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Journal of Physics Conference Series

A study of matter-wave diffraction for particle in the near field regime under the influence of a uniform electric field

C Artyotha, Sarayut Deachapunya, Boonlit Krunavakarn, N Kheaomaingam, Sorakrai Srisuphaphon

Published Dec 1, 2018• 1 citation
Publisher

Abstract

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.

DOI
10.1088/1742-6596/1144/1/012053

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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.
Paths of particles, emitted from distributed sources and passing out through slits of two gratings, G0G_{0}G0​ and G1G_{1}G1​, up to detectors, have been computed in details by the path integral method. The slits are represented by Gaussian functions that simulate fuzzy edges of the slits. Waves of matter be computed by this method show perfect interference patterns both between the gratings and behind the second grating. Coherent and noncoherent the distributed particle sources reproducing the interference patterns are discussed in details. Paraxial approximation stems from the wave function when removing the distributed sources onto infinity. The more hard-edged slits of the grating G1G_{1}G1​ are examined by simulating those slits by a superposition of more hard the Gaussian functions. As for the particles here we consider fullerene molecules. De Broglie wavelength of the molecules is adopted equal to 5 pm.
We discuss new de Broglie coherence experiments in a near-field molecule interferometer with a variety of large organic molecules. While de Broglie coherence is to first order only associated with the center-of-mass motion of the diffracted particle, we here investigate the question as to which extent the internal molecular property is relevant for, compatible with or detrimental for maintaining coherence in the translational degree of freedom. External perturbations, such as inhomogeneous external electric fields, may influence the delocalized molecules inside the matter wave interferometer and they allow us to access the molecular polarizabilities, permanent or even fluctuating electric dipole moments. We extract information about the molecular states from the interference phase shifts as well as from the observed dephasing in a Kapitza-Dirac Talbot-Lau-Stark-deflectometer. We discuss the relevance of our experiments with regard to both molecule metrology and the foundations of quantum mechanics, i.e. the preservation of coherence for highly complex particles in external fields.
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.
Particle paths, emitted from distributed sources and passing out through slits of two gratings, G0 and G1, up to detectors, have been computed in detail by the path integral method. The particles under consideration are fullerene molecules with a De Broglie wavelength equal to 5 pm. The slits are Gaussian functions that simulate fuzzy edges of the slits. Waves of the matter computed by this method show perfect interference patterns both between the gratings and behind the second grating. Coherent and non-coherent distributed particle sources reproducing the interference patterns are discussed in detail. Paraxial approximation results from removing the distributed sources onto innity. This approximation gives a wave function reproducing an exact copy of the Talbot carpet. PACS numbers: 03.75.-b, 03.75.Dg, 42.25.Hz
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