Enhanced quantum sensing of gravitational acceleration constant

Abstract

We investigate the use of quantum probes to accurately determine the strength of the local gravitational field on Earth. Our findings show that delocalized probes generally outperform localized ones, with the precision enhancement scaling quadratically with the separation between the two wavefunction components. This advantage persists under realistic position measurements, which can achieve precision not too far from the ultimate bound. We also discuss the influence of Earth's surface, demonstrating that its effect can be neglected until shortly before the particle hits the floor. Finally, we address the joint estimation of the gravitational acceleration $g$ and the probe mass $m$, proving that the excess estimation noise arising from their inherent incompatibility is negligible.