Diffraction in Time: An Exactly Solvable Model

TL;DR

This paper introduces an exactly solvable quantum model for diffraction in time, describing how matter waves evolve with a time-dependent absorbing barrier, enabling precise analysis of diffraction and interference phenomena.

Contribution

It presents a new, versatile model for diffraction in time with arbitrary initial states and aperture functions, advancing the theoretical understanding of matter-wave interference.

Findings

Provides exact solutions for time evolution with a time-dependent barrier

Enables quantitative analysis of diffraction and interference patterns

Facilitates design of new atom and molecule diffraction experiments

Abstract

In the recent years, mater-wave interferometry has attracted growing attention due to its unique suitability for high-precision measurements and study of fundamental aspects of quantum theory. Diffraction and interference of matter waves can be observed not only at a spatial aperture (such as a screen edge, slit, or grating), but also at a time-domain aperture (such as an absorbing barrier, or "shutter", that is being periodically switched on and off). The wave phenomenon of the latter type is commonly referred to as "diffraction in time". Here, we introduce a versatile, exactly solvable model of diffraction in time. It describes time-evolution of an arbitrary initial quantum state in the presence of a time-dependent absorbing barrier, governed by an arbitrary aperture function. Our results enable a quantitative description of diffraction and interference patterns in a large variety of setups, and may be used to devise new diffraction and interference experiments with atoms and molecules.