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The Journal of Physical Chemistry Letters

Scattering of He Atoms from a Microstructured Grating: Quantum Reflection Probabilities and Diffraction Patterns

Salvador Miret-Artés, Eli Pollak

Published Feb 11, 2017• 15 citations
Publisher

Abstract

The quantum reflection measured previously by Zhao et al. ( Phys. Rev. A 2008 , 78 , 010902(R) ) for the scattering of He atoms off of a microstructured grating is described and analyzed theoretically. Using the close-coupling formalism with a complex absorbing potential and describing the long-range interaction in terms of the Casimir-van der Waals potential, we find probabilities and diffraction patterns that are in fairly good agreement with the experimental results. The central outcomes of this study are two-fold. First is the theoretical confirmation that, indeed, the phenomenon of quantum reflection may be detected not only through the elastic peak but also in terms of a quantum reflected diffraction pattern. Second, we demonstrate that the phenomenon of quantum reflection is the result of a coherent process where all of the potential regions are involved on an equal footing. It is a nonlocal property and cannot be related only to the long-range badlands region of the potential of interaction.

DOI
10.1021/acs.jpclett.6b02991

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The quantum reflection measured previously by Zhao et al. ( Phys. Rev. A 2008 , 78 , 010902(R) ) for the scattering of He atoms off of a microstructured grating is described and analyzed theoretically. Using the close-coupling formalism with a complex absorbing potential and describing the long-range interaction in terms of the Casimir-van der Waals potential, we find probabilities and diffraction patterns that are in fairly good agreement with the experimental results. The central outcomes of this study are two-fold. First is the theoretical confirmation that, indeed, the phenomenon of quantum reflection may be detected not only through the elastic peak but also in terms of a quantum reflected diffraction pattern. Second, we demonstrate that the phenomenon of quantum reflection is the result of a coherent process where all of the potential regions are involved on an equal footing. It is a nonlocal property and cannot be related only to the long-range badlands region of the potential of interaction.
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 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.
Quantum threshold reflection is a well-known quantum phenomenon which prescribes that at threshold, except for special circumstances, a quantum particle scattering from any potential, even if attractive at long range, will be reflected with unit probability. In the past, this property had been associated with the so-called badlands region of the potential, where the semiclassical description of the scattering fails due to a rapid spatial variation of the de Broglie wavelength. This badlands region occurs far from the strong interaction region of the potential and has therefore been used to ``explain'' the quantum reflection phenomenon. In this paper we show that the badlands region of the interaction potential is immaterial. The extremely long wavelength of the scattered particle at threshold is much longer than the spatial extension of the badlands region, which therefore does not affect the scattering. For this purpose, we review and generalize the proof for the existence of quantum threshold reflection to stress that it is only a consequence of continuity and boundary conditions. The nonlocal character of the scattering implies that the whole interaction potential is involved in the phenomenon. We then provide a detailed numerical study of the threshold scattering of a particle by a Morse potential and an Eckart potential, especially in the time domain. We compare exact quantum computations with incoherent results obtained from a classical Wigner approximation. This study shows that close to threshold the time-dependent amplitude of the scattered particle is negligible in the badlands region and is the same whether the potential has a reflecting wall as in the Morse potential or a steplike structure as in the Eckart smooth step potential. The mean flight time of the particle is not shortened due to a local reflection from the badlands region or due to the lower density of the wave function at short distances. This study should serve to definitely rule out the badlands region as a qualitative guide to the properties of quantum threshold reflection.
The coherent reflection of ultra-cold neon and helium atoms from silicon surfaces and surface structures is measured and analyzed. When the silicon surface is flat, the reflection is explained by the quantum reflection due to van der Waals attractive potential near the silicon surface. When the silicon surface is modified to form a grating structure, the reflectivity increases dramatically. For certain ranges of surface structure parameters, the reflection may be interpreted as a coherent summation of Fresnel diffraction of the atomic wave at the ridges of the grating structure.
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.
Quantum reflection of thermal He atoms from various surfaces (glass slide, GaAs wafer, flat, and structured Cr) at grazing conditions is studied within the elastic close-coupling formalism. Comparison with the experimental results of Zhao et al. [Phys. Rev. Lett. 105, 133203 (2010)] is quite reasonable but the conclusions of the present theoretical analysis are different from those discussed in the experimental work. The universal linear behavior observed in the dependence of the reflection probability on the incident wave-vector component perpendicular to the surface is only valid at small values of the component whereas, at larger values, deviation from the linearity is evident, approaching a quadratic dependence at higher values. The surface roughness seems to play no important role in this scattering. Moreover, the claim that one observes a transition from quantum to classical reflection seems to be imprecise.