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Ridged Mirrors as Experimental Evidence of the Spatial Zeno Effect

Dmitrii Kouznetsov, H. Oberst, Jean‐François Bisson

Published Jan 18, 2006• 0 citations
Publisher

Abstract

The specular reflection of waves from a periodic set of absorbers/scatterers is interpreted as a spatial version of the Zeno effect. This interpretation reveals the scaling law for the ridged atomic mirrors and allows the simple estimate of the efficiency. The experimental results with various waves confirm this estimate and validate our interpretation.

DOI
10.1109/cleopr.2005.1569553

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The specular reflection of waves from a periodic set of absorbers/scatterers is interpreted as a spatial version of the Zeno effect. This interpretation reveals the scaling law for the ridged atomic mirrors and allows the simple estimate of the efficiency. The experimental results with various waves confirm this estimate and validate our interpretation.
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.
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.