Beyond-PFA Casimir Force between two spheres at finite temperature

TL;DR

This paper derives a comprehensive semi-analytic formula for the Casimir force between two gold spheres at finite temperature, improving data interpretation beyond the Proximity Force Approximation.

Contribution

It introduces a new semi-analytic expression for the Casimir force between two spheres at finite temperature, valid across all separations, and clarifies the correct PFA corrections for experimental analysis.

Findings

Provides a formula applicable to all separations

Clarifies the parametrization of PFA corrections

Facilitates interpretation of future experiments

Abstract

A recent experiment [J.L. Garrett et al., Phys. Rev. Lett {\bf 120}, 040401 (2018)] measured for the first time the gradient of the Casimir force between two gold spheres at room temperature. The theoretical analysis of the data was carried out using the standard Proximity Force Approximation (PFA). A fit of the data, using a parametrization of the force valid for the sphere-plate geometry, was used by the authors to place a bound on deviations from PFA. Motivated by this work, we compute the Casimir force between two gold spheres at finite temperature. The semi-analytic formula for the Casimir force that we construct is valid for all separations, and can be easily used to interpret future experiments in both the sphere-plate and sphere-sphere configurations. We describe the correct parametrization of the corrections to PFA for two spheres that should be used in data analysis.