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arXiv:2505.10056

Probing the geometry dependence of the Casimir-Polder interaction by matter-wave diffraction at a nano-grating

Matthieu Bruneau, Julien Lecoffre, Gabin Routier, Naceur Gaaloul, G. Dutier, Quentin Bouton, Thorsten Emig A

Published May 15, 2025• 1 citation
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Abstract

Atomic diffraction through a nanograting is a powerful tool to probe the Casimir-Polder potential. Achieving precise measurements require simulations to bridge theory and experiment. In this context, we present various approximations and methods of Casimir-Polder potentials, and we analyze their impact on matter-wave diffraction patterns. Our analysis includes the pairwise summation approach, the proximity force approximation, and multiple scattering expansion method. Furthermore, we demonstrate that the influence of Casimir-Polder interactions extends up to 25 nm before and after the nanograting slit, highlighting the importance of accounting for this effect in any accurate analysis.

DOI
10.48550/arxiv.2505.10056

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Atomic diffraction through a nanograting is a powerful tool to probe the Casimir-Polder potential. Achieving precise measurements require simulations to bridge theory and experiment. In this context, we present various approximations and methods of Casimir-Polder potentials, and we analyze their impact on matter-wave diffraction patterns. Our analysis includes the pairwise summation approach, the proximity force approximation, and multiple scattering expansion method. Furthermore, we demonstrate that the influence of Casimir-Polder interactions extends up to 25 nm before and after the nanograting slit, highlighting the importance of accounting for this effect in any accurate analysis.
Abstract Atomic diffraction through a nanograting is a powerful tool to probe the Casimir-Polder potential. Achieving precise measurements requires simulations to bridge theory and experiment. In this context, we present various approximations and methods of Casimir-Polder potentials, and we analyze their impact on matter-wave diffraction patterns. Our analysis includes the pairwise summation approach, the proximity force approximation, and multiple scattering expansion method. Furthermore, we demonstrate that the influence of Casimir-Polder interactions extends up to 25 nm before and after the nanograting slit, highlighting the importance of accounting for this effect in any accurate analysis.
We present a method utilizing atomic diffraction patterns and statistical analysis tools to infer the Casimir-Polder interaction between argon atoms and a silicon nitride nanograting. The quantum model that supports the data is investigated in detail, as are the roles of nanograting geometry, finite-size effects, slit width opening angles, Lennard-Jones potentials, and patch potentials. Our findings indicate that the atom-surface potential strength parameter is C 3 = 6.9 ± 1.2 meV nm 3 . This value is primarily constrained by the knowledge of the nanograting geometry. The high sensitivity of our method paves the way for precise determination of the Casimir-Polder potential and exploration of new short-distance forces.
We present a method utilizing atomic diffraction patterns and statistical analysis tools to infer the Casimir-Polder interaction between argon atoms and a silicon nitride nanograting. The quantum model that supports the data is investigated in detail, as are the roles of nanograting geometry, finite-size effects, slit width opening angles, Lennard-Jones potentials, and patch potentials. Our findings indicate that the atom-surface potential strength parameter is C3=6.9±1.2meVnm3. This value is primarily constrained by the knowledge of the nanograting geometry. The high sensitivity of our method paves the way for precise determination of the Casimir-Polder potential and exploration of new short-distance forces.
Since the 1950's, atom-surface interactions, also called Casimir-Polder interactions, have been studied through numerous theoretical works. Many experiments have been proposed and performed to measure the atom-surface interactions. However, the experiments did not allow to measure the atom-surface interactions potential with a better accuracy than 10%.In this thesis, we present a cold atom experiment dedicated to the study of Casimir-Polder interactions. The experiment is based on the diffraction of metastable argon atoms by a transmission material nanograting. Regarding the propagation velocities of the atoms, we have developed a simulation based on the numerical solution of the time-dependent Schrödinger equation. This simulation allows us to study the diffraction of a wave packet by a material slit, while considering both the atom-surface interactions and the absorption of the wave function at the surfaces. The results of the simulation are compared with the experimental data using statistical tools to test the model in order to make an accurate measurement.
Diffraction of matter waves is an important demonstration of the fact that objects in nature possess a mixture of particlelike and wavelike properties. Unlike in the case of light diffraction, matter waves are subject to a vacuum-mediated interaction with diffraction obstacles. Here we present a detailed account of this effect through the calculation of the attractive Casimir-Polder potential between a dielectric sphere and an atomic beam. Furthermore, we use our calculated potential to make predictions about the diffraction patterns to be observed in an ongoing experiment where a beam of indium atoms is diffracted around a silicon-dioxide sphere. The result is an amplification of the on-axis bright feature, which is the matter-wave analog of the well-known ``Poisson spot'' from optics. Our treatment confirms that the diffraction patterns resulting from our complete account of the sphere Casimir-Polder potential are indistinguishable from those found via a large-sphere nonretarded approximation in the discussed experiments, establishing the latter as an adequate model.
At nanometer separation, the dominant interaction between an atom and a material surface is the fluctuation-induced Casimir-Polder potential. We demonstrate that slow atoms crossing a silicon nitride transmission nanograting are a remarkably sensitive probe for that potential. A 15% difference between nonretarded (van der Waals) and retarded Casimir-Polder potentials is discernible at distances smaller than 51 nm. We discuss the relative influence of various theoretical and experimental parameters on the potential in detail. Our work paves the way to high-precision measurement of the Casimir-Polder potential as a prerequisite for understanding fundamental physics and its relevance to applications in quantum-enhanced sensing.