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

Abstract

We report improved precision measurements of the Van der Waals potential strength ($C_3$) for Na atoms and a silicon-nitride (SiN${}_x$) surface. We studied diffraction from nano-fabricated 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 $C_3=3.42\pm 0.19\text{eV}{\mathring{\text{A}}}^3$ for Na and a 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.

References in corpus (2)

• Exploring the van der Waals Atom-Surface attraction in the nanometric range
• The van der Waals energy of atomic systems near absorbing and dispersing bodies

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