Coherent Coupling of Two Remote Magnonic Resonators Mediated by Superconducting Circuits

We demonstrate microwave-mediated distant magnon-magnon coupling on a superconducting circuit platform, incorporating chip-mounted single-crystal ${\mathrm{Y}}_3{\mathrm{Fe}}_5{\mathrm{O}}_{12}$ (YIG) spheres. Coherent level repulsion and dissipative level attraction between the magnon modes of the two YIG spheres are demonstrated. The former is mediated by cavity photons of a superconducting resonator, and the latter is mediated by propagating photons of a coplanar waveguide. Our results open new avenues toward exploring integrated hybrid magnonic networks for coherent information processing on a quantum-compatible superconducting platform.

Figure 1

(a) Schematic of the one-YIG-sphere superconducting circuit design. (b) Microscope image of the circular antenna with a mounted YIG sphere. (c) Power transmission of the CPW feed line for the circular-antenna superconducting resonator. Solid spectrum: Rabi splitting (${\omega }_c={\omega }_m$) measured at ${\mu }_0{H}_B=0.171\mathrm{T}$. Dashed spectrum: uncoupled resonator photon mode ($|{\omega }_c-{\omega }_m|\gg g_c$) measured at ${\mu }_0{H}_B=0.25\mathrm{T}$. (d) Full power spectrum of the hybrid circuit showing magnon-photon mode repulsion.

Figure 2

(a) Schematic of the two-YIG-sphere superconducting circuit design with an additional local NbTi superconducting coil. (b) Power transmission of the CPW feed line showing Rabi splitting of the resonator in couple with only one YIG sphere or both YIG spheres, measured at ${\mu }_0{H}_B=0.154\mathrm{T}$. Blue curve: ${\omega }_c={\omega }_{m2}$ with $I_{\mathrm{coil}}=-3.0\mathrm{A}$, where ${\omega }_{m1}$ is far detuned. Green curve: ${\omega }_c={\omega }_{m1}={\omega }_{m2}$ with $I_{\mathrm{coil}}=2.66\mathrm{A}$. (c),(d) Full power spectra of the hybrid magnonic circuit for (c) $I_{\mathrm{coil}}=-3.0\mathrm{A}$ and (d) $I_{\mathrm{coil}}=2.66\mathrm{A}$.

Figure 3

(a) Power spectra showing remote magnon-magnon coupling ($2{\mathrm{\Omega }}_m$) in the dispersive regime, where $\mathrm{\Delta }/2\pi =0.713\mathrm{GHz}$ is much larger than $g_{c1}$, $g_{c2}$. Data are measured at ${\mu }_0{H}_B=0.133\mathrm{T}$. The blue arrow labels the dark mode. (b) Power spectra taken at different ${\mu }_0{H}_B$ showing the evolution of ${\mathrm{\Omega }}_m$. (c) Extracted ${\mathrm{\Omega }}_m$ as a function of $\mathrm{\Delta }$. The error bars indicate single standard deviation uncertainties that arise primarily from the fitting of the resonances. Dashed curve: theoretic prediction by Eq. (2). Solid curve: adding an adjacent resonance mode which also contributes to dispersive magnon-magnon coupling [44].

Figure 4

(a) Extracted magnon-magnon coupling strength mediated by propagating microwave photons. The error bars indicate single standard deviation uncertainties that arise primarily from the fitting of the resonances. Level repulsion and attraction are measured below and above $\omega /2\pi =7.63\mathrm{GHz}$, respectively. Inset: schematic of the coplanar waveguide design for magnon-magnon level attraction. Solid curve: theoretical prediction using ${\omega }_0/2\pi =8.425\mathrm{GHz}$, $g_r/2\pi =8.5\mathrm{MHz}$, and $\epsilon =0.29$. (b)–(d) Power spectra taken at (b) ${\mu }_0{H}_B=0.145\mathrm{T}$, (c) ${\mu }_0{H}_B=0.25\mathrm{T}$, and (d) ${\mu }_0{H}_B=0.285\mathrm{T}$, corresponding to $\omega /2\pi =4.8\mathrm{GHz}$, 7.63 GHz, and 8.56 GHz in (a). Dashed curves are fitting to Eq. (3) in (b) and (d) and a guide to eye in (c). (e)–(g) Theoretical prediction of magnon-magnon coupling mediated by propagating microwave with different $\phi$ matching the conditions in (b)–(d).