|dc.identifier.isbn||978-82-308-1833-6 (print version)||eng
|dc.description.abstract||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
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
|dc.publisher||The University of Bergen||eng
|dc.relation.haspart||Paper A: Poisson’s spot with molecules. T. Reisinger, A. A. Patel, H. Reingruber, K. Fladischer, W. E. Ernst, G. Bracco, H. I. Smith, and B. Holst. Phys. Rev. A, 79(5):053823, 2009. Nature Research Highlights 459, 7246 p.486 (2009). <a href="http://hdl.handle.net/1956/5037" target="blank">http://hdl.handle.net/1956/5037</a>||eng
|dc.relation.haspart||Paper B: Particle-wave discrimination in poisson spot experiments. T. Reisinger, G. Bracco, and B. Holst. New Journal of Physics, 13(6):065016, 2011. <a href="http://hdl.handle.net/1956/5036" target="blank">http://hdl.handle.net/1956/5036</a>||eng
|dc.relation.haspart||Paper C: Neutral atom and molecule focusing using a Fresnel zone plate. T. Reisinger and B. Holst. Journal of Vacuum Science and Technology B, 26:2374–2379 , 2008. <a href="http://hdl.handle.net/1956/5038" target="blank">http://hdl.handle.net/1956/5038</a>||eng
|dc.relation.haspart||Paper D: Free-standing silicon-nitride zoneplates for neutral-helium microscopy. T. Reisinger, S. Eder, M. M. Greve, H. I. Smith, and B. Holst. Microelectronic Engineering, 87(5-8): 1011 – 1014, 2010. Full-text not available in BORA due to publisher restrictions. The published version is available at: <a href="http://dx.doi.org/10.1016/j.mee.2009.11.107" "target="blank">http://dx.doi.org/10.1016/j.mee.2009.11.107</a>||eng
|dc.relation.haspart||Paper E: Virtual-source size of a supersonic-expansion deuterium (D2) beam. T. Reisinger, M. M. Greve, S. Eder, G. Bracco, B. Holst. Full text not available in BORA||eng
|dc.title||Free-standing, axially-symmetric diffraction gratings for neutral matter-waves: experiments and fabrication||eng
|dc.subject.nsi||VDP::Mathematics and natural science: 400::Physics: 430||eng
|dc.rights.holder||Copyright the author. All rights reserved||