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New Journal of Physics

From classical xenon fringes to hydrogen interferometry

Simon R Müller, P. Nédélec, Markus K. Oberthaler

Published Jun 11, 2020• 6 citations
Publisher

Abstract

Abstract A setup with three equally spaced transmission gratings can be described as a moiré deflectometer in the classical regime and as a Talbot–Lau interferometer in the quantum regime. We successfully operate such a three-grating device with a de Broglie wavelength span of more than two orders of magnitude (20 fm to 2.2 pm), employing different particles such as xenon, krypton, argon, helium, and hydrogen. With that we directly observe the transition from the classical description with fast xenon atoms, to the characteristic quantum behaviour of the Talbot–Lau interferometer using hydrogen atoms with correspondingly long de Broglie wavelength. The systematic study of the interference pattern gives important insights in the feasibility of a proton or antiproton interferometer with this setup.

DOI
10.1088/1367-2630/ab9bc1

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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Dec 12, 1994•0 citations
Abstract A setup with three equally spaced transmission gratings can be described as a moiré deflectometer in the classical regime and as a Talbot–Lau interferometer in the quantum regime. We successfully operate such a three-grating device with a de Broglie wavelength span of more than two orders of magnitude (20 fm to 2.2 pm), employing different particles such as xenon, krypton, argon, helium, and hydrogen. With that we directly observe the transition from the classical description with fast xenon atoms, to the characteristic quantum behaviour of the Talbot–Lau interferometer using hydrogen atoms with correspondingly long de Broglie wavelength. The systematic study of the interference pattern gives important insights in the feasibility of a proton or antiproton interferometer with this setup.
We study in detail a peculiar configuration of the Talbot-Lau matter wave interferometer, characterized by unequal distances between the two diffraction gratings and the observation plane. We refer to this apparatus as the ``asymmetric Talbot-Lau setup.'' Particular attention is given to its capabilities as an inertial sensor for particle and atomic beams, also in comparison with the classical moir\'e deflectometer. The present paper is motivated by possible experimental applications in the context of antimatter wave interferometry, including the measurement of the gravitational acceleration of antimatter particles. Therefore we focus our analysis on the current state of the art. To support our findings, we have also performed numerical simulations of realistic particle beams with varying speed distributions.
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.
In 1924 Louis de Broglie introduced the concept of wave-particle duality: the Planck constant hhh relates the momentum ppp of a massive particle to its de Broglie wavelength λ=h/pλ=h/pλ=h/p. The superposition principle is one of the main postulates of quantum mechanics; diffraction and interference phenomena are therefore predicted and have been observed on objects of increasing complexity, from electrons to neutrons and molecules. Beyond the early electron diffraction experiments, the demonstration of single-electron double-slit-like interference was a highly sought-after result. Initially proposed by Richard Feynman as a thought experiment it was finally carried out in 1976. A few years later, positron diffraction was first observed. However, an analog of the double-slit experiment has not been performed to date on any system containing antimatter. Here we present the first observation of matter wave interference of single positrons, by using a period-magnifying Talbot-Lau interferometer based on material diffraction gratings. Individual positrons in the 8-14 keV energy range from a monochromatic beam were detected by high-resolution nuclear emulsions. The observed energy dependence of fringe contrast proves the quantum-mechanical origin of the detected periodic pattern and excludes classical projective effects. Talbot-Lau interferometers are well-suited to the experimental challenges posed by low intensity antimatter beams and represent a promising option for measuring the gravitational acceleration of neutral antimatter.
A dc hot thermal and an ac-modulated cold slow potassium beam copropagate and pass through an atom de Broglie--wave interferometer, consisting of a sequence of three microfabricated diffraction gratings. Talbot-vonLau interference fringes are formed and sensed by measuring transmission with a hot wire as a function of grating position. The hot beam produces diffraction-limited shadow Moir\'e fringes, while the longer de Broglie wavelength slow beam produces interference fringes with high visibility at the fifth and sixth spatial harmonics of the shadow Moir\'e fringes.
Although interferometry's earliest and most familiar use is with photons, the discovery of matter-wave (deBroglie-wave) interference for electrons demanded the development of quantum mechanics. Since then, matter-wave interferometry has been performed with neutrons, Cooper electron-pairs, and most recently, with whole atoms and diatomic molecules. This talk describes our recent high-flux atom interferometry experiments using the generalized Talbot-vonLau effect. Our interferometer consists of a sequence of three planar vacuum-slit diffraction gratings, microfabricated from silicon nitride membranes. DeBroglie-wave interference fringes are sensed by measuring the transmission of potassium atoms on a hot- wire as a function of grating relative position. Different spatial Fourier components (up to sixth) in the diffraction pattern are resonant in the interferometer at different atomic velocities (i.e., at different wavelengths). When a laser cooled slow atomic beam is incident, various different diffraction patterns are observed as a function of atomic velocity. In an alternative `Heisenberg Microscope' configuration an incident thermal beam produces a velocity average over different fringe Fourier components. AC modulated weak laser light passing through the interferometer interacts selectively with atoms at a specific velocity. The associated fringe pattern is then ac modulated and revealed by its selective destruction.