High-Frequency Gravitational Wave Search with ABRACADABRA-10\,cm

ABRACADABRA-10 cm has had great success as a pathfinder lumped-element axion dark matter experiment, setting limits on axion dark matter at the GUT scale. Now, using the interaction of gravitational waves with electrodynamics and a change in readout strategy, we use the ABRA-10 cm detector for the first search for high-frequency gravitational waves using a modified axion detector. Potential sources at these high frequencies (10 kHz to 5 MHz) include merging primordial black hole binaries or superradiance, among other beyond the standard model phenomena. This paper presents the design, results, and challenges from the ABRA-10 cm high-frequency gravitational wave search, showing it is possible to simultaneously look for axions and high-frequency gravitational waves with both searches matching theoretical expectations for sensitivity. Additionally, we conducted the first time series transient search with data from an axion experiment, achieving sensitivity to $10^{-4}$ in strain. Scaled directly to the next generation axion experiment, DMRadio-GUT, this sensitivity would imply a reach to 0.01 $M_{\odot}$ primordial black hole mergers at distances around 3 pc, with prospects to go significantly further with modifications to the readout.