Connecting Fano interference and the Jaynes-Cummings model in cavity magnonics

We show that Fano interference can be realized in a macroscopic microwave cavity coupled to a spin ensemble at room temperature. Via a formalism developed from the linearized Jaynes-Cummings model of cavity electromagnonics, we show that generalized Fano interference emerges from the photon-magnon interaction at low cooperativity. In this regime, the reflectivity approximates the scattering cross-section derived from the Fano-Anderson model. Although asymmetric lineshapes in this system are often associated with the Fano formalism, we show that whilst Fano interference is actually present, an exact Fano form cannot be achieved from the linear Jaynes-Cummings model. In the Fano model an additional contribution arises, which is attributed to decoherence in other systems, and in this case is due to the resonant nature of the photonic mode. The formalism is experimentally verified and accounts for the asymmetric lineshapes arising from the interaction between magnon and photon channels. As the magnon-photon coupling strength is increased, these channels merge into hybridized magnon-photon modes and the generalized Fano interference picture breaks down. Our results are universally applicable to systems underlying the linearized Jaynes-Cummings Hamiltonian at low cooperativity and connect the microscopic parameters of the quantum optical model to generalized Fano lineshapes.