Refined Ultra-Light Scalar Dark Matter Searches with Compact Atom Gradiometers

Atom interferometry is a powerful experimental technique that can be employed to search for the oscillation of atomic transition energies induced by ultra-light scalar dark matter (ULDM). Previous studies have focused on the sensitivity to ULDM of km-length atom gradiometers, where atom interferometers are located at the ends of very-long baselines. In this work, we generalise the treatment of the time-dependent signal induced by a linearly-coupled scalar ULDM candidate for vertical atom gradiometers of any length and find correction factors that especially impact the ULDM signal in short-baseline gradiometer configurations. Using these results, we refine the sensitivity estimates for AION-10, a compact 10m gradiometer that will be operated in Oxford, and discuss optimal experimental parameters that enhance the sensitivity to linearly-coupled scalar ULDM. After comparing the sensitivity reach of devices operating in broadband and resonant modes, we show that well-designed compact atom gradiometers are able to explore regions of dark matter parameter space that are not yet constrained.