Abstract
Exceptional points with coalescence of eigenvalues and eigenvectors are spectral singularities in the parameter space, achieving which often needs fine-tuning of parameters in quantum systems. We predict a \textit{persistent} realization of nodal magnon-photon polariton, i.e., a polariton of long wavelength without any gap splitting in a thin ferromagnetic insulator film sandwiched by two normal metals, which persistently exists when the ferromagnet is sufficiently thick ∼ 100~nm due to the joint effect of dissipation and dissipative coupling. We perform the model calculation \textit{beyond the perturbation theory} using a classical approach, develop a quantum scheme able to account for the Ohmic dissipation, and find ultrastrong coupling with coupling strength comparable to the bare magnon frequency. Via revealing a simple conversion relation we extend this formalism to superconductors and predict the gap opened by the ultrastrong coupling strongly depends on the direction of polariton propagation. Our findings may help search for robust non-Hermitian topological phases in magnonic and spintronic devices.