Enhanced quantum sensing of gravitational acceleration constant

TL;DR

This paper demonstrates that quantum probes, especially delocalized ones, significantly improve the precision of measuring Earth's gravitational acceleration, with practical measurement strategies nearly reaching theoretical limits.

Contribution

It shows that delocalized quantum probes outperform localized ones in gravitational measurements and analyzes the effects of Earth's surface and joint parameter estimation.

Findings

Delocalized probes outperform localized probes in precision.

Precision scales quadratically with wavefunction separation.

Realistic measurements approach the ultimate quantum bound.

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.