Limits on the accuracy of isoelectronic gravity measurements at short separation due to patch potentials

TL;DR

This paper develops a theoretical framework to quantify how electrostatic patch potentials affect the accuracy of isoelectronic gravity measurements at short distances, highlighting the limitations they impose on detecting non-Newtonian signals.

Contribution

The paper introduces analytical expressions for the patch force and torque power spectrum in isoelectronic experiments, providing a means to estimate systematic and noise limitations.

Findings

Patch potentials induce measurable forces and torques that can limit measurement accuracy.

Analytical formulas enable estimation of patch-induced noise in gravity experiments.

Systematic effects from patches set fundamental sensitivity bounds.

Abstract

In force sensing experiments intended to measure non-Newtonian gravitational signals electrostatic patch potentials can give rise to spurious forces, torques, and noise. Undesired patch-induced interactions can lead to systematic effects which limit accuracy, and noise can place lower limits on precision. In this paper we develop the theory for electrostatic patch effects on isoelectronic experiments, where their mean effect is nullified by design. We derive analytical expressions for the patch force and torque power spectrum to estimate the limitations introduced by patch-induced signals.