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arXiv:2609.24709

Pendellösung length-scale neutron and X-ray interferometry

Owen Lailey, Alexandre Boutot, David G. Cory, Joseph P. Cotter, Vishal Dhamgaye, Tao Hong, Michael G. Huber, Young-June Kim, Winfried Kockelmann, Jeremy W. Paster, Dusan Sarenac, Kawal Sawhney, Naume Shentevski, Ivar Taminiau, Dmitry A. Pushin

physics.app-phphysics.opticsquant-phSubmitted Sep 21, 2026• Announced Sep 22, 2026
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Abstract

Neutron and X-ray perfect-crystal interferometers (PCIs) are powerful platforms for studies of fundamental physics and phase-contrast imaging. Further enhancing several PCI capabilities requires reducing crystal blade thickness to the micron scale, which minimizes dynamical-diffraction image blur, permits operation in the pendellösung regime where blade thickness controls beam splitting, and reduces absorption for simultaneous neutron and X-ray operation. However, fabricating multiple crystal blades with identical micrometer-scale thicknesses over centimeter-scale areas remains a major challenge. Here, using a non-etching sub-micron fabrication technique, we demonstrate silicon triple-Laue interferometers with equal-blade-thicknesses of 110 $μ$m and 350 $μ$m, operated with both neutrons and X-rays. These devices are the thinnest PCIs realized to date, enabling a factor-of-six reduction in dynamical-diffraction beam spreading for improved phase-contrast imaging, while reaching the single pendellösung length regime in which crystal thickness provides an experimentally accessible control parameter for engineered quantum-optical beam splitting of plane-wave inputs. These results motivate multi-blade PCI designs utilizing identical half-pendellösung crystal lamellae that are proposed for neutron spin--orbit and electric dipole moment measurements.

Related papers

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Coherent control of neutrons via Bragg diffraction forms the foundation of perfect crystal neutron interferometry, facilitating both fundamental tests of quantum mechanics and applications in quantum information science. In cavity geometries, perfect crystals enable neutron confinement and have been employed in precision measurements of spin-orbit interactions and for neutron electric dipole moment (nEDM) searches. However, in these conventional configurations, neutrons undergo a single pass through the crystal geometry, placing a physical constraint on both crystal and in-flight interaction times and measurement sensitivity. In this work, we introduce a neutron loop cavity that coherently recirculates neutrons through repeated Bragg reflections between perfect silicon crystal blades. This structure is predicted to achieve a neutron survival probability of $\sim64~\%$ for 10,000 Bragg reflections, corresponding to confinement times on the order of seconds. We propose a Schwinger interaction measurement that achieves a $π$ spin rotation in 800 Bragg reflections, representing more than a tenfold improvement in sensitivity over recent measurements. Further applications include high-sensitivity nEDM searches targeting the $10^{-27}~$e$\cdot$cm scale, as well as competitive experimental tests of neutron parity violation, the neutron lifetime, and the quantum Zeno effect with neutrons.

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his was one of the conclusions that emerged from the Vienna Symposium on the Foundations of Modern Physics held in June this year.Organised by Anton Zeilinger, ably assisted by Markus Aspelmeyer and the staff of the Institute of Quantum Optics and Quantum Information (IQOQI) this Symposium, the 2 nd in the series, also served as a Fest-schri for Helmut Rauch and Danny Greenberger, noted experimental and theoretical luminaries in the field.In particular,it was Helmut Rauch who,together withWolfgang Treimer and Ulrich Bonse, was first to demonstrate the first Single Crystal Neutron Interferometer in 1974 [1].Closely analogous to a Mach-Zehnder Interferometer in classical optics, these wonderful devices are carved out of a monolithic piece of highly perfect single crystal of silicon,of the kind used in the semiconductor electronics industry.A photograph and a schematic are shown in fig 1. ree parallel slabs of silicon,connected by a base,contain perfectly aligned planes of atoms,which,by virtue of Bragg Diffraction, coherently split a beam of monochromatic neutrons, whose wavelengths are comparable in magnitude to the lattice spacing of the silicon crystal.Furthermore, the silicon is almost completely transparent to neutrons -so that absorption is essentially negligible.us, the first slab acts as a beam splitter, with a transmitted and a diffracted beam emerging from it.Both these beams continue to the second slab at which Bragg diffraction occurs once again.Ignoring the transmitted beams (which escape from the system), the two diffracted beams continue on their way to the third, equidistant slab, where they recombine in a way similar to the first beam splitter.

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Quantum Information Enabled Neutron Interferometry

J. Nsofini

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.

