Cavity Detection of Gravitational Waves: Where Do We Stand?

High frequency gravitational waves (HFGWs) are predicted in various exotic scenarios involving both cosmological and astrophysical sources. These elusive signals have recently sparked the interest of a diverse community of researchers, due to the possibility of HFGW detection in the laboratory through graviton-photon conversion in strong magnetic fields. Notable examples include the redesign of the resonant cavities currently under development to detect the cosmic axion. In this work, we derive the sensitivities of some existing and planned resonant cavities to detect a HFGW background. As a concrete scenario, we consider the collective signals that originate from the merging of compact objects, such as two primordial black holes (PBHs) in the asteroid mass window. Our findings improve over existing work by explicitly discussing and quantifying the loss in the experimental reach due to the actual coherence of the source. We elucidate on the approach we adopt in relation with recent literature on the topic. Most notably, we give a recipe for the estimate of the stochastic background that focuses on the presence of the signal in the cavity at all times and showing that, in the relevant PBH mass region, the signal is dominated by coherent binary mergers.