Optimizing Superconducting Microwave Cavities for Gravitational Wave Sensing

Abstract

Superconducting microwave cavities loaded with radio frequency fields are a powerful tool to search for weak forces or electromagnetic perturbations due to new physics. One source of such signals can be high-frequency gravitational waves emitted from cosmological or unknown astrophysical events. However, large sensitivity improvements are still necessary to reach the parameter space motivated by theoretical models. In this work, we present a formalism to guide the design of such detectors across a broad range of frequencies and signal forms. By incorporating the interdependencies of all relevant parameters and the back-action of the electromagnetic fields on the cavity structure, we describe how figures of merit can be derived for a broad class of relevant experimental setups. Using a two-dimensional model, we demonstrate this formalism and present examples for optimized cavity geometries. We find that the choice of geometry alone can increase the signal-to-noise power ratio by an order of magnitude compared to an existing prototype of the same size. We also show that different physics goals lead to different optimal cavities, thus proving the need to consider such figures of merit at an early stage when designing a new detector.