Perturbative Input-Output Theory of Floquet Cavity Magnonics and Magnon Energy Shifts

TL;DR

The work addresses how Floquet modulation modifies the spectra of cavity magnonics by developing a perturbative input–output formalism that expands in the small parameter $ε=(2Ns)^{-1/2}$. This yields analytic expressions for reflectance up to second order, capturing Floquet sidebands and a Zeeman-induced magnon detuning of order $Δ_b ∼ G_b^2/ω_b$ that is tied to the modulation volume. A key result is the identification of a measurable 0.8 GHz detuning arising from the Zeeman interaction with the modulation field, plus a mapping between the quantum perturbative parameters and the semi-classical Floquet coupling $Ω$, enabling parameter extraction from spectra. The framework is general and scalable to multi-mode cavities and hybrid quantum devices, providing a practical tool for designing Floquet-engineered magnonic systems and transducers.

Abstract

We develop a perturbative input-output formalism to compute the reflectance and transmittance spectra of cavity magnonics systems subject to a Floquet modulation. The method exploits the strong hierarchy between the magnetic-dipole couplings transverse (drive field) and parallel (modulation field) to the static bias field, which naturally introduces the small parameter $ε= (2Ns)^{-1/2}$ associated with the total spin $Ns$ of the ferromagnet. By organizing the cavity and magnon fields in a systematic expansion in $ε$, we obtain compact analytic expressions for the spectra up to second order. Using these results, we reproduce the characteristic sideband structure observed in recent Floquet cavity electromagnonics experiments. Furthermore, accounting for the Zeeman interaction between the modulation field and the fully polarized ground state - a contribution typically neglected in previous treatments - we predict an additional magnon detuning of approximately $0.8\,\mathrm{GHz}$, independent of both modulation frequency and sample size and determined solely by the spatial volume occupied by the modulation field. This identifies a measurable and previously overlooked shift relevant for the interpretation and design of cavity magnonics experiments.

Figures (6)

• Figure 1: Illustration of the ferromagnet excited by the two microwave fields.
• Figure 2: (Left) Absolute reflectance $|S_{11}|$ in dB as a function of the in-plane detuning $(\omega-\omega_c)/2\pi$ and the squared modulation parameter $u_b^2$. (Right) Reflectance at the threshold of validity, $u_b = u_b^{\mathrm{max}}$.
• Figure 3: (Left) Absolute reflectance $|S_{11}|$ in dB as a function of the in-plane detuning $(\omega-\omega_c)/2\pi$ and the squared in-plane parameter $u_c^2$. (Right) Reflectance at the threshold of validity, $u_c = u_c^{\mathrm{max}}$.
• Figure 4: Second-order reflectance spectra. (a)--(c) Detuning of the cavity mode vs. magnon detuning for modulation frequencies $\omega_b/2\pi =$ (a) $5~\mathrm{MHz}$, (b) $14~\mathrm{MHz}$, and (c) $28~\mathrm{MHz}$. (d) Reflectance as a function of cavity detuning and modulation frequency.
• Figure 5: Ultra-strong Floquet coupling regime. (Left) Reflectance as a function of cavity detuning and modulation frequency $\omega_b/2\pi$. (Right) Reflectance as a function of detuning for fixed $\omega_b/2\pi = 3.85~\mathrm{MHz}$, showing a pronounced reflection dip.