Research ArticleMOLECULAR PHYSICS

Universal diffraction of atoms and molecules from a quantum reflection grating

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Science Advances  18 Mar 2016:
Vol. 2, no. 3, e1500901
DOI: 10.1126/sciadv.1500901
  • Fig. 1 Schematic representation of the experimental setup.

    A collimated atomic or molecular beam is quantum-reflected from the diffraction grating. The figure is not to scale: The actual incidence angles and diffraction angles, which are defined with respect to the grating plane, are on the order of 1 mrad only. As shown here, the azimuth angle φ is chosen such that the facet surfaces are tilted away from the source, leading to a blazing of the negative-order diffraction beams. Out-of-plane diffraction effects have been neglected in this figure for the sake of simplicity. A detailed description of the apparatus is provided in the Supplementary Materials.

  • Fig. 2 Diffraction data for helium atoms and dimers.

    (A) Two-dimensional contour plot of the He+ signal from 64 diffraction spectra measured for φ = −33.5 mrad and incidence angles from θin = 0.5 to 1.56 mrad as a function of incidence and detection angles. The signal is plotted on a logarithmic contour scale ranging from 100.5 to 103 counts/s. White solid lines indicate the calculated nth-order diffraction angles of helium atoms, which are identical to the (2n)th-order diffraction angles of helium dimers. Red solid lines represent the calculated odd-order [(2n − 1)th] diffraction angles of dimers, which do not coincide with diffraction angles of atoms. The vertical lines indicate the calculated Rayleigh incidence angles θR,m corresponding to the emergence of the mth-order diffraction peaks of atoms and dimers as indicated on top of the plot. (B) Diffraction patterns at 10 different incidence angles in the vicinity of the Rayleigh incidence angle θR,−1(He) = θR,−2(He2) = 1.047 mrad, where the –1st- and –2nd-order peaks of the monomer and dimer emerge, respectively. The numbers on top of the arrows indicate the orders of the atomic diffraction peaks. The asterisk marks the –1st-order peak of the dimer, which is shown enlarged in the inset. (C) Diffraction efficiencies (as defined in Materials and Methods) as a function of incidence angle. The dashed vertical lines indicate the same Rayleigh incidence angles as in (A).

  • Fig. 3 Direct scattering and secondary scattering from neighboring grating units.

    The red arrow indicates direct scattering: the scattering of the incident beam from a grating unit. In addition, we consider secondary scattering as visualized by the blue arrow; the incident beam first scatters off a grating unit and propagates parallel to the grating surface plane for a distance deff, until it scatters off from the neighboring grating unit.

  • Fig. 4 Comparison of the –1st-order diffraction efficiency curves for He, He2, and D2 at corresponding conditions.

    The He2 data are replotted from Fig. 2C. The He and D2 data were collected for T0 = 35 K and P0 = 7.3 bar (He) and 0.8 bar (D2) for otherwise identical machine parameters. Under these conditions, the de Broglie wavelengths of He and D2 are 0.17 nm, which is identical to the dimer’s wavelength. The vertical lines indicate Rayleigh angles of incidence for the emergence of mth-order diffraction peaks. As a result of identical de Broglie wavelengths, the Rayleigh angles are the same for all three species. To account for differences in the overall quantum reflection probabilities, the He and D2 data were normalized by factors of 0.09 and 0.15, respectively.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/2/3/e1500901/DC1

    Source and helium beam.

    Slits, apparatus geometry, and definition of angles.

    Mass spectrometer detector and apparatus resolution.

    Derivation of the “rule of thumb” of quantum reflection.

    Fig. S1. Schematic of the quantum-reflection diffraction setup.

    References (32, 33)

  • Supplementary Materials

    This PDF file includes:

    • Source and helium beam.
    • Slits, apparatus geometry, and definition of angles.
    • Mass spectrometer detector and apparatus resolution.
    • Derivation of the “rule of thumb” of quantum reflection.
    • Fig. S1. Schematic of the quantum-reflection diffraction setup.
    • References (32, 33)

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