Abstract
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.
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GENERAL SCIENTIFIC SUMMARY Introduction and background. When atoms approach to within a micron of a surface, they experience an electrical 'Casimir–Polder' force, which strongly attracts them to the surface. This force is created from nothing by quantum mechanics, which allows charged particles and light photons to emerge from a vacuum for a short time before they disappear again. Usually, the Casimir–Polder force accelerates the atoms rapidly to the surface, like gravity making a ball fall to the floor. But if the atoms are cooled to very low temperatures, to within a few billionths of a degree of absolute zero, they behave as a giant quantum-mechanical matter wave, rather than a Newtonian ball. In this case, when the atoms approach the surface, their quantum wave nature can make them suddenly turn around and retreat from the surface against the force of attraction; a process known as quantum reflection. Since the surface itself is at room temperature, quantum reflection provides the ultracold atoms with a heat shield, whose performance is equivalent to keeping a snowball frozen in an environment ~500,000 times hotter than the centre of the sun. This remarkable effect has enabled us to study how ultracold atoms quantum reflect from, or pass through, ring-shaped patterns that form a diffraction grating (black and white in the figure) for quantum waves.
Main results. We have shown that quantum diffraction from the rings sharply focuses the matter waves, so enabling them to be deposited in nm-scale patterns on the surface of microelectronic devices (right part of figure). In turn, this deposition can imprint nm-scale quantum wires and components in thin electron sheets (red in the figure) just below the surface of the device.
Wider implications. In contrast to other microfabrication techniques, this process does not damage the surface and is potentially reversible, suggesting that ultracold atoms could provide a way to make re-writable microelectronic circuits.
Figure. Schematic diagram showing the focusing of ultracold-atom matter waves (blue cone) as they pass through a series of circular rings (black and white pattern) on to a microelectronic device (right). By scanning the device across the focused beam (arrows), atoms may be deposited in patterns (blue) on the device, which control the local properties of a quantum conductor (red) beneath the surface on an nm scale.