Paper detail

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

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 $C_3=3.42\pm 0.19 \textrm{eV} \mathring{\textrm{A}}^3$ 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.