Circuit-based cavity magnonics in the ultrastrong and deep-strong coupling regimes

We theoretically study nonperturbative strong-coupling phenomena in cavity magnonics systems in which the uniform magnetization dynamics (magnons) in a ferromagnet is coupled to the microwave magnetic field (photons) of a single LC resonator. Starting from an effective circuit model that accounts for the magnetization dynamics described by the Landau-Lifshitz-Gilbert equation, we show that a nontrivial frequency shift emerges in the ultrastrong and deep-strong coupling regimes, whose microscopic origin remains elusive within a purely classical framework. The circuit model is further quantized to derive a minimal quantum mechanical model for generic cavity magnonics, which corresponds to a two-mode version of the Hopfield Hamiltonian and explains the mechanism of the frequency shifts found in the {\it classical} circuit model. We also formulate the relation between the frequency shift and quantum quantities, such as the ground-state particle number, quantum fluctuations associated with the Heisenberg uncertainty principle, and entanglement entropy, providing a nondestructive means to experimentally access to these quantum resources. By utilizing soft magnons in an anisotropic ferromagnet, we further demonstrate that these quantum quantities diverge at the zeros of the magnon band edges as a function of the external magnetic field. This work paves the way for cavity magnonics beyond the conventional strong coupling regime.