Casimir interactions as a probe of broadband optical response

TL;DR

This paper demonstrates that Casimir force measurements can be used as a broadband optical spectroscopy tool by reconstructing a material's dielectric response over a wide frequency range using machine learning, linking quantum fluctuations to real-frequency properties.

Contribution

The authors introduce a method to invert Lifshitz theory with machine learning, enabling broadband optical response reconstruction from Casimir force data, bridging quantum fluctuation measurements and optical characterization.

Findings

Casimir forces encode information about a material's dielectric response.

Machine learning can reconstruct complex permittivity over seven orders of magnitude in frequency.

Different force measurements constrain distinct frequency ranges of the dielectric response.

Abstract

Casimir forces arise from quantum electromagnetic fluctuations and depend on the dielectric response of interacting materials across the entire frequency spectrum. Although this dependence is central to Lifshitz theory of the Casimir effect, the formulation of the force in terms of dielectric functions evaluated at imaginary frequencies has largely obscured its connection to real-frequency optical properties, limiting the use of Casimir interactions as a probe of materials. Here we demonstrate that Casimir force measurements encode sufficient information to reconstruct a material's broadband optical response. Using supervised machine learning to invert Lifshitz theory, we determine the complex permittivity of a material over more than seven orders of magnitude in frequency from a single force-distance curve. We show that measurements at different separations selectively constrain distinct frequency ranges of the dielectric response, providing direct physical insight into how quantum fluctuations sample the electromagnetic spectrum. These results establish Casimir interactions as a physically constrained, broadband spectroscopic tool and open new opportunities for optical characterization in regimes inaccessible to conventional techniques.