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Physical Review Letters

Imaging and focusing of atoms by a fresnel zone plate

O. Carnal, M. Sigel, Tycho Sleator, Hiroshi Takuma, J. Mlynek

Published Dec 2, 1991• 167 citations
Publisher

Abstract

Focusing of and imaging with atoms by means of a spherical Fresnel zone plate has been observed for the first time. An intense beam of metastable helium atoms with atomic de Broglie wavelength ${\ensuremath{\lambda}}_{\mathrm{dB}}$=0.5--2.5 \AA{} is passed through either a single or a double slip with dimensions in the 10-\ensuremath{\mu}m range. This transverse intensity distribution is imaged by a Fresnel zone plate, 210 \ensuremath{\mu}m in diameter and with an innermost zone diameter of 18.76 \ensuremath{\mu}m. For ${\ensuremath{\lambda}}_{\mathrm{dB}}$=1.96 \AA{} the focal length is 0.45 m. The imaging properties of the zone plate are presented and compared with numerical calculations.

DOI
10.1103/physrevlett.67.3231

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arXiv:2402.09935•Physica Scripta•Feb 21, 2025•0 citations
Focusing of and imaging with atoms by means of a spherical Fresnel zone plate has been observed for the first time. An intense beam of metastable helium atoms with atomic de Broglie wavelength \ensuremathλdB{\ensuremath{\lambda}}_{\mathrm{dB}}\ensuremathλdB​=0.5--2.5 \AA{} is passed through either a single or a double slip with dimensions in the 10-\ensuremath{\mu}m range. This transverse intensity distribution is imaged by a Fresnel zone plate, 210 \ensuremath{\mu}m in diameter and with an innermost zone diameter of 18.76 \ensuremath{\mu}m. For \ensuremathλdB{\ensuremath{\lambda}}_{\mathrm{dB}}\ensuremathλdB​=1.96 \AA{} the focal length is 0.45 m. The imaging properties of the zone plate are presented and compared with numerical calculations.
In 2008 we presented the first images obtained with a new type of matter wave microscope: NEutral Helium Atom MIcroscopy (NEMI). The main features in NEMI are the low energy of the atoms (<0.1 eV) and the fact that they are neutral. This means that fragile and/or insulating samples can be imaged without surface damage and charging effects. The ultimate resolution limit is given by the de Broglie wavelength (about 0.06 nm for a room-temperature beam), but reaching a small focus spot is still a major challenge. The best result previously was about 2 μ m. The main result of this paper is the focusing of a helium atom beam to a diameter below 1 μ m. A particular challenge for neutral helium microscopy is the optical element for focusing. The most promising option is to manipulate neutral helium via its de Broglie wavelength, which requires optical elements structured to nanometre precision. Here we present an investigation of the helium focusing properties of nanostructured Fresnel zone-plates. Experiments were performed by varying the illuminated area and measuring the corresponding focused spot sizes and focused beam intensities. The results were fitted to a theoretical model. There is a deviation in the efficiency of the larger zone plate, which indicates a distortion in the zone-plate pattern, but nevertheless there is good agreement between model and experiments for the focus size. This together with the demonstration of focusing to below 1 μ m is an important step towards nanometre resolution neutral helium microscopy.
A neutral, ground-state, 4He{}^{4}\mathrm{He}4He atom beam has been focused using Fresnel zone plates. At only moderate demagnification $(0.40\ifmmode\times\else\texttimes\fi{})$, a focused spot diameter of $\ensuremath{\le}2.0\ensuremath{\mu}\mathrm{m}$ is achieved at a signal intensity of 500 counts/s. This is an improvement over previous work by a factor of 10 in resolution, 103{10}^{3}103 in signal intensity, and 108{10}^{8}108 in focused beam density, and allows the full intrinsic intensity profile of a focused atomic Fresnel spot to be measured for the first time. Raster scans of 15 and $25\ensuremath{\mu}\mathrm{m}$ wide slits across the focused spot demonstrate transmission scanning helium de Broglie microscopy of micron resolution.
We have fabricated a free-standing transmission Fresnel zone plate for the focusing of long-thermal-wavelength neutral atoms. The zone plate was fabricated from a 0.7μm thick boron-doped silicon membrane. The pattern was formed by means of electron-beam lithography, and the final grating was generated by reactive ion etching. The zone plate is composed of 100 zones, the diameter of the outermost zone is approximately 80 μm. The zone plate is designed to focus incident atoms having a thermal wavelength of 17 Å into a 2000 Å spot at a focal length of about 1 cm. A maximum of 8% of the incident flux will be transmitted and focused into the primary spot with this design. The use of diffraction optics for the focusing of an atomic beam is novel in that it does not rely on any electromagnetic forces for achieving focusing. As a result, this approach can be used to focus any particle with a long thermal de Broglie wavelength.
