  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.
