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

Optimal baseline exploitation in vertical dark-matter detectors based on atom interferometry