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arXiv:quant-ph/9907053 · Physical Review Letters

Determination of Atom-Surface van der Waals Potentials from Transmission-Grating Diffraction Intensities

R. E. Grisenti, Wieland Schöllkopf, Jan Peter Toennies, Gerhard C. Hegerfeldt, Thorsten Köhler

Published Aug 30, 1999• 190 citations
arXivHTMLPDF

Abstract

Molecular beams of rare gas atoms and ${\mathrm{D}}_{2}$ have been diffracted from 100-nm-period ${\mathrm{SiN}}_{x}$ transmission gratings. The relative intensities of the diffraction peaks out to the eighth order depend on the diffracting particle and are interpreted in terms of effective slit widths. These differences have been analyzed by a new theory which accounts for the long-range van der Waals ${\ensuremath{-}C}_{3}/{l}^{3}$ interaction of the particles with the walls of the grating bars. The values of the ${C}_{3}$ constant for two different gratings are in good agreement and the results exhibit the expected linear dependence on the dipole polarizability.

DOI
10.1103/physrevlett.83.1755

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Molecular beams of rare gas atoms and D2{\mathrm{D}}_{2}D2​ have been diffracted from 100-nm-period SiNx{\mathrm{SiN}}_{x}SiNx​ transmission gratings. The relative intensities of the diffraction peaks out to the eighth order depend on the diffracting particle and are interpreted in terms of effective slit widths. These differences have been analyzed by a new theory which accounts for the long-range van der Waals \ensuremath−C3/l3{\ensuremath{-}C}_{3}/{l}^{3}\ensuremath−C3​/l3 interaction of the particles with the walls of the grating bars. The values of the C3{C}_{3}C3​ constant for two different gratings are in good agreement and the results exhibit the expected linear dependence on the dipole polarizability.
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.
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=2.7pm0.8meVnm3C_{3} = 2.7\\pm 0.8{meV nm}^{3}C3​=2.7pm0.8meVnm3 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.
Rare-gas atoms are diffracted from nanostructured silicon nitride transmission gratings. From the relative intensities of the diffraction maxima the strength of the van der Waals potential between the atoms and the grating bars is inferred. The method is set out theoretically and is validated with the help of several sets of experimental data. The atom-surface potential of metastable helium and -neon is accurately measured for the first time. The atom-optical method is shown to bear a high potential for new versatile and even more accurate measurements of atom-surface potentials.
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 (vdW) 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 ${C}_{3}=2.7\ifmmode\pm\else\textpm\fi{}0.8\phantom{\rule{0.3em}{0ex}}\mathrm{meV}\phantom{\rule{0.3em}{0ex}}{\mathrm{nm}}^{3}$ is determined by fitting a modified Fresnel optical theory to the experimental data. This value of C3{C}_{3}C3​ is consistent with a van der Waals interaction between atomic sodium and a silicon nitride surface.
In atom optics a mechanical structure is commonly regarded as an amplitude mask for atom waves. However, atomic diffraction patterns indicate that mechanical structures also operate as phase masks. In this study a well collimated beam of Na 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 (vdW) interaction with the grating walls. This phase shift depends both on atom position and velocity. As a result the relative intensities of the matter-wave diffraction peaks deviate from optical theory and depend on the de Broglie wavelength of the atoms. The vdW coefficient C3 is determined by fitting a modified Fraunhoffer optical theory to the experimental data.
We report improved precision measurements of the van der Waals potential strength (C3)({C}_{3})(C3​) for Na atoms and a silicon-nitride (SiNx)({\text{SiN}}_{x})(SiNx​) surface. We studied diffraction from nanofabricated gratings with a particular ``magic'' open fraction that allows us to determine C3{C}_{3}C3​ without the need for separate measurements of the width of the grating openings. Therefore, finding the magic open fraction improves the precision of C3{C}_{3}C3​ measurements. The same effect is demonstrated for a grating with an arbitrary open fraction by rotating it to a particular ``magic'' angle, yielding ${C}_{3}=3.42\ifmmode\pm\else\textpm\fi{}0.19\text{ }\text{eV}\text{ }{\text{\AA{}}}^{3}$ for Na and a SiNx{\text{SiN}}_{x}SiNx​ surface. This precision is sufficient to detect a change in C3{C}_{3}C3​ due to a thin metal coating on the grating surface. We discuss the contribution to C3{C}_{3}C3​ of core electrons and edge effects.