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arXiv:1606.09472 · Physical Review A

Impact of Casimir-Polder interaction on Poisson-spot diffraction at a dielectric sphere

Joshua Leo Hemmerich, Robert G. Bennett, Thomas J.G. Reisinger, Stefan Nimmrichter, Johannes Fiedler, Horst Hahn, H. Gleiter, Stefan Yoshi Buhmann

Published Aug 17, 2016• 18 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.94.023621

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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.
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.
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.
Matter–wave interferometry has been used extensively over the last few years to demonstrate the quantum-mechanical wave nature of increasingly larger and more massive particles. We have recently suggested the use of the historical Poisson spot setup to test the diffraction properties of larger objects. In this paper, we present the results of a classical particle van der Waals (vdW) force model for a Poisson spot experimental setup and compare these to Fresnel diffraction calculations with a vdW phase term. We include the effect of disc-edge roughness in both models. Calculations are performed with D 2 and with C 70 using realistic parameters. We find that the sensitivity of the on-axis interference/focus spot to disc-edge roughness is very different in the two cases. We conclude that by measuring the intensity on the optical axis as a function of disc-edge roughness, it can be determined whether the objects behave as de Broglie waves or classical particles. The scaling of the Poisson spot experiment to larger molecular masses is, however, not as favorable as in the case of near-field light-grating-based interferometers. Instead, we discuss the possibility of studying the Casimir–Polder potential using the Poisson spot setup.
The phase of de Broglie matter waves is a sensitive probe for small forces. In particular, the attractive van der Waals force experienced by polarizable atoms in the close vicinity of neutral surfaces is of importance in nanoscale systems. It results in a phase shift that can be observed in matter-wave diffraction experiments. Here, we observe Poisson spot diffraction of indium atoms at submillimeter distances behind spherical submicron silicon dioxide particles to probe the dispersion forces between atoms and the particle surfaces. We compare the measured relative intensity of Poisson's spot to theoretical results derived from first principles in an earlier communication and find a clear signature of the atom-surface interaction.
The influence of the Casimir-Polder potential upon matter-wave scattering near a dielectric disk is considered. We employ a rescaled Dyson series in order to take into account the disk geometry, and compare this with a previously used approach based on the proximity-force approximation. In the latter approach one uses a simplified potential that is sharply switched on in the region of the disk. This intrinsically neglects edge and saturation effects. We show that under appropriate conditions the previous simpler model works very well for the calculation of the phase accumulated along the full path of the particle due to approximate cancellations of the errors. We present specific results for experimentally relevant scenarios, namely indium atoms or deuterium molecules interacting with a silicon nitride or silicon dioxide disk. Finally we compare our calculations to the analytically solvable problem of an infinitely thin perfectly reflecting disk, finding the expected qualitative agreement.
Since de Broglie's work on the wave nature of particles, various optical phenomena have been observed with matter waves of atoms and molecules. However, the analogy between classical and atom/molecule optics is not exact because of different dispersion relations. In addition, according to de Broglie's formula, different combinations of particle mass and velocity can give the same de Broglie wavelength. As a result, even for identical wavelengths, different molecular properties such as electric polarizabilities, Casimir-Polder forces, and dissociation energies modify (and potentially suppress) the resulting matter-wave optical phenomena such as diffraction intensities or interference effects. We report on the universal behavior observed in matter-wave diffraction of He atoms and He2 and D2 molecules from a ruled grating. Clear evidence for emerging beam resonances is observed in the diffraction patterns, which are quantitatively the same for all three particles and only depend on the de Broglie wavelength. A model, combining secondary scattering and quantum reflection, permits us to trace the observed universal behavior back to the peculiar principles of quantum reflection.