Floquet Cavity Electromagnonics

Hybrid magnonics has recently attracted intensive attention as a promising platform for coherent information processing. In spite of its rapid development, on-demand control over the interaction of magnons with other information carriers, in particular, microwave photons in electromagnonic systems, has been long missing, significantly limiting the potential broad applications of hybrid magnonics. Here, we show that, by introducing Floquet engineering into cavity electromagnonics, coherent control on the magnon-microwave photon coupling can be realized. Leveraging the periodic temporal modulation from a Floquet drive, our first-of-its-kind Floquet cavity electromagnonic system enables the manipulation of the interaction between hybridized cavity electromagnonic modes. Moreover, we have achieved a new coupling regime in such systems: the Floquet ultrastrong coupling, where the Floquet splitting is comparable with or even larger than the level spacing of the two interacting modes, beyond the conventional rotating-wave picture. Our findings open up new directions for magnon-based coherent signal processing.

Figure 1

(a) Device schematics. A YIG sphere is placed underneath a dielectric resonator inside a copper housing, with a bias magnetic field $H$ along $x$ direction. The coaxial probe loop is for microwave excitation and readout; the drive loop provides the Floquet driving field along $x$. (b) Simulated magnetic components ($h$ field) of the cavity field for the ${\mathrm{TE}}_{01\delta }$ mode of the dielectric resonator. Color, field intensity; arrows, field direction. (c) Measured cavity reflection at various magnetic fields (controlled by magnet position). Two avoided crossings correspond to the strong coupling between the cavity photon mode ($\widehat{c}$) and two magnon modes (${\widehat{m}}_0$ and ${\widehat{m}}_1$). Freq., frequency. (d) Cavity reflection measured at $x=21.75\mathrm{mm}$ with different dc bias conditions applied to the drive loop. Curves are shifted vertically for clarity. (e) Energy level diagram. $\widehat{m}$, magnon mode; $\widehat{c}$, microwave photon mode; $\delta \omega$, magnon detuning; $g_{\mathrm{cm}}$, magnon-photon coupling strength; ${\widehat{d}}_{\pm }$, upper (lower) hybrid mode; $\mathrm{\Delta }\omega$, energy separation between two hybrid modes; $\mathrm{\Delta }{\omega }_{\mathrm{AT}}$, Autler-Townes splitting. A driving field is applied to enable the transition between hybrid modes ${\widehat{d}}_{-}$ and ${\widehat{d}}_{+}$.

Figure 2

(a)–(c) Measured cavity reflection ($|S_{11}|$) spectra versus the bias magnetic field at a 10-V peak-to-peak driving amplitude for three frequencies: ${\omega }_D=2\pi \times 5,15,28\mathrm{MHz}$, respectively. In addition to the avoided crossing caused by the strong coupling between the cavity photon mode ($\widehat{c}$) and magnon mode (${\widehat{m}}_0$), sidebands are created by the ac driving fields. (d) Measured cavity reflection spectra as a function of driving frequency at $x=21.762\mathrm{mm}$ when $\delta \omega =0$. The dashed lines correspond to conditions for (a)–(c). (e) Measured cavity reflection spectra as a function of driving amplitude, with $\delta \omega =0$ and ${\omega }_D=2\pi \times 28\mathrm{MHz}$. (f) Extracted Autler-Townes splitting ($\mathrm{\Delta }{\omega }_{\mathrm{AT}}$) for both ${\widehat{d}}_{-}$ (square), ${\widehat{d}}_{+}$ (circle) modes in (e) as a function of the driving voltage. Solid line is from the numerical fitting. SB, sideband; Mag. pos., magnet position.

Figure 3

(a),(b) Measured cavity temporal response under different driving frequencies after a rectangular pulsed excitation (center frequency, $2\pi \times 8.52\mathrm{GHz}$; width, 20 ns; peak-to-peak amplitude, 10 V) at time zero when the Floquet drive is on and off, respectively. (c),(d) Calculated cavity temporal response with and without the Floquet drive, respectively. (e),(f) Enlarged line plot of the theoretical (solid line) and experimental (grayed area) temporal responses at Floquet driving frequencies as indicated by the vertical dashed lines in (a)–(d) (${\omega }_D=2\pi \times 28\mathrm{MHz}$ for the theoretical calculation, while ${\omega }_D=2\pi \times 31\mathrm{MHz}$ for experiment results, which is slightly higher because of magnon nonlinearity effects induced by the strong microwave input) with and without the Floquet drive, respectively. Norm. refl., normalized reflection.

Figure 4

(a)–(c) Cavity reflection spectra when the driving frequency ${\omega }_D$ is swept at a fixed driving amplitude (10 V peak to peak), obtained from experiment, Floquet model, and RWA model, respectively. (d)–(f) Cavity reflection spectra when the driving amplitude is swept at a fixed driving frequency (${\omega }_D=2\pi \times 3.85\mathrm{MHz}$), obtained from experiment, Floquet model, and RWA model, respectively.