Bilayer Cuprate Antiferromagnets Enable Programmable Cavity Optomagnonics

TL;DR

The work tackles the trade-offs of conventional cavity-magnon systems by using bilayer cuprate antiferromagnets, notably YBa$_2$Cu$_3$O$_{6+x}$, which host a gapless in-plane alpha magnon and a gapped in-plane beta magnon. By deriving a neutron-constrained bilayer Hamiltonian and performing a Bogoliubov transformation, the authors uncover a two-mode Gamma-point spectrum and show how a single microwave cavity can couple to both modes with distinct, tunable behaviors: a field-dependent $|\mathcal{G}_{\alpha}|$ and a near-field-independent $|\mathcal{G}_{\beta}|$, enabling continuous access from dispersive to strong coupling. The theory predicts clear spectroscopic signatures, including vacuum–Rabi splittings, dispersive shifts, and Fano-like lineshapes, and reveals a triple-resonance bright/dark mode restructuring with a single collective scale $\mathcal{G}$ that can act as a robust interface for microwave–GHz to THz transduction and programmable filtering. Overall, bilayer cuprate AFMs emerge as a flexible platform for adaptable quantum information processing that bridges microwave and THz domains within a single reconfigurable system.

Abstract

Hybrid platforms that couple microwave photons to collective spin excitations offer promising routes for coherent information processing, yet conventional magnets face inherent trade-offs among coupling strength, coherence, and tunability. We demonstrate that bilayer cuprate antiferromagnets, exemplified by YBa2Cu3O6+x, provide an alternative approach enabled by their unique magnon spectrum. Using a neutron-constrained bilayer spin model, we obtain the complete Gamma-point spectrum and identify an in-plane acoustic alpha mode that remains gapless and Zeeman-linear, alongside an in-plane optical beta mode stabilized by weak anisotropy whose frequency can be tuned from the gigahertz to terahertz range. When coupled to a single-mode microwave cavity, these modes create two distinct channels with a magnetically tunable alpha-photon interaction and a nearly field-independent beta-photon interaction. This asymmetric behavior enables continuous, single-parameter control spanning from dispersive to strong coupling regimes. In the dispersive limit, our analysis reveals cavity-mediated magnon-magnon coupling, while near triple resonance the normal modes reorganize into bright and dark superpositions governed by a single collective energy scale. The calculated transmission exhibits vacuum-Rabi splittings, dispersive shifts, and Fano-like lineshapes that provide concrete experimental benchmarks and suggest potential for programmable filtering and coherent state transfer across the gigahertz-terahertz frequency range if realized experimentally with suitable interfaces.

Figures (5)

• Figure 1: Bilayer cuprate crystal structure and its magnon dispersions. (a) Crystal and spin structure of YBa$_2$Cu$_3$O$_{6+x}$ with the in-plane superexchange $J_\parallel=100\mathrm{meV}$, intra-bilayer exchange $J_{\perp1}=2.6\mathrm{meV}$, and weak inter-bilayer coupling $J_{\perp2}=0.026\mathrm{meV}$ mediated by Cu(1)-O chains. The magnetic field $\mathbf{B}$ induces uniform spin canting within the ab-plane. Structural parameters include the in-plane lattice constant $a$, intra-bilayer Cu-Cu separation $zc$, inter-bilayer spacing $c$, and fractional $z$-coordinate defining the bilayer asymmetry. (b) Computed mode $\alpha$ dispersion across the magnetic Brillouin zone at $k_z = 0$, demonstrating the two-dimensional character with high-symmetry points $\Gamma$, $X$, and $M$ indicated. (c) Complete four-branch magnon spectrum along $\Gamma \to X \to M \to \Gamma$(left) and c-axis dispersion at fixed in-plane momentum (right) in zero field. (d) Magnetic field evolution of $\Gamma$ point frequencies. Solid (dotted) lines are for $\alpha_D = 1.0\times10^{-4}$ ($\alpha_D = 1.0\times10^{-5}$).
• Figure 2: Cavity magnon–polariton spectra and gap evolution. Hybrid eigenfrequencies (solid) of the coupled cavity–AFM system versus magnetic field $B$ for cavity frequencies $f_c=10~\mathrm{GHz}$ (a) and $50~\mathrm{GHz}$ (b), with $\alpha_D=1.0\times10^{-4}$ and $\rho\eta_\mathrm{B}=10^{24}$. Dashed lines show the uncoupled photon ($f_c$) and magnon modes $f_\alpha(B)$ and $f_\beta(B)$. Insets highlight avoided crossings: photon–$\alpha$ splittings of $\Delta f_{\alpha\mathrm{p}}=8.57~\mathrm{GHz}$ in both panels, and $\alpha$–$\beta$ gaps of $\Delta f_{\alpha\beta}=790~\mathrm{kHz}$ (a) and $4.2~\mathrm{MHz}$ (b). (c,d) Magnitudes of the mode splittings, $|\Delta f_{\alpha p}|$ and $|\Delta f_{\alpha\beta}|$, plotted versus $f_c$ for different $\alpha_D$ and $\rho\eta_\mathrm{B}$. The inset in (d) shows the low-$f_c$ regime.
• Figure 3: Transmission spectra as a function of magnetic field, with the probe frequency locked to the $\alpha$ mode, $f_\mathrm{probe}=f_\alpha(B)$. (a) Good-cavity regime with $\kappa_{1,2}=0.02$, $\kappa_\mathrm{int}=0.002$. (b) Bad-cavity regime with $\kappa_{1,2}=0.2$, $\kappa_\mathrm{int}=2$. In both magnon linewidths are $\gamma_\alpha=0.2$ GHz and $\gamma_\beta=0.5$GHz and $\alpha_D=1\times10^{-5}$ and $\rho\eta_{\mathrm{B}}=10^{24}$. Solid curves include both bright magnon modes ($\alpha$ and $\beta$), while dashed curves show the case with the $\beta$ mode switched off ($\mathcal{G}_\beta=0$). Curves are color-coded by cavity frequency. Insets enlarge the vicinity of the reference field $B=7.21$ T, where $f_\alpha=f_\beta=f_\mathrm{probe}$, highlighting the emergence of a magnetically tunable Fano-like resonance, disappearing for $\mathcal{G}_\beta\!\to\!0$.
• Figure 4: Field-tuned transmission with the probe locked to the cavity ($f_{\mathrm{probe}}=f_c$). (a) Good-cavity ($\kappa_c\!\ll\!\gamma_\alpha$) and (b) bad-cavity ($\kappa_c\!\gg\!\gamma_\alpha$) maps of $|S_{21}|^{2}$ versus $H$ and $f_c$. Dashed line trace $f_{\alpha}(H)$. (c) Line cuts at selected $f_c$; vertical guides mark fields $H$ where $f_c=f_{\alpha}(H)$. Parameters are as in Fig. \ref{['Fig3']}.
• Figure 5: Transmission vs probe frequency at fixed cavity frequency $f_c=12.0$ GHz for magnon–cavity detunings $\Delta_{\alpha p}=0,\pm5$ GHz. Solid curves denote the coupled system, dashed curves the bare cavity, and dotted lines locate $f_\alpha(B)$. Parameters match the bad-cavity regime in Fig. \ref{['Fig3']}.