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arXiv:2601.10118

Casimir-force spectroscopy of broadband optical response

Calum F. Shelden, Jeremy N. Munday

quant-phphysics.app-phSubmitted Jan 15, 2026• Announced Jan 16, 2026• Revised May 21, 2026 (v2)
v1 · Jan 15, 2026v2 · May 21, 2026v3 · Sep 4, 2026
arXivHTMLPDF

Abstract

Broadband optical response governs light-matter interactions across photonics, plasmonics, thermal radiation, and quantum fluctuation electrodynamics, yet determining a continuous dielectric function over many decades in frequency typically requires combining multiple spectroscopies, extrapolations, and material models. Here we show that quantum-fluctuation forces provide a route to broadband optical characterization. Casimir interactions depend on the dielectric response of materials across the electromagnetic spectrum, but this information is encoded through Lifshitz theory in a spectrally weighted and nontrivial way. By training physics-constrained supervised learning models on synthetic dielectric spectra and their corresponding Casimir force curves, we invert this relationship and reconstruct the complex permittivity of materials over more than seven orders of magnitude in frequency from force-distance data. The reconstruction reveals a direct separation-frequency correspondence: large separations constrain low-frequency free-carrier response, whereas shorter separations encode higher-frequency resonant structure. Applying the method to measured force gradients identifies the current experimental limits imposed by measurement noise, restricted separation range, and model complexity. These results establish fluctuation-induced forces as a spectrally weighted route to broadband optical characterization and define the experimental and physical limits that govern what spectral information is accessible from near-field quantum electromagnetic measurements.

Comments
Revised version with expanded discussion of fluctuation-enabled optical characterization, experimental limits, and broadband optical-response reconstruction. 18 pages, 9 figures

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Broadband optical response governs light-matter interactions across photonics, plasmonics, thermal radiation, and quantum fluctuation electrodynamics, yet determining a continuous dielectric function over many decades in frequency typically requires combining multiple spectroscopies, extrapolations, and material models. Here we show that quantum-fluctuation forces provide a route to broadband optical characterization. Casimir interactions depend on the dielectric response of materials across the electromagnetic spectrum, but this information is encoded through Lifshitz theory in a spectrally weighted and nontrivial way. By training physics-constrained supervised learning models on synthetic dielectric spectra and their corresponding Casimir force curves, we invert this relationship and reconstruct the complex permittivity of materials over more than seven orders of magnitude in frequency from force-distance data. The reconstruction reveals a direct separation-frequency correspondence: large separations constrain low-frequency free-carrier response, whereas shorter separations encode higher-frequency resonant structure. Applying the method to measured force gradients identifies the current experimental limits imposed by measurement noise, restricted separation range, and model complexity. These results establish fluctuation-induced forces as a spectrally weighted route to broadband optical characterization and define the experimental and physical limits that govern what spectral information is accessible from near-field quantum electromagnetic measurements.
A broadband electromagnetic source is important for scientific and technological applications. Quantum vacuum fluctuations, which manifest most prominently in the Casimir effect, provide a fundamentally broadband electromagnetic source. Here we explore a potential consequence of the broadband nature of quantum vacuum fluctuations, by showing that such fluctuations can enable measurement of material permittivity over a broad frequency range. Specifically, we consider the Casimir force in a parallel-plate geometry, with one plate covered by a nanoscopic thin film. Using a machine learning approach, we show that one can infer both the thickness of the film and its permittivity over a broad frequency range, starting from the dependency of the Casimir forces on the spacing between the two plates. Our work highlights the application potential of using vacuum fluctuations as a naturally-existing broadband electromagnetic source for material characterization, and shows that the inverse problem in Casimir force calculation can be solved with machine learning.
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The Casimir-Polder (CP) effect -- the force between a neutral atom and an uncharged conducting plate in empty space -- is an intriguing consequence of quantum vacuum fluctuations. The typically attractive CP potential crosses over from a scaling of z−3z^{-3}z−3 at short separations to z−4z^{-4}z−4 at long distances, where retardation effects due to the finite speed of light become important. At intermediate distances, where the atom--surface separation is of the order of the wavelength of the dominant atomic transition, experiments have so far relied on indirect methods, such as diffraction or quantum reflection, to observe the CP effect. Here, we directly reveal the CP force between strontium atoms and a dielectric surface via the induced shifts in the atomic energy levels in the intermediate regime. We spectroscopically probe the CP-induced kHz-frequency shift of ultracold atoms confined by a magic-wavelength optical lattice at 189(2)~nm from the surface -- on the scale of the dominant 461-nm transition. Our measurements agree well with QED calculations and differ from the short-range approximation, while excluding the long-distance one. This paves the way for studying the CP effect across various surface properties and geometries, as well as exploring the tensor nature of the atom-surface potential -- all important for the development of hybrid atomic optical-magnetic quantum devices.