Bilayer Cuprate Antiferromagnets Enable Programmable Cavity Optomagnonics

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.

💡 Research Summary

This paper introduces a novel hybrid quantum platform based on bilayer cuprate antiferromagnets, specifically YBa₂Cu₃O₆₊ₓ (YBCO), coupled to a single‑mode microwave cavity. The authors begin by highlighting the limitations of conventional ferromagnetic insulators such as yttrium iron garnet (YIG), which, despite achieving very high cooperativities, suffer from intrinsic trade‑offs among mode volume, coherence time, and tunability. Antiferromagnetic insulators overcome many of these issues because they exhibit negligible stray fields, ultrafast dynamics, and broad frequency tunability. Cuprate antiferromagnets stand out due to their exceptionally large in‑plane superexchange (J∥≈100 meV), quasi‑two‑dimensional correlations, and a bilayer crystal structure that introduces a hierarchy of exchange couplings (J⊥₁≈2.6 meV, J⊥₂≈0.026 meV).

Using neutron‑scattering‑constrained parameters, the authors construct a spin Hamiltonian that includes in‑plane exchange, inter‑layer exchanges, a weak easy‑plane anisotropy (αD≪J∥), and a static magnetic field applied in‑plane. After rotating the spin basis to account for canting, they perform a Holstein‑Primakoff expansion and a Bogoliubov transformation in an eight‑dimensional Nambu space. This yields four positive‑energy magnon branches: an in‑plane acoustic (α) Goldstone mode, an in‑plane optical (β) mode, and two out‑of‑plane counterparts (η, ζ). At the Brillouin‑zone centre (Γ), the α mode is gapless and scales linearly with the Zeeman energy (Eα≈gμBB), while the β mode acquires a gap set by the anisotropy (∝√αD) and is essentially field‑independent. The crossing of α and β can be tuned from the gigahertz to terahertz regime by varying αD (through strain, oxygen stoichiometry, or chemical substitution) and the external field B.

The coupling to a microwave cavity is introduced via the Zeeman interaction H_I=g_Cuμ_B∑_n B̂(r_n)·Ŝ_n. Quantizing the cavity field in the usual way and projecting onto a single resonant mode, the authors derive collective coupling strengths G_α and G_β. Crucially, G_α∝|g₀|·Λ_α·B⁻¹ᐟ², i.e., it can be tuned continuously by the magnetic field, whereas G_β≈|g₀|·Λ_β remains nearly constant. Here g₀ depends on the spin density (≈1.1×10²⁸ m⁻³ for YBCO), the cavity frequency, and the overlap factor between the sample and the cavity mode. This asymmetric, field‑dependent coupling provides a single‑parameter (magnetic field) knob that can sweep the system from a purely dispersive regime (weak α‑photon interaction) to a strong‑coupling regime where both α and β hybridize with the cavity.

In the dispersive limit, a Schrieffer‑Wolff transformation reveals an effective cavity‑mediated magnon‑magnon interaction g_eff≈G_αG_β/(ω_m−ω_c). Near triple resonance (ω_c≈ω_α≈ω_β) the normal modes reorganize into bright (symmetric) and dark (antisymmetric) superpositions, governed by a single collective energy scale. The authors formulate an input–output theory to compute the transmission coefficient S₂₁(ω) for three experimental configurations: (i) a probe coupled only to the α mode, producing a magnetic‑field‑controlled linewidth and dispersive shift; (ii) a probe coupled directly to the cavity, yielding a programmable notch or transparency window as B tunes the α‑photon detuning; and (iii) a fixed‑frequency sweep at 2f_c that traverses the triple‑resonance point, displaying vacuum‑Rabi doublets for both α and β, with the β branch contributing a weak, field‑independent background and a characteristic Fano‑like asymmetric lineshape. These spectral features constitute concrete experimental benchmarks.

Finally, the paper discusses practical routes to engineer the anisotropy. Reducing αD by an order of magnitude shifts the β mode from the THz down to the sub‑THz or even GHz range, enabling a fully microwave‑compatible platform where both α and β can be addressed with standard cavity QED hardware. Conversely, retaining a larger αD keeps β in the THz band, allowing the bilayer cuprate to act as a quantum frequency converter bridging microwave and THz photons. The authors argue that such programmable control opens pathways to on‑chip filtering, quantum state transfer across three orders of magnitude in frequency, and scalable quantum information processing architectures that exploit the unique magnon spectrum of bilayer cuprates.