The manipulation of low-energy beams of neutral atoms and molecules via their de Broglie wavelength is a branch of atom optics often referred to as de Broglie matter wave optics. The application areas include fundamental quantum mechanics, atom interferometry, and the development of new microscopy instrumentation. The focusing of de Broglie matter waves with a Fresnel zone plate was used to demonstrate the first neutral helium microscopy imaging. The ultimate resolution of such a microscope is limited by the width of the outermost zone. Because a Fresnel zone plate for atoms cannot be fabricated on a substrate (the low-energy atom beams would not be able to penetrate the substrate material), this gives a fabrication determined limit for the first-order focus of around 30--50 nm. Therefore, it is important to search for alternative optical elements that enable higher resolution. Photon sieves consist of a large number of pinholes, arranged suitably relative to the Fresnel zones. The great advantages are that the width of the pinholes can be larger than the respective Fresnel zones and a free-standing pinhole is much easier to fabricate than a free-standing zone. Thus, with a photon-sieve structure applied for de Broglie matter wave manipulation, the fabrication limit for focusing is reduced to potentially around 3--5 nm. Here we present a realization of such an ``atom sieve,'' which we fabricated out of a silicon nitride (SiN) membrane, using electron-beam lithography and reactive ion etching. Our atom sieve is 178 $\ensuremath{\mu}\mathrm{m}$ in diameter and has 31 991 holes. The diameter of the holes varies from 1840 to 150 nm. Using a beam of neutral, ground-state helium atoms with an average wavelength of 0.055 nm, we demonstrate helium atom focusing down to a spot size of less than 4 $\ensuremath{\mu}\mathrm{m}$. The focus size is limited by the intrinsic velocity spread of the helium beam.
Matter wave optics is a fascinating area of physics touching many scientific disciplines ranging from microscopy to high precision gravity measurements. One of the major recent breakthroughs was the realization in 1995 of a Bose-Einstein condensate of atoms - a perfectly coherent atom source. Bose-Einstein condensates have been studied intensely over the last couple of decades, but surprisingly little work has been done on manipulation of the condensates using their de Broglie wavelength. The original aim of this thesis was to create a Fresnel zone plate for the first focusing of a Bose-Einstein condensate via the de Broglie wavelength. The zone plate design parameters were chosen to fit the experimental setup of Prof. Zeilinger in Vienna, currently one of the only setups in the world where this experiment can be carried out. The original aim of the thesis has been fulfilled. A free-standing silicon nitride zone plate with a diameter of 5 mm, and a focal length of 60 cm for a wavelength of 100 nm has been successfully created, tested with laser light and is now ready for experiments in Vienna. The zone plate has 44 zones, a 2 mm central stop and the width of the outermost zone is 12 µm. To the best of our knowledge this zone plate has a diameter more than an order of magnitude larger than any zone plates previously created for the focusing of matter waves. The much larger wavelength of the Bose-Einstein condensate compared to previous experiments meant that previously used fabrication methods could not be applied and new methods had to be developed as part of this thesis. Aluminium wet etching, dry-etching of SiO2 and silicon nitride using only a PMMA mask and quantified wet-etching of silicon were all established for the first time at the UiB NanoStructures laboratory as part of this thesis.
Abstract The evolution from classical optics to quantum matter wave optics has been influenced by transformative optical devices like Fresnel zone plates (FZP). This study investigates the focusing of helium atoms by an electrically biased FZP, made of chromium (Cr), using numerical solutions of the time-dependent Schrödinger equation (TDSE) with the split-step Fourier method. The nth opaque zone of an amplitude-type FZP is subject to electrostatic biasing using three methods: (i) V n = V 1, where V 1 is the biasing voltage applied to the central zone (n = 1), (ii) V n = V 1 n , and (iii) V n = V 1 sin ( k E n ) , with k E being the radial modulation factor in the biasing voltage. The effects of electrostatic biasing on the transmitted wave packet distribution, transmission coefficient (T c ), focal length (f), size of the focused wave packet (σ F ), and focusing efficiency (η) are analyzed. Results show that electrical biasing modulates diffractive focusing via induced polarization potential. Biasing with V n = V 1 reduces the wave packet transmission and focusing efficiency. Biasing with V n = V 1 n enhances T c by ∼ 38%, f by ∼ 73.5%, and η from 6% to 20%. Biasing with V n = V 1 sin ( k E n ) offers better control, achieving a focusing efficiency of ∼ 10.5%. These findings suggest new methods for higher efficiency focusing of matter waves, with applications in helium microscopes, cold atom trapping, and high-precision atom lithography for quantum electronic devices.