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Physical Review A

Scattering of atomic matter waves from ridged surfaces

Dmitrii Kouznetsov, H. Oberst

Published Jul 28, 2005• 28 citations
Publisher

Abstract

Motivated by recent experiments that demonstrated a strongly enhanced reflection efficiency of atoms on microfabricated, gratinglike surface structures, we develop a detailed description of the scattering of atomic matter waves on such structures. We start with a simple model that describes the ridged surface as an equivalent absorbing medium. This model correctly predicts the experimentally observed scaling and magnitude of the reflection efficiency. We then calculate the accurate solutions for the Fresnel diffraction of waves at grazing incidence at a periodic set of idealized, parallel edges. Both numerical and analytical solutions are presented. The specular reflectivity and its phase, as well as the efficiencies of higher diffraction orders are calculated. We compare our results to experimental data in a wide range of parameters. We extend the model including the finite size of the grating ridges and the van der Waals attraction and suggest a more general estimate of the reflection coefficient.

DOI
10.1103/physreva.72.013617

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Motivated by recent experiments that demonstrated a strongly enhanced reflection efficiency of atoms on microfabricated, gratinglike surface structures, we develop a detailed description of the scattering of atomic matter waves on such structures. We start with a simple model that describes the ridged surface as an equivalent absorbing medium. This model correctly predicts the experimentally observed scaling and magnitude of the reflection efficiency. We then calculate the accurate solutions for the Fresnel diffraction of waves at grazing incidence at a periodic set of idealized, parallel edges. Both numerical and analytical solutions are presented. The specular reflectivity and its phase, as well as the efficiencies of higher diffraction orders are calculated. We compare our results to experimental data in a wide range of parameters. We extend the model including the finite size of the grating ridges and the van der Waals attraction and suggest a more general estimate of the reflection coefficient.
We have experimentally demonstrated a material-independent mirror for atomic waves that uses the Fresnel diffraction at an array of parallel ridges. He* (2 (3)S(1)) and Ne* (1s(3)) atomic waves were reflected coherently on a silicon plate with a microfabricated grating structure, consisting of narrow wall-like ridges. We measured the reflectivity at grazing incidence as a function of the incident velocity and angle. Our data show that the reflectivity on this type of mirror depends only on the distance between the ridges, the wavelength, and the incident angle, but is insensitive to the material of the grating structure. The reflectivity is observed to increase by 2 orders of magnitude, compared to that of a flat polished silicon surface, where the reflection is caused by the attractive surface potential. For He* atoms, the measured reflectivity exceeds 10% for normal incident velocities below about 25 cm/s.
Recent results on the reflection of waves from ridged mirrors are discussed. Numerical calculations, analytical estimates and the direct measurements of coefficient of specular reflection of atomic waves from solid-state mirrors are combined. The reflectivity is approximated as an elementary function of period L of ridges, their width ℓ, wavenumber K, grazing angle θ and effective depth w of the van der Waals potential. In a special case L = ℓ, the fit reproduces the reflectivity of flat surfaces. Our approximation allows us to optimize the L at given ℓ and estimate the maximum performance of a ridged mirror. Such a mirror is suggested as a focusing element for the nano-scale imaging system. 1.
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.
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.
In atom optics a material structure is commonly regarded as an amplitude mask for atom waves. However, atomic diffraction patterns formed using material gratings indicate that material structures also operate as phase masks. In this study a well collimated beam of sodium atoms is used to illuminate a silicon nitride grating with a period of 100 nm. During passage through the grating slots atoms acquire a phase shift due to the van der Waals interaction with the grating walls. As a result the relative intensities of the matter-wave diffraction peaks deviate from those expected for a purely absorbing grating. Thus a complex transmission function is required to explain the observed diffraction envelopes. An optics perspective to the theory of atomic diffraction from material gratings is put forth in the hopes of providing a more intuitive picture concerning the influence of the vdW potential. The van der Waals coefficient C3=2.7±0.8meVnm3C_{3} = 2.7\pm 0.8{meV nm}^{3}C3​=2.7±0.8meVnm3 is determined by fitting a modified Fresnel optical theory to the experimental data. This value of C3C_{3}C3​ is consistent with a van der Waals interaction between atomic sodium and a silicon nitride surface.