Matter-wave near-field interferometric experiments require interference contrast as high as possible in order to extract information from the interference patterns. One of the tasks to accomplish this requirement is to align the distances between gratings and detection. We present here a method for this precision alignment. An electron beam as a matter-wave source, a diffraction grating, and mask grating were used in this study. The simulations show that the longitudinal scanning of the mask grating with the detection can specify the exact location of the near-field or so-called Talbot distance with the condition of using the gratings with small open fractions. Therefore, the various open fractions were done in the calculation. Due to the lack of commercial gratings with small open fractions, a technique of two overlapping gratings can be applied for changing arbitrary grating shapes and open fractions. We conclude that smaller open fraction of the gratings gives better longitudinal alignment. The results show that the Talbot distance is located at the highest throughput behind the gratings. The present study can provide a method for implementing matter-wave diffraction experiments in the future.
Matter-wave near-field interferometric experiments require interference contrast as high as possible in order to extract information from the interference patterns. One of the tasks to accomplish this requirement is to align the distances between gratings and detection. We present here a method for this precision alignment. An electron beam as a matter-wave source, a diffraction grating, and mask grating were used in this study. The simulations show that the longitudinal scanning of the mask grating with the detection can specify the exact location of the near-field or so-called Talbot distance with the condition of using the gratings with small open fractions. Therefore, the various open fractions were done in the calculation. Due to the lack of commercial gratings with small open fractions, a technique of two overlapping gratings can be applied for changing arbitrary grating shapes and open fractions. We conclude that smaller open fraction of the gratings gives better longitudinal alignment. The results show that the Talbot distance is located at the highest throughput behind the gratings. The present study can provide a method for implementing matter-wave diffraction experiments in the future.
This thesis describes theoretical work carried out in connection with the high-mass matter-wave interference experiments at the University of Vienna. Its scope ranges from the simulation and analysis of experimental data to the proposal of a trapped interference scheme applicable to a variety of matter-wave platforms. The first main result of the thesis is the phase-space description of a near-field interferometer with any number of gratings. This theory is used to analyze a four-grating Talbot-Lau interferometer, in which passive compensation of low-frequency vibrations and of the Coriolis force are expected. The compensation is numerically confirmed and its effectiveness is compared to existing techniques. The second main result is the demonstration of Bragg diffraction of complex molecules on optical gratings, to which the author contributed the basic experimental design, simulations, and the interpretation of the data. This demonstration is a first step towards applying large momentum transfer coherent manipulation techniques to the interference of heavy molecules and clusters. The third main result is a new interference scheme for matter waves in toroidal confinement. The beam splitting and recombination in this scheme rely on the free evolution in the waveguide and require no interaction with the matter waves. The scheme is within reach of state-of-the-art experiments with Bose-Einstein condensates, where it could be used to measure weak atom-atom interactions or magnetic field gradients.
We show our progress in setting up a three grating near-field Talbot-Lau interferometer (TLI) for large molecules such as C60. The TLI is the preferred tool for showing the wave nature of large particles, as it accepts beams of poor spatial coherence and because of its scaling properties with increasing mass of the particles. The spatial coherence is prepared by the first grating, it can be seen as an array of many collimation slits. Our setup is highly flexible in terms of the possibility of changing most of the parameters (such as distances between the gratings and grating angles) from the outside of the UHV-chamber. As the interferometer and the molecular beam source are place in separate vacuum chambers, refilling the oven and adjusting the setup parameters to different molecules is possible without opening the interferometer chamber. This is necessary, as the pressure in the interferometer chamber has to be lower than 5.10-7 mbar in order to observe high interference contrast. The TLI is highly sensitive to vibrations, especially in the range of 1 kHz (the inverse time-of-flight of the molecules through the interferometer), which makes vibration damping crucial for the success of observing interference. We observed vibration amplitudes of up to 75 nm at low frequencies (158 Hz). Compared to the inverse time-of-flight of the molecules, these vibrations are not 'seen' by the molecules and are non-critical. We observed interference of C60 with a contrast of 27 %, by scanning the self-image of the diffraction grating. In the present setup, an interference contrast of 60 % should be observed with perfect alignment of the gratings. Time-of-flight measurements showed small modulations of the velocity distribution at for interference expected distances of 2.5 ms. We also show the possibility of reconstructing the Wigner distribution function out of measurements for the case of Talbot interference under experimental conditions.
