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

TL;DR

The paper investigates nonperturbative light–matter coupling in cavity magnonics by coupling a single-mode LC resonator to a uniform magnon in a ferromagnet through an effective circuit model derived from the LLG equation. It derives a minimal quantum description as a two-mode Hopfield Hamiltonian with magnon self-interaction, which explains a nontrivial positive frequency shift observed in USC/DSC and shows that the model avoids a superradiant phase transition. It further connects spectral shifts to ground-state quantum properties, including mean photon/magnon numbers, quantum fluctuations, and entanglement entropy, and reveals their divergence near soft-magnon critical fields. These results provide a framework for exploring cavity magnonics beyond conventional strong coupling, with implications for nondestructive quantum-resource readout and tunable quantum states in anisotropic ferromagnets.

Abstract

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.

Figures (11)

• Figure 1: Effective circuit model of cavity magnonics systems in which ${\bf h}(t)$ is a microwave magnetic field (photon) in an inductor and ${\bf m}(t)$ is uniform magnetization dynamics (magnon) in a ferromagnet (FM) biased by an external static magnetic field ${\bf H}_0$. Here, the cross-section of the inductor is assumed to be circuital, which is characterized by $d$ and $d_{\rm M}$ being diameters of the inductor and ferromagnet, respectively. Depending on the balance between the external magnetic field and demagnetization field, the equilibrium position of the magnetization is determined, which is characterized by a polar angle $\theta_{\infty}$ measured from the $z$-axis.
• Figure 2: Calculated transmission amplitude ($|S_{21}|^2$) of the MP hybridized modes as functions of an input frequency ($\omega/(2\pi)$) and an external magnetic field ($\mu_0H_0$) for $d_{\rm M}/d = 1$. Asymmetric Rabi-like splittings emerges at the original mode crossing points, which is an experimental signature of the nonperturbative strong coupling.
• Figure 3: Calculated eigenfrequency ($\omega_\pm$) of the MP hybridized modes as a function of an external magnetic field ($\mu_0H_0$) for different values of $d_{\rm M}/d$: (a) 0.02, (b) 0.2, (c) 0.4, and (d) 1. The solid lines are results of the no RWA case that is equivalent to the eigenfrequency of the two-mode Hopfield model ($\omega_\pm^{\rm Hopfield}$ in Eq. (\ref{['omegaHopfield']})). Green arrows represent positive frequency shifts at each external magnetic field.
• Figure 4: (a) Calculated coupling ratios ($g/\omega_{\rm c}$) of the hybridized MP modes as a function of $d_{\rm M}/d$ for different values of an external magnetic field. For this calculation, $d = 2$ mm is fixed. (b) Calculated frequency shift ($\delta\omega_\pm$) at the original modes crossing point as a function of $g/\omega_{\rm c}$.
• Figure 5: Normalized coupling strength ($g/\omega_{\rm c}$) and coefficient ($D_{\rm m}/\omega_{\rm c}$) as a function of an external magnetic field ($\mu_0H_0$). For this calculation, $d_{\rm M}/d = 1$ is used.