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ChemPhysChem

Universal Diffraction of Atomic and Molecular Matter‐Waves: A Comparison of He and D2 Quantum Reflected from a Grating

Weiqing Zhang, Ju Hyeon Lee, Hye Ah Kim, Byung Gwun Jin, Bong Jun Kim, Lee Yeong Kim, Bum Suk Zhao, Wieland Schöllkopf

Published Oct 17, 2016• 7 citations
Publisher

Abstract

Abstract Molecular beams of He and D2 are scattered from a ruled diffraction grating in conical‐mount geometry under grazing‐incidence conditions. Fully resolved diffraction patterns as a function of detection angle are recorded for different grating azimuth angles and for two different kinetic energies of the particle beams. Variations in diffraction peak widths are traced back to different velocity spreads of He and D2 determined by time‐of‐flight measurements. A comprehensive analysis of diffraction intensities confirms universal diffraction, that is, for identical de Broglie wavelengths, the relative diffraction intensities for He and D2 are the same. Universal diffraction results from peculiarities of quantum reflection of the atoms and molecules from the diffraction grating. In quantum reflection particles scatter many nanometers in front of the surface from the long‐range attractive branch of the particle–surface interaction potential without probing the potential well and the short‐range repulsive branch of the potential.

DOI
10.1002/cphc.201600965

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Abstract Molecular beams of He and D2 are scattered from a ruled diffraction grating in conical‐mount geometry under grazing‐incidence conditions. Fully resolved diffraction patterns as a function of detection angle are recorded for different grating azimuth angles and for two different kinetic energies of the particle beams. Variations in diffraction peak widths are traced back to different velocity spreads of He and D2 determined by time‐of‐flight measurements. A comprehensive analysis of diffraction intensities confirms universal diffraction, that is, for identical de Broglie wavelengths, the relative diffraction intensities for He and D2 are the same. Universal diffraction results from peculiarities of quantum reflection of the atoms and molecules from the diffraction grating. In quantum reflection particles scatter many nanometers in front of the surface from the long‐range attractive branch of the particle–surface interaction potential without probing the potential well and the short‐range repulsive branch of the potential.
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.
Quantum reflection is a universal property of atoms and molecules when scattered from surfaces in ultracold collisions. Recent experimental work has documented the quantum reflection and diffraction of He atoms, dimers, trimers, and neon atoms when reflected from a grating. Conditions for the observation of emerging beam resonances have been discussed and measured. In this paper, we provide a theoretical simulation of the quantum reflection from a grating for those systems. We confirm the universal dependence on the incident de Broglie wavelength with the threshold angles where the emerging beam resonances are observed. However, the angular dependence of the reflection efficiencies, that is, the ratio of scattered intensity into specific diffraction channels relative to the total intensity is found to be dependent on the details of the particle surface interaction.
Abstract When Otto Stern embarked on molecular-beam experiments in his new lab at Hamburg University a century ago, one of his interests was to demonstrate the wave-nature of atoms and molecules that had been predicted shortly before by Louis de Broglie. As the effects of diffraction and interference provide conclusive evidence for wave-type behavior, Otto Stern and his coworkers conceived two matter-wave diffraction experiments employing their innovative molecular-beam method. The first concept assumed the molecular ray to coherently scatter off a plane ruled grating at grazing incidence conditions, while the second one was based on the coherent scattering from a cleaved crystal surface. The latter concept allowed Stern and his associates to demonstrate the wave behavior of atoms and molecules and to validate de Broglie’s formula. The former experiment, however, fell short of providing evidence for diffraction of matter waves. It was not until 2007 that the grating diffraction experiment was retried with a modern molecular-beam apparatus. Fully resolved matter-wave diffraction patterns were observed, confirming the viability of Otto Stern’s experimental concept. The correct explanation of the experiment accounts for quantum reflection, another wave effect incompatible with the particle picture, which was not foreseen by Stern and his contemporaries.
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.
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 report on the non-destructive scattering and diffraction of He, He2 and He3 from a plane ruled reflection grating. At grazing incidence the normal component of the particle’s wave-vector is sufficiently small to allow for quantum reflection at the attractive Casimir–van der Waals particle–surface interaction potential. Quantum reflection occurs tens of nanometres in front of the surface, before the dimers and trimers reach the region where the surface-induced forces would inevitably cause the breakup of the fragile bonds. The reflected particles are identified via their mass-dependent diffraction angles and by mass spectrometry. The intensity distributions of the observed diffraction patterns are discussed in terms of the grating’s blaze angle.