Signatures of High-Frequency Gravitational Waves in Electromagnetic Cavities

TL;DR

This paper investigates how high-frequency gravitational waves can produce detectable electromagnetic signals in resonant cavities, analyzing their sensitivity and response to various GW sources, including primordial black hole mergers.

Contribution

It provides a detailed theoretical framework for detecting high-frequency GWs via electromagnetic cavities, including coupling coefficients and mode superpositions, with practical insights on sensitivity limitations.

Findings

High-Q cavities do not always improve sensitivity for transient signals.

Only nearby black hole mergers within the solar system produce observable energy deposits.

Coupling coefficients are derived for cylindrical and spherical cavities in the transverse-traceless gauge.

Abstract

Similar to axions, gravitational waves (GW) can induce oscillating electromagnetic fields inside electromagnetic cavities. We explore their experimental sensitivity to monochromatic and non-monochromatic GW signals, using the total deposited energy as a primary measure. Focusing on cylindrical and spherical cavities, we present the coupling coefficients of GWs to the dominant electromagnetic resonances in transverse-traceless gauge, which is most appropriate in this regime. By considering the superposition of degenerate modes, we further examine their angular sensitivity. In addition, we calculate the response of a spherical cavity to non-monochromatic GWs emitted by primordial black hole mergers. We find that, for transient signals, a high quality factor with $Q \gtrsim 10^5$ does not necessarily enhance experimental sensitivity. In fact, even in the most optimistic scenario, only mergers within the solar system yield an observable energy deposit in the cavity.