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arXiv:0804.3006 · Physical Review A

Theory of near-field matter-wave interference beyond the eikonal approximation

Stefan Nimmrichter, Klaus Hornberger

Published Aug 6, 2008• 46 citations
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Abstract

A generalized description of Talbot-Lau interference with matter waves is presented, which accounts for arbitrary grating interactions and realistic beam characteristics. The dispersion interaction between the beam particles and the optical elements strongly influences the interference pattern in this near-field effect, and it is known to dominate the fringe visibility if increasingly massive and complex particles are used. We provide a general description of the grating interaction process by combining semiclassical scattering theory with a phase space formulation. It serves to systematically improve the eikonal approximation used so far, and to assess its regime of validity.

DOI
10.1103/physreva.78.023612

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A generalized description of Talbot-Lau interference with matter waves is presented, which accounts for arbitrary grating interactions and realistic beam characteristics. The dispersion interaction between the beam particles and the optical elements strongly influences the interference pattern in this near-field effect, and it is known to dominate the fringe visibility if increasingly massive and complex particles are used. We provide a general description of the grating interaction process by combining semiclassical scattering theory with a phase space formulation. It serves to systematically improve the eikonal approximation used so far, and to assess its regime of validity.
We present a theoretical framework to describe the effects of decoherence on matter waves in Talbot-Lau interferometry. Using a Wigner description of the stationary beam the loss of interference contrast can be calculated in closed form. The formulation includes both the decohering coupling to the environment and the coherent interaction with the grating walls. It facilitates the quantitative distinction of genuine quantum interference from the expectations of classical mechanics. We provide realistic microscopic descriptions of the experimentally relevant interactions in terms of the bulk properties of the particles and show that the treatment is equivalent to solving the corresponding master equation in paraxial approximation.
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.
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.
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.
We discuss modern developments in quantum optics with organic molecules, clusters and nanoparticles -- in particular recent realizations of near-field matter-wave interferometry. A unified theoretical description in phase space allows us to describe quantum interferometry in position space and in the time domain on an equal footing. In order to establish matter-wave interferometers as a universal tool, which can accept and address a variety of nanoparticles, we elaborate on new quantum optical elements, such as diffraction gratings made of matter and light, as well as their absorptive and dispersive interaction with complex materials. We present Talbot-Lau interferometry (TLI), the Kapitza-Dirac-Talbot-Lau interferometer (KDTLI) and interferometry with pulsed optical gratings (OTIMA) as the most advanced devices to study the quantum wave nature of composite matter. These experiments define the current mass and complexity record in interferometric explorations of quantum macroscopicity and they open new avenues to quantum assisted metrology with applications in physical chemistry and biomolecular physics.
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.