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Molecule interference in the near-field Talbot regime

Carola Szewc

Published Sep 1, 2012• 0 citations

Abstract

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.

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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.

The Talbot-Lau interferometer is a proven tool to perform measurements in the near-field regime. It has been extensively used for investigating the wave nature of electrons, atoms, and complex organic molecules. However, when designing devices with high geometrical acceptances, which would be desirable when dealing with low-intensity sources of particles, the alignment requirements become much more stringent. Furthermore, if the particles are charged, the influence of external fields becomes quickly non-negligible when increasing the length of the device. This paper focuses on both the geometric and physical constraints of an ion Talbot-Lau interferometer, with emphasis on the scaling of such constraints with the size of the device. Mathematical formulas which set limits on the critical parameters are derived and applied to a test setup for protons.

We demonstrate a near-field Talbot-Lau interferometer for C70 fullerene molecules. Such interferometers are particularly suitable for larger masses. Using three free-standing gold gratings of 1 microm period and a transversally incoherent but velocity-selected molecular beam, we achieve an interference fringe visibility of 40% with high count rate. Both the high visibility and its velocity dependence are in good agreement with a quantum simulation that takes into account the van der Waals interaction of the molecules with the gratings and are in striking contrast to a classical moiré model.

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 study the theory behind a Talbot–Lau interferometer. This consists of three gratings in each other's Fresnel near field and accepts spatially incoherent illumination. Our formalism gives a clear physical picture and permits efficient numerical simulations. We concentrate on the case of matter waves and provide an adequate description of recent fullerene experiments taking into account the Casimir–Polder interaction between a molecular beam and mechanical gratings. For more massive molecules, the influence of this interaction is more drastic and leads to a forbiddingly narrow velocity distribution requirement for future experiments with very massive molecules. This problem can be avoided by configurations where at least one mechanical grating is replaced with an optical grating, i.e. a standing light wave. Such interferometers show improved scaling behaviour. Magnifying or demagnifying interferometer variants are also discussed.

We report on the theoretical investigation of Wigner distribution function (WDF) reconstruction of the motional quantum state of large molecules in de Broglie interference. De Broglie interference of fullerenes and as the like already proves the wavelike behaviour of these heavy particles, while we aim to extract more quantitative information about the superposition quantum state in motion. We simulate the reconstruction of the WDF numerically based on an analytic probability distribution and investigate its properties by variation of parameters, which are relevant for the experiment. Even though the WDF described in the near-field experiment cannot be reconstructed completely, we observe negativity even in the partially reconstructed WDF. We further consider incoherent factors to simulate the experimental situation such as a finite number of slits, collimation, and particle-slit van der Waals interaction. From this we find experimental conditions to reconstruct the WDF from Talbot interference fringes in molecule Talbot-Lau interferometry.

We study

{\mathrm{C}}_{70}

fullerene matter waves in a Talbot-Lau interferometer as a function of their temperature. While the ideal fringe visibility is observed at moderate molecular temperatures, we find a gradual degradation of the interference contrast if the molecules are heated before entering the interferometer. A method is developed to assess the distribution of the microcanonical temperatures of the molecules in free flight. This way the heating-dependent reduction of interference contrast can be compared with the predictions of quantum theory. We find that the observed loss of coherence agrees quantitatively with the expected decoherence rate due to the thermal radiation emitted by the hot molecules.