Detecting High-Frequency Gravitational Waves with Microwave Cavities

TL;DR

This paper develops a precise theoretical framework for detecting high-frequency gravitational waves using microwave cavities, showing existing axion experiments can be reanalyzed for GW detection with high sensitivity.

Contribution

It provides an exact analytic formalism accounting for gauge dependence and short-wavelength effects, enabling existing cavity experiments to search for high-frequency GWs.

Findings

Existing cavity experiments can detect GWs with strains as small as 10^{-22} to 10^{-21}.

Reanalysis of current data can reveal high-frequency gravitational waves.

Directional detection is theoretically possible using multiple cavity modes.

Abstract

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