Quantum-information approach to dynamical diffraction theory

Abstract

We present a simplified model for dynamical diffraction of particles through a periodic thick perfect crystal based on repeated application of a coherent beam splitting unitary at coarse-grained lattice sites. By demanding translational invariance and a computationally tractable number of sites in the coarse-graining we show how this approach reproduces many results typical of dynamical diffraction theory and experiments. This approach has the benefit of being applicable in the thick, thin, and intermediate crystal regimes. The method is applied to a three-blade neutron interferometer to predict the output beam profiles, interference patterns, and contrast variation.

Generalizing the Quantum Information Model for Dynamic Diffraction

“…It has been shown previously in [25] that propagating a neutron inside a lattice by exciting a single node at the entrance yielded intensity profiles consistent with dynamic diffraction theory, with accuracy for a specific choice of γ depending on the number of layers used in the simulation. Here, we generalize this theory to any value of γ, and show that one has a degree of freedom when choosing a combination of γ and the crystal thickness n. Furthermore, we show that the intensity profiles generated by the model exactly reduce to the spherical wave solutions of the T-T equations, equations 3 and 4, in the appropriate limit.…”

“…In the model developed in [25], a perfect crystal is represented as a two-dimensional lattice of nodes, through which the incident neutron travels column by column. As shown in Fig.…”

“…Nsofini et al [25][26][27] demonstrated that many of the results of dynamical diffraction can be reproduced in the Laue case using a quantum information (QI) model, in which neutrons travel through a quantum Galton board where every peg corresponds to the application of a unitary operator on the neutron state. The intensity profiles predicted by the standard results of dynamical diffraction were reproduced with accuracy depending on the amount of layers used to model the crystal thickness.…”

Coherence optimization in neutron interferometry through defocusing

“…The QI formalism of DD is based on the discretization of the scattering media into coarse-grained units which acts as unitary operators [17]. The action of an NI blade is also a unitary operator expressed as a combination of multiple 2 × 2 unitary operators at coarse-grained sites (nodes).…”

“…Furthermore, we propose an experiment to verify the increase in contrast with the original DFS NI geometry. Our simulations rely on the recently developed quantum information (QI) formalism of dynamical diffraction (DD) which is based on the repeated application of a unitary at coarse-grained site [17]. * jnsofini@uwaterloo.ca This article is organized as follows: In Sec.…”