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arXiv:2512.12103

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

T. Aguiar, M. C. de Oliveira

cond-mat.mes-hallphysics.app-phquant-phSubmitted Dec 13, 2025• Announced Dec 16, 2025
v1 · Dec 13, 2025v2 · Jun 11, 2026
arXivHTMLPDF

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.

Journal reference
New J. Phys. 28 043501 (2026)
DOI
10.1088/1367-2630/ae537d

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Laser Physics Letters•Nov 2, 2022•1 citation
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)−1/2ε= (2Ns)^{-1/2}ε=(2Ns)−1/2 associated with the total spin NsNsNs of the ferromagnet. By organizing the cavity and magnon fields in a systematic expansion in εεε, 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 GHz0.8\,\mathrm{GHz}0.8GHz, 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.
We present a direct collective-spin derivation of the effective uniform-mode Hamiltonian used in cavity magnonics. Starting from a nearest-neighbor Heisenberg ferromagnet coupled to long-wavelength magnetic fields, we show that the relevant dynamics can be restricted to the fully symmetric spin sector, where the exchange interaction contributes only a constant energy shift and the ferromagnet behaves as a macrospin of length NsNsNs. Applying the Holstein--Primakoff transformation directly to this total spin yields the usual uniform magnon mode and its leading nonlinear corrections without first introducing site-resolved bosonic operators. This collective formulation makes explicit the interpretation of the ferromagnet as a synthetic large-spin atom and provides a compact route to the effective Hamiltonians used in driven and Floquet cavity magnonics. As a physical consequence, the leading nonlinear correction produces an occupation-dependent reduction of the effective magnon--photon coupling, providing a simple signature of finite-spin saturation under strong uniform-mode driving.
Cavity electromagnonics has increasingly emerged as a new platform for the fundamental study of quantum mechanics and quantum technologies. Since the coupling between the microwave field and magnon Kittle modes in current experiments is much weaker than their resonant frequencies, the anti-rotating terms in magnon-microwave-photon interaction can be neglected and only the beam-splitter-like part takes effect. In this situation, the direct generation of magnonic nonclassical states is impossible, unless other subsystems e.g. phonons, squeezed photons or superconducting qubits are incorporated. In this paper, we consider two-tone modulated cavity electromagnonics to keep the nontrivial anti-rotating terms and obtain tunable phase factors, resulting in an effective Hamiltonian exactly the same as that of generic linearized cavity optomechanics. This can therefore be exploited to directly prepare macroscopic magnonic quantum states, as detailedly exemplified by the generation of steady and strongly squeezed and entangled states, realize ultra-sensitive magnon-based sensing by engineering backaction-evading interaction of magnons and photons, and develop spintronics-related quantum information processing devices.
A scheme of an ultrasensitive magnetometer in the cavity quantum electromagnonics is proposed, where the intracavity microwave mode is coupled to a magnonic mode via magnetic dipole interaction. It is shown that by driving both magnonic and microwave modes with external classical fields and controlling the system parameters, one can reduce the added noise of magnetic field measurement below the standard quantum limit (SQL). Surprisingly, we show that beyond the rotating wave approximation (RWA), not only can the added noise be suppressed but also the output cavity response to the input signal can be substantially amplified in order to achieve a precise magnetic-field measurement. The estimated theoretical sensitivity of the proposed magnetic amplifier-sensor is approximately on the order of ${10}^{\ensuremath{-}18}\phantom{\rule{0.28em}{0ex}}\mathrm{T}/\sqrt{\mathrm{Hz}}$, which is competitive compared to the current state-of-the-art magnetometers like superconducting quantum interference devices (SQUIDs) and atomic magnetometers. The advantages of the proposed sensor in comparison with the other magnetometers is its high sensitivity at room temperature, sensing in a wide range of frequencies up to MHz, and its capability for signal-response amplification.
We theoretically study Floquet engineering of magnetic molecules via a time-periodic magnetic field that couples to the emergent total electronic spin of the metal center. By focusing on the low-lying energy levels using an S = 1 spin Hamiltonian containing the zero-field and Zeeman terms, we demonstrate their continuous tunability under the Floquet field. Remarkably, under the action of linearly polarized Floquet controls, the energy levels of a clock transition qubit retain their stability against variations in an external static magnetic field. This property is closely linked to having a net-zero total Zeeman shift, which results from both static and effective dynamical contributions. Furthermore, using second-order Van Vleck degenerate perturbation theory, we derived an effective Hamiltonian analytically, which explicitly shows the dependence of the renormalized zero-field tensor on the driving field. Based on our theoretical predictions, experimentalists will be able to dynamically tune qubit energy gaps to values that are useful in their specific laboratory settings, while retaining the spin decoherence suppressing effect of maintaining a clock transition.
We propose a scheme to engineer the superradiant phase transition (SPT) in cavity magnonics by periodically modulating the frequency of the magnon mode. The studied system is composed of a yttrium iron garnet (YIG) sphere positioned inside a microwave cavity, where magnons in the YIG sphere are strongly coupled to microwave photons. Under the Floquet drive, the effective frequencies of both the cavity and magnon modes can be readily controlled via the frequency and strength of Floquet field. This tunability allows the cavity magnonic system to support a rich steady-state phase diagram, featuring parity-symmetric, parity-symmetry-broken, bistable, and unstable phases. With the increase of Floquet-field strength, the system exhibit a discontinuous phase transition from the parity-symmetric phase to the parity-symmetry-broken phase at a critical threshold, accompanied by an abrupt jump of the magnon occupation from zero to a finite value. Upon further increase of Floquet-field strength, the magnon occupation declines continuously from a nonzero value back to zero, corresponding to a second-order phase transition that restores the parity-symmetric phase. Additionally, fluctuations in magnon number during the SPT process are examined. Our work establishes an alternative route to engineer the cavity-magnon SPT without relying on microwave parametric drive.
Abstract We propose a scheme to describe magnon-mediated multi-channel high-order sideband generation in a cross cavity magnonic system. The high-order sideband generation is composed of equally spaced discrete output frequency components, which is essential tools for light communication, precision metrology, timing and spectroscopy. Beyond the generally linearized description by using the perturbative method, we deal with the Heisenberg–Langevin equations in the non-perturbative regime to obtain the output spectrum of high-order sidebands. Unlike conventional methods of using power that requires externally adjustable incident beams, here we demonstrate magnon-mediated high-order sideband generation in a cavity magnonic device by utilizing its intrinsically good tunability. Furthermore, until now most of the work in cavity magnonics is mainly restricted to the frequency/time domain, while we realize the modulation of sideband effects by the manipulation of cavity-magnon polaritons in real space, that is the external magnetic field with a tunable angle. By tuning the angle, we can obtain multi-channel high-order sideband generation, which may offer the potential for selectively transferring coherent information processing technologies.