We have developed a nozzle source that delivers a continuous beam of atomic helium or molecular hydrogen having a high degree of transverse coherence and with adequate optical brightness to enable new kinds of experiments. Using this source we have measured single slit diffraction patterns and the first ever speckle-diffraction patterns using atomic and molecular de Broglie waves. Our results suggest fruitful application of coherent matter beams in dynamic scattering and diffractive imaging at short wavelength and with extreme surface sensitivity.
We have developed a nozzle source that delivers a continuous beam of atomic helium or molecular hydrogen having a high degree of transverse coherence and with adequate optical brightness to enable new kinds of experiments. Using this source we have measured single slit diffraction patterns and the first ever speckle-diffraction patterns using atomic and molecular de Broglie waves. Our results suggest fruitful application of coherent matter beams in dynamic scattering and diffractive imaging at short wavelength and with extreme surface sensitivity.
Abstract When Otto Stern embarked on molecular-beam experiments in his new lab at Hamburg University a century ago, one of his interests was to demonstrate the wave-nature of atoms and molecules that had been predicted shortly before by Louis de Broglie. As the effects of diffraction and interference provide conclusive evidence for wave-type behavior, Otto Stern and his coworkers conceived two matter-wave diffraction experiments employing their innovative molecular-beam method. The first concept assumed the molecular ray to coherently scatter off a plane ruled grating at grazing incidence conditions, while the second one was based on the coherent scattering from a cleaved crystal surface. The latter concept allowed Stern and his associates to demonstrate the wave behavior of atoms and molecules and to validate de Broglie’s formula. The former experiment, however, fell short of providing evidence for diffraction of matter waves. It was not until 2007 that the grating diffraction experiment was retried with a modern molecular-beam apparatus. Fully resolved matter-wave diffraction patterns were observed, confirming the viability of Otto Stern’s experimental concept. The correct explanation of the experiment accounts for quantum reflection, another wave effect incompatible with the particle picture, which was not foreseen by Stern and his contemporaries.
We describe the state of the art in preparing, manipulating and detecting coherent molecular matter. We focus on experimental methods for handling the quantum motion of compound systems from diatomic molecules to clusters or biomolecules.Molecular quantum optics offers many challenges and innovative prospects: already the combination of two atoms into one molecule takes several well-established methods from atomic physics, such as for instance laser cooling, to their limits. The enormous internal complexity that arises when hundreds or thousands of atoms are bound in a single organic molecule, cluster or nanocrystal provides a richness that can only be tackled by combining methods from atomic physics, chemistry, cluster physics, nanotechnology and the life sciences.We review various molecular beam sources and their suitability for matter-wave experiments. We discuss numerous molecular detection schemes and give an overview over diffraction and interference experiments that have already been performed with molecules or clusters.Applications of de Broglie studies with composite systems range from fundamental tests of physics up to quantum-enhanced metrology in physical chemistry, biophysics and the surface sciences.Nanoparticle quantum optics is a growing field, which will intrigue researchers still for many years to come. This review can, therefore, only be a snapshot of a very dynamical process.
We have measured the diffraction of metastable helium atoms by a transmission grating with a period of 500 nm. The atomic beam is derived from a supersonic nozzle by adiabatic gas expansion with a velocity ratio v/Δv 20; with the nozzle cooled to liquid nitrogen temperature, the corresponding de Broglie wave length of the helium atoms is 1.08 Å. We have observed diffraction peaks up to the third order with a good signal-to-noise ratio. The position and the height of the different orders are in satisfactory agreement with the measured grating shape and the mean velocity in the atomic beam. As was pointed out previously, such transmission gratings offer one way to realize an atom-wave interferometer.1 In this context, our results demonstrate that an efficient diffraction can also be obtained with excited-state atoms: Here the use of metastable rare-gas atoms is of special interest because they are easy to handle and can be detected on almost zero background. As an alternative to the use of transmission gratings in matter-wave interferometry, we also discuss a simple double-slit arrangement that may provide another approach to the study of atomic interference phenomena.
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.
Since de Broglie's work on the wave nature of particles, various optical phenomena have been observed with matter waves of atoms and molecules. However, the analogy between classical and atom/molecule optics is not exact because of different dispersion relations. In addition, according to de Broglie's formula, different combinations of particle mass and velocity can give the same de Broglie wavelength. As a result, even for identical wavelengths, different molecular properties such as electric polarizabilities, Casimir-Polder forces, and dissociation energies modify (and potentially suppress) the resulting matter-wave optical phenomena such as diffraction intensities or interference effects. We report on the universal behavior observed in matter-wave diffraction of He atoms and He2 and D2 molecules from a ruled grating. Clear evidence for emerging beam resonances is observed in the diffraction patterns, which are quantitatively the same for all three particles and only depend on the de Broglie wavelength. A model, combining secondary scattering and quantum reflection, permits us to trace the observed universal behavior back to the peculiar principles of quantum reflection.
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.