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Journal of Applied Physics

Time-domain simulation of charged particle diffraction by an electrostatically biased grating: Transmission tunability and shaping of the quantum point contact for protons

Sushanta Barman, Sudeep Bhattacharjee

Published Jul 19, 2022• 3 citations
Publisher

Abstract

A numerical simulation of a two-dimensional Gaussian wave packet of charged particles has been performed to investigate the diffraction phenomena from a single-, double-, and multi-slit grating biased with an electrostatic potential (Ve0). The wave packet dynamics are obtained by solving the time-dependent Schrödinger’s equation using the generalized finite difference time domain (GFDTD-Q) method for quantum systems. The effect of Ve0 on transmission properties, fringe pattern, motion of the peaks, and wave number distribution in the diffracted wave has been studied. It is found that Ve0 changes the shape of the quantum point contact of diffracting constriction, which controls the allowed quantum states in the diffracted wave and the transmission coefficient Tc can be tuned by Ve0. It is observed that the number of peaks, their relative intensity, and quantization of lateral wavenumber depend upon Ve0. This study will be helpful in optimizing the parameters for material grating-based matter–wave interferometers employing charged particle such as proton beams.

DOI
10.1063/5.0098030

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A numerical simulation of a two-dimensional Gaussian wave packet of charged particles has been performed to investigate the diffraction phenomena from a single-, double-, and multi-slit grating biased with an electrostatic potential (Ve0). The wave packet dynamics are obtained by solving the time-dependent Schrödinger’s equation using the generalized finite difference time domain (GFDTD-Q) method for quantum systems. The effect of Ve0 on transmission properties, fringe pattern, motion of the peaks, and wave number distribution in the diffracted wave has been studied. It is found that Ve0 changes the shape of the quantum point contact of diffracting constriction, which controls the allowed quantum states in the diffracted wave and the transmission coefficient Tc can be tuned by Ve0. It is observed that the number of peaks, their relative intensity, and quantization of lateral wavenumber depend upon Ve0. This study will be helpful in optimizing the parameters for material grating-based matter–wave interferometers employing charged particle such as proton beams.
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We performed time-evolved numerical simulation of a two-dimensional electron wave packet through a quantum point contact using the finite difference method to simulate the diffraction phenomenon of a single electron. We found that the transmitted wave packet has diffracted subpeaks which show the following properties: (1) The traces of diffracted subpeaks start from the center of the slit entrance. (2) Lateral wave number of diffracted subpeaks is quantized. (3) The diffraction angles are determined by slit width and the initial electron wave packet energy. (4) The number of allowed diffracted subpeaks is determined by potential barrier thickness. (5) There is a delay in the motion of diffracted subpeaks due to quantization inside the slit.
The stationary eigenstates and eigenvalues for the ponderomotive potential of an optical crystal confined in a one-dimensional infinite square well are numerically obtained. The initial states of the incoming particles taken as Gaussian, are expanded in the basis of the stationary eigenstates of the ponderomotive potential, to obtain the subsequent time evolution of the wave function of the particle during the interaction with the optical crystal. From the results of the time evolution of the probability density, it is observed that the particles get localized at equidistant positions in the transverse direction, which results in the diffraction pattern. The temporal evolution of the diffraction pattern is analyzed. As an application, the diffraction of proton beams is studied, where the experimental parameters are optimized to observe the diffraction pattern for a microwave plasma-based proton beam system. The observations are important for design of proton based matter-wave interferometers.
We performed time-evolved numerical simulation of a two-dimensional electron wave packet through a double slit by solving the time-dependent Schrödinger equation using the finite difference method to simulate the electron interference phenomenon of a single electron. The propagating directions of interference peaks show that the starting point of electron interference is the center between the two slit exits. The number of interference peaks and their angles are found to be independent of potential barrier thickness. These results are compared with the results of our previous calculation of electron diffraction through a single slit.
Abstract The goal of this paper is to study double-slit diffraction at the nanometric scale. We treat the time evolution of a Gaussian wave packet in quantum mechanics traveling until it reaches a double-slit wall. A detailed investigation and analysis of the diffraction phenomenon and its progress is developed by numerically solving the Schrödinger equation. This is written using a potential intended to model the wall. It is solved by using finite differences in the time domain method, so that the probability amplitude, ψ , is obtained as a function of the spatial coordinates at discretized times. Then, the probability density, ρ , is found in a straightforward way and used to plot graphics or make videos. Furthermore, the time evolution of the wave packet is registered at several fixed points to acquire local information. Fourier transforms are calculated to complement the knowledge obtained. Students interested in didactic approaches, or in applications for nanodevices, could find interest in this approach.
We study the quantum slit diffraction problem in three dimensions. In the treatment of diffraction of particles by a slit, it is usually assumed that the motion perpendicular to the slit is classical. Here we take into account the effect of the quantum nature of the motion perpendicular to the slit using the Green function approach [18]. We treat the diffraction of a Gaussian wave packet for general boundary conditions on the shutter. The difference between the standard and our three-dimensional slit diffraction models is analogous to the diffraction in time phenomenon introduced in [16]. We derive corrections to the standard formula for the diffraction pattern, and we point out situations in which this might be observable. In particular, we discuss the diffraction in space and time in the presence of gravity.