Refined ultralight 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 ultralight 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 generalize 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 in the limit where shot noise dominates for AION-10, a compact 10 m gradiometer that will be operated in Oxford, and discuss optimal experimental parameters that enhance the reach of searches for linearly-coupled scalar ULDM. After comparing the 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.