Structured matter wave evolution in external time-dependent fields

TL;DR

This paper investigates the evolution of structured matter waves in external magnetic and time-dependent fields, providing exact propagator kernels and analyzing quantum properties relevant to interferometry and microscopy.

Contribution

It introduces exact propagator kernels for matter wave evolution in external fields, improving upon approximate methods like the axial approximation.

Findings

Derived exact propagator kernels from PDEs based on Heisenberg equations.

Analyzed uncertainties, angular momentum, and inertia tensor of the evolved wave.

Results are more reliable for quantum interferometry and electron microscopy.

Abstract

In the present work, we have analyzed the motion of a structured matter wave in the presence of a constant magnetic field and under the influence of a time-dependent external force. We have introduced exact propagator kernels obtained from partial differential equations based on the Heisenberg equations of motion. The initial wave function is assumed as a Gauss-Hermite wave function. For the evolved wave function, we have obtained and discussed the uncertainties, orbital angular momentum, and the inertia tensor in the center of mass frame of the density function. From the point of view of the quantum interferometry of matter waves, and also non-relativistic quantum electron microscopy, the results obtained here are important and more reliable than the approximate methods like the axial approximation.