The manipulation of neutral atoms and molecules via their de Broglie wave properties, also referred to as de Broglie matter wave optics, is relevant for several fields ranging from fundamental quantum mechanics tests and quantum metrology to measurements of interaction potentials and new imaging techniques. However, there are several challenges. For example, for diffractive focusing elements, the zero-order beam provides a challenge because it decreases the signal contrast. Here we present the experimental realization of a zero-order filter, also referred to as an order-sorting aperture for de Broglie matter wave diffractive focusing elements. The zero-order filter makes it possible to measure even at low beam intensities. We present measurements of zero-order filtered, focused, neutral helium beams generated at source stagnation pressures between 11 and 81 bars. We show that for certain conditions the atom focusing at lower source stagnation pressures (broader velocity distributions) is better than what has previously been predicted. We present simulations with the software ray-tracing simulation package mcstas using a realistic helium source configuration, which gives very good agreement with our measurements.
The manipulation of neutral atoms and molecules via their de Broglie wave properties, also referred to as de Broglie matter wave optics, is relevant for several fields ranging from fundamental quantum mechanics tests and quantum metrology to measurements of interaction potentials and new imaging techniques. However, there are several challenges. For example, for diffractive focusing elements, the zero-order beam provides a challenge because it decreases the signal contrast. Here we present the experimental realization of a zero-order filter, also referred to as an order-sorting aperture for de Broglie matter wave diffractive focusing elements. The zero-order filter makes it possible to measure even at low beam intensities. We present measurements of zero-order filtered, focused, neutral helium beams generated at source stagnation pressures between 11 and 81 bars. We show that for certain conditions the atom focusing at lower source stagnation pressures (broader velocity distributions) is better than what has previously been predicted. We present simulations with the software ray-tracing simulation package mcstas using a realistic helium source configuration, which gives very good agreement with our measurements.
A simple focusing device is proposed for de Broglie matter-waves - a diffractive lens, based on the optical effect of diffractive multifocal focusing of radiation. This matter-wave lens consists of two co-axial circular apertures in which the second aperture of smaller diameter is located where the Fresnel number of the first aperture is unity. It is shown that diffraction of a de Broglie matter wave by a system of two pinholes on an optical axis exhibits the multifocal focusing effect of matter waves in the near-field (Fresnel) zone. The focusing, defocusing and refocusing phenomenon is explained as resulting from periodic phase changes at singular points, which are points where the intensity is zero and the phase is undefined. It is shown that the proposed matter-wave lens could create a very intense, spatially-localized beam of atoms. Theoretical predictions for the focusing efficiency of a neutral atomic beam by the diffractive lens are: the spot diameter is ~ 0.1 &mgr;m, the ratio of focal and incident intensities is ~ 15, the focal length of the diffractive lens is in the range ~ 0.13.6 cm, the focusing depth is in the range ~ 15.30 cm, and the energy transmitting efficiency is ~ 30%. For the relatively-large diameters of the pinholes, ⩾ 5.0 &mgr;m, the proposed configuration acts as a matter-wave lens with a large focal length and a long focusing depth.
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.
A simple focusing device is proposed for de Broglie matter waves—a diffractive lens, based on the optical effect of diffractive multifocal focusing of radiation. This matter-wave lens consists of two coaxial circular apertures in which the second aperture of smaller diameter is located where the Fresnel number of the first aperture is unity. It is shown that diffraction of a de Broglie matter wave by a system of two pinholes on an optical axis exhibits the multifocal focusing effect of matter waves in the near-field (Fresnel) zone, which creates a very intense, spatially localized beam of atoms. Theoretical predictions for the focusing efficiency of a neutral atomic beam by the diffractive lens are as follows. The spot diameter is ~0.1 µm, the ratio of focal and incident intensities is ~15, the focal length of the diffractive lens is in the range ~0.13 to 6 cm, the focusing depth is in the range ~15 to 30 cm, and the energy transmitting efficiency is ~30 %. For the relatively large diameters of the pinholes, 5.0 µm, the proposed configuration acts as a matter-wave lens with a large focal length and a long focusing depth.
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.
Diffraction of a de Broglie matter wave by a system of two pinholes on an optical axis exhibits the multifocal focusing effect of matter waves in the near-field (Fresnel zone). The focusing, defocusing and refocusing phenomenon results from periodic phase changes at singular points, which are observed for the even Fresnel numbers, where the intensity is zero and the phase is undefined. As an on-axis observation point passes through a singular point, the nature of the wave in the neighborhood of the axis changes from that of a diverging wave to that of a converging wave, i.e., the wave refocuses. The amplitudes of the oscillations in the intensity and phase of the de Broglie wave depend on the ratio of the radii of the two apertures in the system. This effect of diffractive multifocal focusing of de Broglie waves can be used for designing a diffractive lens for matter-wave beams.
