Possibility of measuring the thermal Casimir interaction between a plate and a cylinder attached to a micromachined oscillator

TL;DR

This paper explores the feasibility of measuring the thermal Casimir force between a plate and a microfabricated cylinder using a micromachined oscillator, providing theoretical formulas and analyzing potential experimental accuracy.

Contribution

It derives Lifshitz-type formulas for the plate-cylinder configuration using proximity force approximation and assesses experimental conditions for measuring thermal Casimir effects.

Findings

Derived formulas for thermal Casimir force in plate-cylinder setup.

Estimated errors due to nonparallelism and finite cylinder length.

Proposed static experiments as more suitable for thermal effect measurement.

Abstract

We investigate the possibility of measuring the thermal Casimir force and its gradient in the configuration of a plate and a microfabricated cylinder attached to a micromachined oscillator. The Lifshitz-type formulas in this configuration are derived using the proximity force approximation. The accuracy for the obtained expressions is determined from a comparison with exact results available in ideal metal case. Computations of the thermal correction to both the Casimir force and its gradient are performed in the framework of different theoretical approaches proposed in the literature. The correction to the Casimir force and its gradient due to lack of parallelism of the plate and cylinder is determined using the nonmultiplicative approach. The error introduced in the theory due to the finite length of the cylinder is estimated. We propose that both static and dynamic experiments measuring the thermal Casimir interaction between a cylinder and a plate using a micromachined oscillator can shed additional light on the thermal Casimir force problem. Specifically, it is shown that the static experiment is better adapted for the measurement of thermal effects.