Comparison between two models of absorption of matter waves by a thin time-dependent barrier

TL;DR

This paper compares two theoretical models of matter wave absorption by a thin, time-dependent barrier, demonstrating their agreement in a semiclassical regime relevant to ultracold atom experiments.

Contribution

It provides a detailed analytical and numerical comparison of two models of matter wave absorption, linking boundary condition approaches with delta-potential models.

Findings

Models agree in semiclassical regime

Analytical and numerical methods used

Applicable to ultracold atom experiments

Abstract

We report a quantitative, analytical and numerical, comparison between two models of the interaction of a non-relativistic quantum particle with a thin time-dependent absorbing barrier. The first model represents the barrier by a set of time-dependent discontinuous matching conditions, which are closely related to Kottler boundary conditions used in stationary wave optics as a mathematical basis for Kirchhoff diffraction theory. The second model mimics the absorbing barrier with an off-diagonal $\delta$-potential with a time-dependent amplitude. We show that the two models of absorption agree in their predictions in a semiclassical regime -- the regime readily accessible in modern experiments with ultracold atoms.