Observation of Long-Lifetime Magnon Pairs by Fano Resonance of Photons

TL;DR

This work demonstrates a Fano resonance in microwave transmission arising from nonlinear magnon dynamics in a YIG sphere under strong driving near the ferromagnetic resonance. A three‑magnon interaction between the Kittel mode and magnon pairs with opposite wave vectors, coupled via driven steady states, leads to a photon scattering process described by a Lippmann‑Schwinger formalism; the resulting self‑energy structure reproduces both the asymmetric Fano line shapes and the pump‑induced splitting, and reveals that the magnon pairs have a substantially longer lifetime than the Kittel mode. The model quantitatively matches experimental spectra and clarifies how the resonance shape depends on the detuning $ω_d-ω_0$ and on pump power, highlighting the potential of microwave spectroscopy to probe back‑action and lifetimes of nonlinear magnonic modes. These insights advance nonlinear magnonics and suggest routes to harness long‑lived magnon pairs for information processing and coherent magnon–photon interfacing, while noting that additional nonlinear channels may contribute in real systems.

Abstract

Mode fluctuations with a long lifetime are essential for quantum information and logic operations in magnonic devices. We probe the broadband nonlinear magnetization dynamics of a high-quality ferromagnet under a strong microwave drive using microwave spectroscopy. We observe an \textit{unexpected} Fano resonance in the microwave transmission when the driven amplitude of the magnetization is large and the drive frequency $ω_d$ is close to but not at the ferromagnetic resonance. We interpret this Fano resonance by a scattering theory of photons considering the three-magnon interaction between the Kittel magnon and magnon pairs with opposite wave vectors of frequency $ω_d/2$. The theoretical model suggests that the microwave spectroscopy measures the dynamics of the fluctuation $δ\hatα$ of the Kittel magnon and $δ\hatβ_{\pm k}$ of the magnon pairs over the driven steady states, which are coupled coherently by the steady-state amplitudes. With the damping of $δ\hatβ_{\pm k}$ much smaller than that of $δ\hatα$, the theoretical calculation well reproduces the observed Fano resonance, indicating the magnon pairs hold a recorded long lifetime.

Figures (8)

• Figure 1: Coupled harmonic oscillators with different dampings. The red ball represents the fluctuation $\delta \hat{\alpha}$ of the Kittel magnon, and the blue ball represents fluctuations $\delta \hat{\beta}_{\pm k}$ of magnon pairs with wave vector $\pm k$. They hold very different damping $\gamma_0\gg \gamma_{\pm k}$.
• Figure 2: Experimental configuration. A YIG sphere is loaded on top of the coplanar waveguide (CPW), biased by a magnetic field $H_{\rm ext }\hat{\bf y}$ along the central strip. The "pump" and "probe" microwave signals are generated, respectively, by the signal generator and vector network analyzer (VNA), which interact with the YIG sphere. The microwave transmission $S_{21}$ from Port "1" to Port "2" in the probe microwaves detects the dynamics of the magnetization when driven by the pump microwaves.
• Figure 3: Measured microwave transmission spectra at a constant pump power $P_d=-5$ dBm and different pump frequencies. (a) When $\omega_d<\omega_0$, we change the pump frequency $\omega_d/(2\pi)$ from $2.7650$ to $2.7800$ GHz, i.e., the pump frequency approaches the FMR frequency. Unstable signals appear when $\omega_d/(2\pi)$ varies from $2.7650$ to $2.7660$ GHz; Fano resonance occurs from $2.7662$ to $2.7700$ GHz; the pump-induced mode splitting is observed from $2.7702$ to $2.7800$ GHz. (b) When $\omega_d>\omega_0$, we change the pump frequency $\omega_d/(2\pi)$ from $2.7940$ to $2.7800$ GHz, i.e., away from the FMR frequency. Within this range, the FMR absorption spectrum is unaffected when the pump frequency is between $2.7940$ and $2.7920$ GHz; Fano resonance emerges when $\omega_d/(2\pi)$ exceeds $2.7918$ GHz; as the pump frequency increases, the Fano resonance gradually disappears while the modes split.
• Figure 4: Measured microwave transmission spectra at different pump powers under a fixed pump frequency. (a) When the fixed pump frequency is set to $\omega_d/(2\pi)=2.770$ GHz (below the FMR frequency), the pump power $P_d=-20$ dBm causes a signal instability at $\omega_d/(2\pi)$; increasing the pump power to $P_d=-7$ dBm induces the Fano resonance that persists until $P_d=0$ dBm. (b) When the pump frequency is fixed at $\omega_d/(2\pi)=2.788$ GHz (above the FMR frequency), no significant phenomenon appears at $P_d=-20$ dBm; when $P_d=-7$ dBm, a Fano resonance with the shape opposite to that observed at $\omega_d/(2\pi)=2.770$ GHz emerges; as the power increases to $P_d=0$ dBm, the Fano resonance characteristics become more pronounced.
• Figure 5: Three-magnon interaction in the magnetic sphere driven by a strong "pump" microwave of frequency $\omega_d$. $\hat{m}_{0}$ and $\hat{a}_{k}$ represent, respectively, the Kittel magnon and the microwave photon, coupled via a coupling strength $q_k$. $\hat{m}_{k}$ and $\hat{m}_{-k}$ are a pair of magnons with opposite wave vectors, which couple to $\hat{m}_0$ with the coupling strengths $g_k$.