Multi-Mode Localization and Multi-Frequency Search of High Frequency Gravitational Waves with a Single Resonant Cavity

The GHz band remains an uncharted frontier for gravitational-wave (GW) astronomy with compelling targets from the early universe and new physics. Recent theoretical works have shown that resonant microwave cavities operated in strong static magnetic fields – such as those used in axion haloscopes – have sensitivity to high frequency GW (HFGW). The network approach proposed in GravNet relies on triangulation using three cavities, and recent multi-mode studies in non-cylindrical geometries have noted the feasibility of single-instrument GW direction reconstruction. However, an explicit reconstruction formalism tailored to cylindrical cavities has not been developed. We develop a formalism that exploits the direction-dependent overlap factors of nearly-degenerate eigenmodes in a cylindrical cavity to infer both arrival direction and polarization of a coherent HFGW signal. Our multi-mode approach allows direction reconstruction as well as a broadband detection scheme inside a single cavity. We thus demonstrate that axion haloscopes can act as self-contained HFGW antennas, and with advancements in superconducting cavities and quantum-limited readout chains, axion haloscopes can potentially reach even better sensitivities relevant for primordial black hole mergers and bosonic clouds.