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Physical Review Letters

Fresnel Diffraction Mirror for an Atomic Wave

H. Oberst, Dimitrii Kouznetsov, Kazuko Shimizu, Jun‐ichi Fujita, Fujio Shimizu

Published Jan 11, 2005• 73 citations
Publisher

Abstract

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.

DOI
10.1103/physrevlett.94.013203

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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.
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.
The specular reflectivity of slow, metastable neon atoms from a silicon surface was found to increase markedly when the flat surface was replaced by a grating structure with parallel narrow ridges. For a surface with ridges that have a sufficiently narrow top, the reflectivity was found to increase more than two orders of magnitude at the incident angle of 10 mRad from the surface. The slope of the reflectivity vs the incident angle near zero was found to be nearly an order of magnitude smaller than that of a flat surface. A grating with 6.5% efficiency for the first-order diffraction was fabricated by using the ridged surface structure.
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.
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.
A cold beam of He∗(23S1){\mathrm{He}}^{*}\phantom{\rule{0.3em}{0ex}}(2\phantom{\rule{0.2em}{0ex}}^{3}S_{1})He∗(23S1​) atoms is used at grazing incidence to study the quantum reflection on a flat polished silicon surface. We measure the reflectivity as a function of the normal incident velocity component between 3 and 30cm∕s30\phantom{\rule{0.3em}{0ex}}\mathrm{cm}∕\mathrm{s}30cm∕s. Our result is in reasonable agreement with a calculation of the attractive van der Waals surface potential using the dielectric function of Si and the dipole polarizability of He∗{\mathrm{He}}^{*}He∗. We discuss the influence of the conductivity and of a thin oxide layer on the potential. By comparing our data to those previously measured with Ne∗{\mathrm{Ne}}^{*}Ne∗ atoms, we are also able to confirm the scaling of the reflectivity with atomic mass.
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.