A unified quantum random walk model for internal crystal effects in dynamical diffraction

TL;DR

This paper introduces a comprehensive quantum random walk model for dynamical diffraction in crystals, capable of simulating various internal effects and imperfections to aid in designing advanced neutron optical devices.

Contribution

The authors develop a unified quantum random walk model that accurately reproduces all known dynamical diffraction effects, including complex internal crystal phenomena.

Findings

Model reproduces effects like temperature gradients and Talbot effect.

Demonstrates agreement with experimental data for ideal and imperfect crystals.

Provides a flexible framework for designing neutron interferometers.

Abstract

The theory of dynamical diffraction (DD) in perfect crystals is the backbone of high-precision neutron and X-ray diffraction experiments, enabling accurate determination of crystal structure factors and the realization of perfect crystal interferometers. In practice, however, real crystals exhibit deformations and imperfections, including surface roughness, defects, temperature gradients, angled crystal faces, and curvature, that degrade interferometer performance and are difficult to model using conventional DD theory, particularly in complex geometries. To address these challenges, a quantum information (QI) model for DD has been under development, with demonstrated experimental agreement for both ideal crystals and in the presence of some imperfections such as surface roughness and defects. Here, we present a unified quantum random walk model that is now suitable for reproducing all established DD effects. We demonstrate this by incorporating a broad range of internal crystal effects influencing DD intensity distributions, including linear temperature gradients, the DD Talbot effect, and angled or miscut crystals. These results establish the QI model as a comprehensive and flexible framework for experimental analysis, as well as for the design of next-generation perfect crystal neutron interferometers and neutron optical components, such as condensing monochromators.