Remarkable progress can be observed in recent years in the controlled emission, guiding, and detection of coherent, free electrons. Those methods were applied in matter wave interferometers leading to high phase sensitivities and precise sensor technologies for dephasing influences such as mechanical vibrations or electromagnetic frequencies. However, the previous devices have been large laboratory setups. For future sensor applications or tests of the coherence properties of an electron source, small, portable interferometers are required. Here, we demonstrate a compact biprism electron interferometer that can be used for mobile applications. The design was optimized for small dimensions by beam path simulations. The interferometer has a length between the tip and the superposition plane before magnification of only 47 mm and provides electron interference patterns with a contrast up to 42.7%. The detection of two dephasing frequencies at 50 and 150 Hz was demonstrated applying second order correlation and Fourier analysis of the interference data.
For various experiments to investigate quantum effects, matter-wave diffraction is an apparent example. Particle diffractions have been measured even at the large molecular level, such as the C 60 molecules. In order to describe the matter-wave diffraction of C 60 beam, we assume the initial wave functions behind a grating in form of the Fourier series with a Gaussian distribution function. By applying the Feynman path integral, the exact wave functions of the molecule diffraction in the near-field regime can be derived analytically. The obtained probability density distributions are corresponding to interference fringes as found in the Fresnel diffraction. The probability of finding C 60 molecules, behind the grating at the Talbot length, consistency with the mentioned experimental data of C 60 diffractions.
Abstract Self-imaging in near-field diffraction is a practical application of coherent manipulation of matter waves in Talbot interferometry. In this work, near-field diffraction of protons by a nanostructured metallic grating under the influence of (a) uniform, (b) spatially modulated, and (c) temporally modulated electric fields are investigated. Time-domain simulations of two-dimensional Gaussian wave packets for protons are performed by solving the time-dependent Schrödinger’s equation using the generalized finite difference time domain method for quantum systems. Effects of strength (E 0) and orientation (θ) of the uniform electric field on the diffraction properties, such as fringe pattern, intensity of the peaks, fringe shift, and visibility, are investigated. The results show that the Talbot fringes shift significantly in the transverse direction even for a small change in the applied electric field ( <?CDATA ΔE0=0.1?> Δ E 0 = 0.1 V m−1) and its orientation ( <?CDATA Δθ=0.1∘?> Δ θ = 0.1 ∘ ). Moreover, electric field-dependent fringe visibility is observed, which can be tuned by E 0 and θ. The potential barriers arising from a spatially modulated electric field are observed to cause significant distortions in the Talbot patterns when the modulation length ( <?CDATA λ′?> λ ′ ) is equal to the de Broglie wavelength ( <?CDATA λdB?> λ d B ). Sidebands are observed in the Talbot pattern due to the efficient transfer of energy from the oscillating field to the wave packet when the frequency of oscillation (ω) is of the order of ω 0 ( <?CDATA $ = 2\pi/T_0$?> = 2 π / T 0 ), where T 0 is the interaction time. This study will be helpful in uniform electric field-controlled precision metrology, developing a highly sensitive electric field sensor based on Talbot interference, and precisely aligning the matter wave optical setup. Furthermore, the sidebands in the Talbot fringe can be used as a precise tool for momentum splitter in matter wave interferometry.
We examine how partial coherence and wavefront curvature of beams affect interference fringes behind diffraction gratings. We simulate (1) the Talbot effect, (2) far-field diffraction, (3) Mach-Zehnader interferometers, (4) Talbot-Lau interferometers, and (5) Lau interferometers using a numerically efficient expression. We show how interference fringes in each case depend on the beam's initial width, its coherence width (transverse coherence length), and its wavefront curvature in directions both parallel and perpendicular to the grating bars. The separation between gratings and the rotational alignment of the gratings about the optical axis are also considered. The formula used for our simulations is derived using the mutual intensity function of a Gaussian Schell-model beam.