•Jun 12, 2017•0 citations
Neutron and X-ray perfect-crystal interferometers (PCIs) are powerful platforms for studies of fundamental physics and phase-contrast imaging. Further enhancing several PCI capabilities requires reducing crystal blade thickness to the micron scale, which minimizes dynamical-diffraction image blur, permits operation in the pendellösung regime where blade thickness controls beam splitting, and reduces absorption for simultaneous neutron and X-ray operation. However, fabricating multiple crystal blades with identical micrometer-scale thicknesses over centimeter-scale areas remains a major challenge. Here, using a non-etching sub-micron fabrication technique, we demonstrate silicon triple-Laue interferometers with equal-blade-thicknesses of 110 μμμm and 350 μμμm, operated with both neutrons and X-rays. These devices are the thinnest PCIs realized to date, enabling a factor-of-six reduction in dynamical-diffraction beam spreading for improved phase-contrast imaging, while reaching the single pendellösung length regime in which crystal thickness provides an experimentally accessible control parameter for engineered quantum-optical beam splitting of plane-wave inputs. These results motivate multi-blade PCI designs utilizing identical half-pendellösung crystal lamellae that are proposed for neutron spin--orbit and electric dipole moment measurements.
Coherent control of neutrons via Bragg diffraction forms the foundation of perfect crystal neutron interferometry, facilitating both fundamental tests of quantum mechanics and applications in quantum information science. In cavity geometries, perfect crystals enable neutron confinement and have been employed in precision measurements of spin-orbit interactions and for neutron electric dipole moment (nEDM) searches. However, in these conventional configurations, neutrons undergo a single pass through the crystal geometry, placing a physical constraint on both crystal and in-flight interaction times and measurement sensitivity. In this work, we introduce a neutron loop cavity that coherently recirculates neutrons through repeated Bragg reflections between perfect silicon crystal blades. This structure is predicted to achieve a neutron survival probability of ∼64 %\sim64~\%∼64 % for 10,000 Bragg reflections, corresponding to confinement times on the order of seconds. We propose a Schwinger interaction measurement that achieves a πππ spin rotation in 800 Bragg reflections, representing more than a tenfold improvement in sensitivity over recent measurements. Further applications include high-sensitivity nEDM searches targeting the 10−27 10^{-27}~10−27 e⋅\cdot⋅cm scale, as well as competitive experimental tests of neutron parity violation, the neutron lifetime, and the quantum Zeno effect with neutrons.
his was one of the conclusions that emerged from the Vienna Symposium on the Foundations of Modern Physics held in June this year.Organised by Anton Zeilinger, ably assisted by Markus Aspelmeyer and the staff of the Institute of Quantum Optics and Quantum Information (IQOQI) this Symposium, the 2 nd in the series, also served as a Fest-schri for Helmut Rauch and Danny Greenberger, noted experimental and theoretical luminaries in the field.In particular,it was Helmut Rauch who,together withWolfgang Treimer and Ulrich Bonse, was first to demonstrate the first Single Crystal Neutron Interferometer in 1974 [1].Closely analogous to a Mach-Zehnder Interferometer in classical optics, these wonderful devices are carved out of a monolithic piece of highly perfect single crystal of silicon,of the kind used in the semiconductor electronics industry.A photograph and a schematic are shown in fig 1. ree parallel slabs of silicon,connected by a base,contain perfectly aligned planes of atoms,which,by virtue of Bragg Diffraction, coherently split a beam of monochromatic neutrons, whose wavelengths are comparable in magnitude to the lattice spacing of the silicon crystal.Furthermore, the silicon is almost completely transparent to neutrons -so that absorption is essentially negligible.us, the first slab acts as a beam splitter, with a transmitted and a diffracted beam emerging from it.Both these beams continue to the second slab at which Bragg diffraction occurs once again.Ignoring the transmitted beams (which escape from the system), the two diffracted beams continue on their way to the third, equidistant slab, where they recombine in a way similar to the first beam splitter.
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.
A zero-area four-blade perfect crystal neutron interferometer (NI) possess a decoherence-free subspace (DFS) for low-frequency mechanical vibrations and thus is easier to site. However, unlike the standard three-blade Mach-Zehnder NI the ideal contrast of this four-blade NI geometry is less than 1. By applying a recently introduced quantum information model for dynamical diffraction we show that the contrast for the four-blade DFS NI can be increased by offsetting the focusing condition. The contrast optimization leads to an NI geometry where the distances between the centers of the blades are equidistant. An experiment is proposed to verify the increase in contrast.
The phenomenon of interference plays a crucial role in the field of precision measurement science. Wave-particle duality has expanded the well-known interference effects of electromagnetic waves to massive particles. The majority of the wave-particle interference experiments require a near monochromatic beam which limits its applications due to the resulting low intensity. Here we demonstrate white beam interference in the far-field regime using a two-phase-grating neutron interferometer and its application to phase-contrast imaging. The functionality of this interferometer is based on the universal moir\'e effect that allows us to improve upon the standard Lau setup. Interference fringes were observed with monochromatic and polychromatic neutron beams for both continuous and pulsed beams. Far-field neutron interferometry allows for the full utilization of intense neutron sources for precision measurements of gradient fields. It also overcomes the alignment, stability, and fabrication challenges associated with the more familiar perfect-crystal neutron interferometer, as well as avoids the loss of intensity due to the absorption analyzer grating requirement in Talbot-Lau interferometer.
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.