Quantum reflection effects in the diffraction of matter waves^(a)

¹ Department of Physics and Technology, University of Bergen - Alléegaten 55, 5007 Bergen, Norway
² Institut für Physik, Universität Kassel - Heinrich-Plett-Str. 40, 34132 Kassel, Germany
³ Universitat de Barcelona - Carrer de Martí i Franquès 1-11, Les Corts, 08028, Barcelona, Spain
⁴ Laboratoire de Physique des Lasers, Université Sorbonne Paris Nord, CNRS UMR 7538 F-93430, Villetaneuse, France

Received: 28 April 2025
Accepted: 3 July 2025

Abstract

Among the fundamental quantum effects, quantum reflection (QR) is one of the most notable phenomena. Approximating arbitrary potentials in the Schrödinger equation as multistep potentials allows us to determine the reflection coefficient by means of a Riccati equation. We introduce a measure for the wave function's characteristic reflection distance and derive an analytical expression for this reflection point in an arbitrary power-law potential. We study the associated QR rate in the context of Casimir-Polder atom surface interactions, revealing its strong dependence on critical parameters such as velocity and interaction duration. As an application, we demonstrate how the matter-wave diffraction of a low-velocity metastable argon beam impinging on a rotated grating facilitates high-precision potential analysis.