Detection sensitivity enhancement of magnon Kerr nonlinearity in cavity magnonics induced by coherent perfect absorption

We show how to enhance the detection sensitivity of magnon Kerr nonlinearity (MKN) in cavity magnonics. The considered cavity-magnon system consists of a three-dimensional microwave cavity containing two yttrium iron garnet (YIG) spheres, where the two magnon modes (one has the MKN, while the other is linear) in YIG spheres are simultaneously coupled to microwave photons. To obtain the effective gain of the cavity mode, we feed two input fields into the cavity. By choosing appropriate parameters, the coherent perfect absorption of the two input fields occurs, and the cavity-magnon system can be described by an effective non-Hermitian Hamiltonian. Under the pseudo-Hermitian conditions, the effective Hamiltonian can host the third-order exceptional point (EP3), where the three eigenvalues of the Hamiltonian coalesce into one. When the magnon frequency shift $\Delta_K$ induced by the MKN is much smaller than the linewidths $\Gamma$ of the peaks in the transmission spectrum of the cavity (i.e., $\Delta_K\ll \Gamma$), the magnon frequency shift can be amplified by the EP3, which can be probed via the output spectrum of the cavity. The scheme we present provides an alternative approach to measure the MKN in the region $\Delta_K\ll \Gamma$ and has potential applications in designing low-power nonlinear devices based on the MKN.