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arXiv:0904.3289 · Physical Review A

Magic ratio of window width to grating period for van der Waals potential measurements using material gratings

Vincent Lonij, William F. Holmgren, Alexander D. Cronin

Published Dec 18, 2009• 24 citations
arXivHTMLPDF

Abstract

We report improved precision measurements of the van der Waals potential strength $({C}_{3})$ for Na atoms and a silicon-nitride $({\text{SiN}}_{x})$ surface. We studied diffraction from nanofabricated gratings with a particular ``magic'' open fraction that allows us to determine ${C}_{3}$ without the need for separate measurements of the width of the grating openings. Therefore, finding the magic open fraction improves the precision of ${C}_{3}$ 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 ${\text{SiN}}_{x}$ surface. This precision is sufficient to detect a change in ${C}_{3}$ due to a thin metal coating on the grating surface. We discuss the contribution to ${C}_{3}$ of core electrons and edge effects.

DOI
10.1103/physreva.80.062904

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APS•May 1, 2003•0 citations
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 ${C}_{3}$ without the need for separate measurements of the width of the grating openings. Therefore, finding the magic open fraction improves the precision of ${C}_{3}$ measurements. The same effect is demonstrated for a grating with an arbitrary open fraction by rotating it to a particular magic'' angle, yielding C3=3.42\ifmmode±\else\textpm\fi0.19 eV A˚3{C}_{3}=3.42\ifmmode\pm\else\textpm\fi{}0.19\text{ }\text{eV}\text{ }{\text{\AA{}}}^{3}C3​=3.42\ifmmode±\else\textpm\fi0.19 eV A˚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.
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.
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 (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.
This dissertation describes new measurements of the van der Waals (vdW) potential energy for atoms near a surface. The measurements presented here were accomplished by studying diffraction a beam of atoms transmitted through a nanograting. I will describe how we improved precision by a factor of 10 over previous diffraction measurements by studying how different types of atoms interact with the same surface. As a result of this new precision, we were able to show for the first time the contribution of atomic core electrons to the atom-surface potential, and experimentally test different atomic structure calculation methods.In addition, this dissertation will describe how changing the width of the grating bars to achieve a particular "magic" grating bar width or rotating a grating to a particular "magic" angle allows us to determine both the atom-surface potential strength and the geometry of the grating. This represents an improvement over several recent studies where uncertainties in the nanograting geometry limited precision in the measurements of the vdW potential.For a complementary measurement, also discussed in this dissertation, we collaborated with the Vigue group in Toulouse, France. In this collaboration we used an atom interferometer to measure the phase shift due to transmission through a nanograting. By combining diffraction data from Tucson with interferometry data from Toulouse we improved the precision of interferometry measurements of the atom-surface potential of a single atomic species by almost a factor of 10 over previous interferometric measurements of the vdW potential. These interferometry measurements also serve to measure the shape of the vdW potential and set a limit on non-Newtonian gravitational interactions at 1-2 nm length scales.Finally, this dissertation will discuss how nanogratings with optimized geometry can improve atom interferometers, for example, with blazed gratings. We discuss next generation atom-surface potential measurements and examine new ways of analyzing diffraction data.
We measured ratios of van der Waals potential coefficients (C3) for different atoms (Li, Na, K, and Rb) interacting with the same surface by studying atom diffraction from a nanograting. These measurements are a sensitive test of atomic structure calculations because C3 ratios are strongly influenced by core electrons and only weakly influenced by the permittivity and geometry of the surface. Our measurement uncertainty of 2% in the ratio C(3)(K)/C(3)(Na) is close to the uncertainty of the best theoretical predictions, and some of these predictions are inconsistent with our measurement.
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.