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 ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6+x}$—provide an alternative approach enabled by their unique magnon spectrum. Using a neutron-constrained bilayer spin model, we obtain the complete $\mathrm{\Gamma }$-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 GHz to THz ranges. When coupled to a single-mode microwave cavity, these modes create two distinct channels with a magnetically tunable $\alpha$-photon coupling where $|{\mathcal{G}}_{\alpha }|\propto B^{-1/2}$ and a nearly field-independent $\beta$0photon coupling. This asymmetric behavior enables continuous, single-parameter control spanning from dispersive to strong coupling regimes. In the dispersive limit, Schrieffer-Wolff analysis reveals cavity-mediated magnon-magnon coupling $g_{\alpha \beta }^{\mathrm{eff}}\propto g_{\alpha }{g}_{\beta }/({\omega }_m-{\omega }_c)$, while near triple resonance ($f_c=f_{\alpha }=f_{\beta }$) 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 the potential for programmable filtering and coherent state transfer across the GHz-THz frequency range if realized experimentally with suitable interfaces.

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• Magnons
• Open quantum systems & decoherence
• Quantum harmonic oscillator
• Quantum interference effects
• Quantum state transfer