Stationary quantum entanglement and steering between two distant macromagnets

Generating and manipulating magnon quantum states for quantum information processing is a central topic in quantum magnonics. The conventional strategy amplifies the nonlinear interaction among magnons to manifest their quantum correlations at cryogenic temperatures, which is challenging for magnets with vanishingly small nonlinearities. Here we propose an unconventional approach to prepare entangled states of two distant magnon modes by applying a two-tone Floquet field to each magnet inside a microwave cavity. The Floquet driving can effectively generate parametric interaction between magnons and photons, and thus opens an indirect entanglement channel between the two magnon modes mediated by cavity photons. By optimizing the relative ratio of the magnon-photon coupling and the detuning between the magnon modes, the two magnon modes can reach a stationary and robust entanglement, of which the strength is enhanced compared with entanglement generated via magnetic nonlinearities. Furthermore, one-way steering between the two magnets is realized by engineering unequal damping rates of the two magnets while the steering asymmetry can be efficiently modulated by tuning the coupling strength of magnons and cavity photons. The essential physics of our findings universally applies to a wide class of magnets with small nonlinearities and may find promising applications in engineering robust magnon quantum states for quantum information science.