Strengthening constraints on Yukawa-type corrections to Newtonian gravity from measuring the Casimir force between a cylinder and a plate

TL;DR

This paper derives exact formulas for Yukawa-type forces in a cylinder-plate setup and shows that a proposed experiment could significantly improve constraints on non-Newtonian gravity at nanometer scales.

Contribution

It provides analytical expressions for Yukawa forces in a cylinder-plate configuration and demonstrates potential for stronger experimental constraints.

Findings

Up to 70 times stronger constraints on Yukawa forces possible

Analytical expressions for force calculations in cylinder-plate geometry

Potential to improve limits over 12.5 to 630 nm range

Abstract

We discuss possibility to obtain stronger constraints on non-Newtonian gravity from measuring the gradient of the Casimir force between a cylinder and a plate. Exact analytical expression for the Yukawa-type force in a cylinder-plate configuration is obtained, as well as its asymptotic expansions. The gravitational force is compared with the Casimir force acting between a cylinder and a plate. Numerical computations for the prospective constraints on non-Newtonian gravity are performed for recently proposed experiment using a microfabricated cylinder attached to a micromachined oscillator. Specifically, it is shown that this experiment is expected to obtain up to 70 times stronger constraints on the Yukawa-type force, compared with the best present day limits, over a wide interaction range from 12.5 to 630 nm.