Detecting high-frequency gravitational waves with microwave cavities

We give a detailed treatment of electromagnetic signals generated by gravitational waves (GWs) in resonant cavity experiments. Our investigation corrects and builds upon previous studies carefully accounting for the gauge dependence relevant quantities. work preferred frame laboratory, proper detector frame, show how to resum short-wavelength effects provide analytic results that are exact GWs arbitrary wavelength. This formalism allows us firmly establish that, contrary claims, experiments designed detection axion dark matter only need reanalyze existing data search high-frequency with strains as small $h\sim 10^{-22}-10^{-21}$. also argue directional is possible principle using readout multiple modes. Further improvements sensitivity expected cutting-edge advances superconducting technology.