Zone-plate focusing of Bose-Einstein condensates for atom optics and erasable high-speed lithography of quantum electronic components

We show that Fresnel zone plates (ZPs), fabricated in a solid surface, can sharply focus atomic Bose-Einstein condensates that quantum reflect from the surface or pass through the etched holes. The focusing process compresses the condensate by orders of magnitude despite inter-atomic repulsion. Crucially, the focusing dynamics are insensitive to quantum fluctuations of the atom cloud and largely preserve the condensates' coherence, suggesting applications in passive atom-optical elements, for example ZP lenses that focus atomic matter waves and light at the same point to strengthen their interaction. We explore transmission ZP focusing of alkali atoms as a route to erasable and scalable lithography of quantum electronic components in two-dimensional electron gases (2DEGs) embedded in semiconductor nanostructures. To do this, we calculate the density profile of a 2DEG immediately below a patch of alkali atoms deposited on the surface of the nanostructure by zone-plate focusing. Our results reveal that surface-induced polarization of only a few thousand adsorbed atoms can locally deplete the electron gas. We show that, as a result, the focused deposition of alkali atoms by existing ZPs can create quantum electronic components on the 50 nm scale, comparable to that attainable by ion beam implantation but with minimal damage to either the nanostructure or electron gas.