Limits on the accuracy of force sensing at short separations due to patch potentials

Recent theoretical developments in gravitational physics have motivated experimental searches for violations of Newton's inverse square law of gravity at small separations. There has also been considerable theoretical and experimental progress in establishing the Casimir effect. These two classes of experiments and others in fundamental physics measure the forces between polycrystalline metals at micron-order separations, and are thus susceptible to forces due to electrostatic patch fields on their surfaces. We develop the theory for the patch force power spectra which provides the necessary tools to estimate the magnitude of random patch signals. We apply our results to two experiments intending to measure nonNewtonian gravitational signals using the isoelectronic technique where the mean effect of patches is nullified by design but random patch signals may still spoil the measurement sensitivity. Our results help gauge the sensitivity limitations of real experimental setups and the analytical formulas we derive suggest useful strategies for engineering and minimizing undesired patch effects in future experiments.