Huygens-Fresnel-Kirchhoff construction for quantum propagators with application to diffraction in space and time

TL;DR

This paper develops a Huygens-Fresnel-Kirchhoff approach to model quantum diffraction of matter waves through openings, capturing space and time effects, and demonstrates its effectiveness with practical diffraction pattern calculations.

Contribution

It introduces a novel quantum propagator expansion based on classical diffraction principles, enabling analysis of diffraction in space and time for matter waves.

Findings

Accurately models quantum diffraction in space and time.

Effectively predicts diffraction patterns for dynamic openings.

Bridges classical wave optics and quantum matter wave phenomena.

Abstract

We address the phenomenon of diffraction of non-relativistic matter waves on openings in absorbing screens. To this end, we expand the full quantum propagator, connecting two points on the opposite sides of the screen, in terms of the free particle propagator and spatio-temporal properties of the opening. Our construction, based on the Huygens-Fresnel principle, describes the quantum phenomena of diffraction in space and diffraction in time, as well as the interplay between the two. We illustrate the method by calculating diffraction patterns for localized wave packets passing through various time-dependent openings in one and two spatial dimensions.