  We show that Fresnel zone plates, 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 zone plate lenses that focus atomic matter
waves and light at the same point to strengthen their interaction. We explore
transmission zone-plate focusing of alkali atoms as a route to erasable and
scalable lithography of quantum electronic components in two-dimensional
electron gases embedded in semiconductor nanostructures. To do this, we
calculate the density profile of a two-dimensional electron gas 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 zone
plates 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.
