The development of novel neutron optics devices that rely on perfect crystals and nanoscale features are ushering in a new generation of neutron science experiments, from fundamental physics to material characterization of emerging quantum materials. However, the standard theory of dynamical diffraction (DD) that analyzes neutron propagation through perfect crystals does not consider complex geometries, deformations, and/or imperfections, which are now becoming a relevant systematic effect in high-precision interferometric experiments. In this work, we expand upon a quantum information (QI) model of DD that is based on propagating a particle through a lattice of unitary quantum gates. We show that the model output is mathematically equivalent to the spherical wave solution of the Takagi-Taupin equations when in the appropriate limit, and that the model can be extended to the Bragg as well as the Laue-Bragg geometry where it is consistent with experimental data. The presented results demonstrate the universality of the QI model and its potential for modeling scenarios that are beyond the scope of the standard theory of DD.
The development of novel neutron optics devices that rely on perfect crystals and nanoscale features are ushering in a new generation of neutron science experiments, from fundamental physics to material characterization of emerging quantum materials. However, the standard theory of dynamical diffraction (DD) that analyzes neutron propagation through perfect crystals does not consider complex geometries, deformations, and/or imperfections, which are now becoming a relevant systematic effect in high-precision interferometric experiments. In this work, we expand upon a quantum information (QI) model of DD that is based on propagating a particle through a lattice of unitary quantum gates. We show that the model output is mathematically equivalent to the spherical wave solution of the Takagi-Taupin equations when in the appropriate limit, and that the model can be extended to the Bragg as well as the Laue-Bragg geometry where it is consistent with experimental data. The presented results demonstrate the universality of the QI model and its potential for modeling scenarios that are beyond the scope of the standard theory of DD.
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.
Neutron interferometry with its ability to encode and extract information provides a test \nbed for quantum mechanics and precise measurement of physical quantities of significant \nimportance in physics. However, this significant key investigative technique is weakened \nby its very fragile nature; neutron interferometry has proven to be highly sensitive to \nenvironmental noise. \n \nOnce brought to its optimal state, the use of neutron interferometry enabled with \nquantum information, represents a milestone. Indeed a realization of high-quality neutron \ninterferometry could pave a way to probe materials research such as probing properties \nwater in proteins and topological materials. Thus understanding and solving the sensitivity \nof neutron interferometers to noise is a key step toward possible applications. This is the \ncore of the work done in this Thesis. \n \nWe incorporated two theoretical techniques developed for quantum information sciences \ninto the construction of a new polarized neutron interferometry beam line: The technique \nof quantum error correction and the technique of open quantum system. One focus of this \nwork is to report on the design, the construction as well as the characteristic features of \nthis beamline. \n \nThis thesis involves experimental data, showing how the neutron beam intensity at the \nexit of a three-blade neutron interferometer can be controlled by the interferometer blades \nthickness. Secondly, is also presents an alternative and simplified quantum information \napproach to dynamical diffraction, based on repeated application of a coherent beam- \nsplitting unitary at coarse-grained lattice sites. Demanding translational invariance added \nto a computationally tractable number of sites in the coarse-graining reproduced many \nresults typical of standard dynamical diffraction theory and experiments. Building on that, \na proposal for a new five-blade neutron interferometer is presented and its robustness to \nnoise, resulting from dynamical diffraction together with low-frequency external mechanical \nvibration is discussed. \n \nSteps ahead in our work, neutron interferometry may be improved as well as adapted to \nmore applications by incorporating the spin and orbital degrees of freedom to a path-based \nivinterferometer. In this concern, we propose a method to prepare the spin-orbit state by \npassing a polarized neutron beam through a quadrupole magnetic field. Initially designed \nfor a beam the size of a coherent length, we extend this method to work for spatially \ndisplaced beams by using linear magnetic gradients.
Dynamical diffraction leads to an interesting, unavoidable set of interference effects for neutron interferometers. This experiment studies the interference signal from two and three successive Bragg diffractions in the Laue geometry. We find that intrinsic Bragg-plane misalignment in monolithic, "perfect" silicon neutron interferometers is relevant between successive diffracting crystals, as well as within the Borrmann fan for typical interferometer geometries. We show that the dynamical phase correction employed in the Colella, Overhauser, and Werner gravitationally induced quantum interference experiments is attenuated by slight, intrinsic misalignments between diffracting crystals, potentially explaining the long-standing 1% discrepancy between theory and experiment. This systematic may also impact precision measurements of the silicon structure factor, affecting previous and future measurements of the Debye-Waller factor and neutron-electron scattering length as well as potential fifth-force searches. For the interferometers used in this experiment, Bragg planes of different diffracting crystals were found to be misaligned by 10 to 40 nrad.
Abstract Quantum mechanics is a part of physics where experiment and theory are inseparably intertwined. This general theme permeates the 2nd edition of this book. It discusses more than 40 neutron interferometry experiments along with their theoretical motivations and explanations. The basic ideas and results of interference experiments related to coherence and decoherence of matter waves and certain post-selection variations, gravitationally induced quantum phase shifts, Berry's geometrical phases, spinor symmetry and spin superposition, and Bell's inequalities are all discussed in this book. Both the scalar and vector Aharonov-Bohm topological interference effects and the neutron version of the Sagnac effect are presented in a self-contained and pedagogical way. Interferometry with perfect crystals, artificial lattices, and spin-echo systems are described in some detail. The book includes the theoretical underpinning as well as connections to other areas of experimental physics, such as quantum optics, nuclear physics, gravitation, and atom interferometry. The observed phase shifts due to the Earth's gravity and rotation indicate a close connection to relativity theory. Neutron interferometry can be considered as a central technique of quantum optics with massive particles. It has stimulated the development of interferometry with atoms, molecules, and clusters. Quantum interference experiments with massive particles have direct consequences on the discussion of epistemological questions since they show explicitly the wave-particle duality, and the entanglement and the contextuality of various parameters governing our modern view of nature.
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.
An exciting frontier in quantum information science is the realization and control of complex quantum many-body systems. Hybrid nanophotonic system with cold atoms has emerged as the paradigmatic platform for engineering long-range spin models from the bottom up, exploiting their modal geometry and group dispersion for tailored interactions. An important challenge is the physical limitation imposed by the photonic bath, constraining the types of local Hamiltonians that decompose the available physical models and restricting the spatial dimensions to that of the dielectric media. However, at the nanoscopic scale, atom-field interaction inherently accompanies significant driven-dissipative quantum forces that may be tamed as a new form of a mediator for controlling the atomic internal states. Here, we formulate a quantum optics toolbox for constructing a universal quantum matter with individual atoms in the vicinity of 1D photonic crystal waveguides. The enabling platform synthesizes analog quantum materials of universal 2-local Hamiltonian graphs mediated by phononic superfluids of the trapped atoms. We generalize our microscopic theory of analog universal quantum simulator to the development of dynamical gauge fields. In the spirit of gauge theories, we investigate emergent lattice models for strongly coupled SU(n)-constrained excitations driven by an underlying multi-body interaction. As a minimal model in the infrared, we explore the realization of an archetypical strong coupling quantum field theory, SU(n) Wess-Zumino-Witten model, and discuss a diagnostic tool to extract the entire conformal data of the field theory by the static and dynamical correlators of the fluctuating photons in the guided mode.