Since de Broglie’s famous postulation of the wave-nature of material particles and its subsequent experimental verification, it is known that atoms and molecules behave like waves on a small scale. The investigation of matter waves is a fundamental topic in quantum mechanics. Furthermore, matter waves have many applications in a number of scientific fields. For example they are used to investigate materials by studying the diffraction of atoms (Helium Atom Scattering) or electrons (Low-energy electron-diffraction) from the material’s surface. The topic of this thesis has been to make nano-structured optical elements for matter-waves and use them in a number of experiments. A major result of this thesis is the performance of the classical Poisson-spot experiment with neutral matter-waves. The Poisson-spot refers to the bright interference spot observed in the shadow of a circular obstacle. The experiment gave convincing evidence of the wave nature of light at the beginning of the 19th century. The first two articles (A&B) in this thesis are concerned with the Poisson-spot experiment for matter waves and its applications. The experiment was performed using low-energy deuterium molecules (normal D2, 23.5 meV), which is described in the first article. In the second article the feasibility of using the Poisson-spot experiment to demonstrate the wave-nature of large molecules is studied. The wave properties of large molecules are an important topic in current research. The remaining three articles are concerned with Fresnel zone-plates. Fresnel zoneplates are axially symmetric diffraction gratings that can be used to focus waves. Loosely formulated the relationship between Fresnel zone-plates and the circular object in the Poissonspot experiment is the same as the relationship between multiple-slit gratings and a single straight edge. Paper C studies the application of microscopy with neutral atoms and molecules and the limitations of focusing matter waves with zone plates. The fabrication of the nanostructured free-standing zone-plates using electron-beam lithography is the topic of paper D. A second, new application of Fresnel zone-plates is introduced in paper E: There a zone plate is used for a direct size measurement of the so-called virtual source in a supersonic expansion. The main-result from the Poisson-spot experiment was the observation of the Poisson spot with a molecular-deuterium beam and the successful comparison of the collected experimental data with Fresnel-diffraction theory. The wave-length independence of the on-axis interferencecondition in the Poisson-spot experiment and the weak constraints on angular alignment and position of the circular object led us to conclude that the Poisson spot is a good candidate for demonstrating the wave nature of larger molecules. This idea is studied further in paper B, where among other things the feasibility of a Poissonspot experiment with the fullerene molecule C70 is examined. The main conclusion from this article was that the wave-nature of a molecular-beam can be demonstrated in diffraction experiments with circular discs that have varying amount of intended edge-corrugation. This is because the dependence of the bright spot on the edge-corrugation in the particle-model is different than in the wave-model. The result for the C70 Poisson-spot was that the experiment would be very challenging with count rates as low as 10−4 s−1. However, one possibility would be, due to the simplicity of the setup, to parallelize the experiment and measure the diffraction pattern behind many circular discs at once. This could be realized using the fabrication techniques discussed in chapter 4. Other applications of the Poisson spot could include the study of the Casmir-Polder potential, molecule-lithography and diffraction experiments with atom-lasers from Bose-Einstein condensates. While Fresnel zone-plates can be used to focus any type of wave they suffer from strong chromatic aberration since their focal length is inversely proportional to wavelength. In the case of neutral atom and molecule focusing this is what limits resolution. Paper C presents the highest resolution helium transmission-images hitherto and results from the first focusing of molecular deuterium with a zone plate. In addition the paper discusses the resolution-limit and finds that with presently available techniques a minimal spot size of 300 nm full-width-athalf- maximum is feasible using a zone plate of 200 μm diameter and a beam with speed ratio of about 500. The Fresnel zone-plates used to focus the supersonic-expansion beams need to be freestanding, since the low-energy atoms and molecules do not penetrate any material. In paper D an electron-beam lithography fabrication-process for free-standing zone-plates is presented. The process uses a 200-nm-thin layer of low-stress silicon-nitride for the material of the zone plates. The fabricated zone plates were tested in the supersonic-expansion beam apparatus. The transmission and first-order diffraction-efficiency are close to the theoretical prediction for the smaller 190 μm-diameter zone plates patterned with a single electron-beam write-field. A reduction to 70 % for the 388-μm-diameter zone-plate was observed which was attributed to stitching errors since it was stitched together from four write-fields. In chapter 4 additional unpublished results are presented on spatial-phase-locked electron-beam lithography, which aims at the reduction of stitching errors and other pattern-placement errors in electron-beam lithography. Finally in paper E one of the fabricated zone plates in addition to a previously existing one is used to measure the virtual source-width of a molecular deuterium supersonic-expansion beam. The virtual source-width is a measure of the beam’s temperature perpendicular to the beam axis. The beam’s energy distribution along the beam axis is measured using the timeof- flight method. Data sets for source temperatures T0=310 K and T0=106 K were collected in the stagnation pressure ranges p0=3-171 bar and p0=3-131 bar, respectively. The measured parameters were compared to a simple model of the expansion which explicitly includes the coupling between translational and rotational degrees of freedom. The data generally corresponded very well to the model, except for the virtual source size which was systematically about 2/3 of the model’s prediction. For the cold source-conditions the beam is increasingly heated due to condensation effects at increasing pressures, which results in a clear deviation from the model. This could be used to estimate the fraction of condensed molecules in the beam.