with a strong red-detuned microwave field, and the driving photons are scattered onto two sidebands induced by the mechanical motion. We show that two cavity fields can be prepared in a stationary entangled state if they are respectively resonant with two mechanical sidebands. The present scheme illustrates a new mechanism for creating entangled states of optical fields, and enables potential applications in quantum information science and quantum tasks that require entangled microwave fields.