Quantum Reflection Effects in the Diffraction of Matter Waves

TL;DR

This paper investigates quantum reflection effects in matter wave diffraction, deriving analytical expressions for reflection points in power-law potentials and demonstrating their application in high-precision potential analysis using atom-surface interactions.

Contribution

It introduces a new measure for the wavefunction's reflection distance and provides an analytical expression for reflection points in arbitrary power-law potentials.

Findings

Reflection rate depends strongly on velocity and interaction duration.

Diffraction of low-velocity Argon atoms enables high-precision potential measurements.

Analytical methods improve understanding of quantum reflection in surface interactions.

Abstract

Among the fundamental quantum effects, quantum reflection (QR) is one of the most notable phenomena. Approximating arbitrary potentials in the Schr\"odinger equation as multistep potentials allows us to determine the reflection coefficient by means of a Riccati equation. We introduce a measure for the wavefunction'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.