de Broglie Wave Phase Shifts Induced by Surfaces Closer than 25 nm

Four atom optics experiments that each serve to measure atom-surface interactions near nanofabricated gratings are presented here. In these experiments atoms in a beam travel within 25 nm of a material grating bar, and the analysis incorporates phase shifts for the atomic de Broglie waves due to interactions betwen Na atoms and silicon nitride surfaces. One atom diffraction experiment determines the van der Waals coefficient $C_3=2.7\pm$0.8 meVnm$^3$, and one atom interferometer experiment determines $C_3=4\pm$1 meVnm$^3$. The results of all four experiments are consistent with the Lifshitz prediction that is explicitly calculated here for Na-silicon nitride to be $C_3=3.25$ meVnm$^3$. The four atom optics experiments and review of van der Waals theory are complemented by similar experiments using electron beams and analysis of image-charge effects.