  Several terrestrial detectors for gravitational waves and dark matter based
on long-baseline atom interferometry are currently in the final planning stages
or already under construction. These upcoming vertical sensors are inherently
subject to gravity and thus feature gradiometer or multi-gradiometer
configurations using single-photon transitions for large momentum transfer.
While there has been significant progress on optimizing these experiments
against detrimental noise sources and for deployment at their projected sites,
finding optimal configurations that make the best use of the available
resources are still an open issue. Even more, the fundamental limit of the
device's sensitivity is still missing. Here we fill this gap and show that (a)
resonant-mode detectors based on multi-diamond fountain gradiometers achieve
the optimal, shot-noise limited, sensitivity if their height constitutes 20% of
the available baseline; (b) this limit is independent of the dark-matter
oscillation frequency; and (c) doubling the baseline decreases the ultimate
measurement uncertainty by approximately 65%. Moreover, we propose a
multi-diamond scheme with less mirror pulses where the leading-order
gravitational phase contribution is suppressed, compare it to established
geometries, and demonstrate that both configurations saturate the same
fundamental limit.
