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Physical Chemistry Chemical Physics

Experimental test of Babinet's principle in matter-wave diffraction

Lee Yeong Kim, Ju Hyeon Lee, Yun-Tae Kim, Sanghwan Park, Chang Young Lee, Wieland Schöllkopf, Bum Suk Zhao

Published Jan 1, 2021• 2 citations
Publisher

Abstract

We report on an experimental test of Babinet's principle in quantum reflection of an atom beam from diffraction gratings. The He beam is reflected and diffracted from a square-wave grating at near grazing-incidence conditions. According to Babinet's principle the diffraction peak intensities (except for the specular-reflected beam) are expected to be identical for any pair of gratings of complementary geometry. We observe conditions where Babinet's principle holds and also where it fails. Our data indicate breakdown conditions when either the incident or a diffracted beam propagates close to the grating surface. At these conditions, the incident or the diffracted He beam is strongly affected by the dispersive interaction between the atoms and the grating surface. Babinet's principle is also found to break down, when the complementary grating pair shows a large asymmetry in the strip widths. For very small strip widths, edge diffraction from half planes becomes dominant, whereas for the complementary wide strips the atom-surface interactions leads to a strong reduction of all non-specular diffraction peak intensities.

DOI
10.1039/d0cp05694d

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We report on an experimental test of Babinet's principle in quantum reflection of an atom beam from diffraction gratings. The He beam is reflected and diffracted from a square-wave grating at near grazing-incidence conditions. According to Babinet's principle the diffraction peak intensities (except for the specular-reflected beam) are expected to be identical for any pair of gratings of complementary geometry. We observe conditions where Babinet's principle holds and also where it fails. Our data indicate breakdown conditions when either the incident or a diffracted beam propagates close to the grating surface. At these conditions, the incident or the diffracted He beam is strongly affected by the dispersive interaction between the atoms and the grating surface. Babinet's principle is also found to break down, when the complementary grating pair shows a large asymmetry in the strip widths. For very small strip widths, edge diffraction from half planes becomes dominant, whereas for the complementary wide strips the atom-surface interactions leads to a strong reduction of all non-specular diffraction peak intensities.
We report on reflection and diffraction of beams of He and D_{2} from square-wave gratings of a 400-μm period and strip widths ranging from 10 to 200 μm at grazing-incidence conditions. In each case we observe fully resolved matter-wave diffraction patterns including the specular reflection and diffracted beams up to the second diffraction order. With decreasing strip width, the observed diffraction efficiencies exhibit a transformation from the known regime of quantum reflection from the grating strips to the regime of edge diffraction from a half-plane array. The latter is described by a single-parameter model developed previously to describe phenomena as diverse as quantum billiards, scattering of radio waves in urban areas, and reflection of matter waves from microstructures. Our data provide experimental confirmation of the widespread model. Moreover, our results demonstrate that neither classical reflection nor quantum reflection are essential for reflective diffraction of matter waves from a structured solid, but it can result exclusively from half-plane edge diffraction.
Thermal-energy atom scattering at a surface under grazing incidence conditions is an innovative method for investigating dispersive atom-surface interactions with potential application in quantum sensing interferometry. The complete establishment of this technique requires a detailed peak analysis, which is yet to be achieved. We examine peak-width fluctuations in atomic and molecular beams diffracted by a grating under grazing incidence conditions. Careful measurements and analyses of the diffraction patterns of He atoms and D2{\mathrm{D}}_{2}D2​ molecules from three square-wave gratings with different periods and radii of curvature enable the identification of factors influencing the peak-width variations as a function of incidence angle. The effects of macroscopic surface curvature, grating magnification, and beam emergence are substantial under these conditions but negligible for incidence angles close to the normal. Our results shed light on the phenomena occurring in grazing incidence thermal-energy atom scattering.
We observe high-resolution diffraction patterns of a thermal-energy helium atom beam reflected from a microstructured surface grating at grazing incidence. The grating consists of $10\text{\ensuremath{-}}\ensuremath{\mu}\mathrm{m}$-wide Cr strips patterned on a quartz substrate and has a periodicity of $20\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{m}$. Fully resolved diffraction peaks up to the seventh order are observed at grazing angles up to 20mrad20\phantom{\rule{0.3em}{0ex}}\mathrm{mrad}20mrad. With changes in de Broglie wavelength or grazing angle the relative diffraction intensities show significant variations which shed light on the nature of the atom-surface interaction potential. The observations are explained in terms of quantum reflection at the long-range attractive Casimir--van der Waals potential.
We report on emerging beam resonances appearing in diffraction patterns of a helium atom beam reflected at grazing incidence from a grating. The plane ruled grating is mounted in an out-of-plane diffraction configuration. We present the measured angular diffraction patterns as a function of the atom's energy change along the grating normal. This presentation allows us to readily trace back the peak positions and widths to the geometry of the out-of-plane diffraction configuration. In the diffraction patterns, an interference effect due to emerging beam resonances is found to progress side by side with a new emerging diffraction beam.
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.
We report on the observation of emerging beam resonances, well known as Rayleigh-Wood anomalies and threshold resonances in photon and electron diffraction, respectively, in an atom-optical diffraction experiment. Diffraction of He atom beams reflected from a blazed ruled grating at grazing incidence has been investigated. The total reflectivity of the grating as well as the intensities of the diffracted beams reveal anomalies at the Rayleigh angles of incidence, i.e., when another diffracted beam emerges parallel to the grating surface. The observed anomalies are discussed in terms of the classical wave-optical model of Rayleigh and Fano.