Observation of long-lifetime magnon pairs by Fano resonance of photons

Mode fluctuations with a long lifetime are essential for quantum information and logic operations in magnonic devices. We probe the broadband nonlinear magnetization dynamics of a high-quality ferromagnet under a strong microwave drive using microwave spectroscopy. We observe an unexpected Fano resonance in the microwave transmission when the driven amplitude of the magnetization is large and the drive frequency ωd is close to but not at the ferromagnetic resonance. We interpret this Fano resonance by a scattering theory of photons considering the three-magnon interaction between the Kittel magnon and magnon pairs with opposite wave vectors of frequency ωd/2. The theoretical model suggests that the microwave spectroscopy measures the dynamics of the fluctuation δα̂ of the Kittel magnon and δβ̂±k of the magnon pairs over the driven steady states, which are coupled coherently by the steady-state amplitudes. With the damping of δβ̂±k much smaller than that of δα̂, the theoretical calculation well reproduces the observed Fano resonance, indicating that the magnon pairs hold a recorded long lifetime.