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Journal of Physics Conference Series

Role of wavefront and velocity distribution with magnetic lens on matter-wave diffraction in near-field regime

K. Wongrach, J Janpoon, Sarayut Deachapunya, Sorakrai Srisuphaphon

Published Jan 1, 2021• 0 citations
Publisher

Abstract

Abstract Near-field diffraction has been widely studied and applied in many research fields including optics, quantum mechanics and sensor technology. High accuracy sensors, for instance, have been developed based on the Talbot effect, i.e., the self-imaging effect, due to the high sensitivity of the near-field diffraction pattern. Since the visibility of the diffraction pattern depends intensively on velocity distribution and wavefront of the incoming wave, the Talbot-Lau effect is generally used to improve the spatial coherence of the incident wave and hence a better fringe contrast. This research aims to investigate the influences of the wavefront spreading out radially involving the Gaussian velocity distribution on the diffraction pattern of a matter-wave which are key points in design optimization and development of tools for improving fringe quality. The probability density to find the particles in the Talbot-Lau interference pattern can be obtained by employing Feynman path integrals. The theoretical simulation results show that the alteration of wavefront leads to changes in fringe contrast and the width of fringe peaks, whereas the velocity distribution affects only the fringe visibility.

DOI
10.1088/1742-6596/1719/1/012022

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Abstract Near-field diffraction has been widely studied and applied in many research fields including optics, quantum mechanics and sensor technology. High accuracy sensors, for instance, have been developed based on the Talbot effect, i.e., the self-imaging effect, due to the high sensitivity of the near-field diffraction pattern. Since the visibility of the diffraction pattern depends intensively on velocity distribution and wavefront of the incoming wave, the Talbot-Lau effect is generally used to improve the spatial coherence of the incident wave and hence a better fringe contrast. This research aims to investigate the influences of the wavefront spreading out radially involving the Gaussian velocity distribution on the diffraction pattern of a matter-wave which are key points in design optimization and development of tools for improving fringe quality. The probability density to find the particles in the Talbot-Lau interference pattern can be obtained by employing Feynman path integrals. The theoretical simulation results show that the alteration of wavefront leads to changes in fringe contrast and the width of fringe peaks, whereas the velocity distribution affects only the fringe visibility.
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 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.
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.
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\Delta E_0 = 0.1ΔE0​=0.1?> Δ E 0 = 0.1 V m−1) and its orientation ( <?CDATA Δθ=0.1∘\Delta \theta = 0.1^{\circ}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′\lambda^{\prime}λ′?> λ ′ ) is equal to the de Broglie wavelength ( <?CDATA λdB\lambda_\mathrm{dB}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.
Talbot effect in the space-time evolution of matter waves is analyzed and shown that the matter waves at relativistic and non-relativistic velocities exhibit coherence beyond the grating and display Talbot self-imaging. The grating is realized by considering equidistant narrowly peaked coherent probability distributions at the onset. Theoretical frame work is based on a quantum particle at relativistic and non-relativistic velocities in a one dimensional box. The matter waves, in their evolution, display Talbot self-imaging and fractional self-imaging as restructuring, respectively, at Talbot length and fractional Talbot lengths.
Nearly two centuries ago Talbot first observed the fascinating effect whereby light propagating through a periodic structure generates a ‘carpet’ of image revivals in the near field. Here we report the first observation of the spatial Talbot effect for light interacting with periodic Bose-Einstein condensate interference fringes. The Talbot effect can lead to dramatic loss of fringe visibility in images, degrading precision interferometry, however we demonstrate how the effect can also be used as a tool to enhance visibility, as well as extend the useful focal range of matter wave detection systems by orders of magnitude. We show that negative optical densities arise from matter-wave induced lensing of detuned imaging light – yielding Talbot-enhanced single-shot interference visibility of > 135% compared to the ideal visibility for resonant light.