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

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 ( V e 0). 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 V e 0 on transmission properties, fringe pattern, motion of the peaks, and wave number distribution in the diffracted wave has been studied. It is found that V e 0 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 T c can be tuned by V e 0. It is observed that the number of peaks, their relative intensity, and quantization of lateral wavenumber depend upon V e 0. This study will be helpful in optimizing the parameters for material grating-based matter–wave interferometers employing charged particle such as proton beams.