Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1911.07974

On coherence and the transverse spatial extent of a neutron wave packet

C. F. Majkrzak, N. F. Berk, Brian B. Maranville, Joseph A. Dura, Terrence Jach

Published Nov 18, 2019• 0 citations
arXivHTMLPDF

Abstract

In the analysis of neutron scattering measurements of condensed matter structure, it normally suffices to treat the incident and scattered neutron beams as if composed of incoherent distributions of plane waves with wavevectors of different magnitudes and directions which are taken to define an instrumental resolution. However, despite the wide-ranging applicability of this conventional treatment, there are cases in which the wave function of an individual neutron in the beam must be described more accurately by a spatially localized packet, in particular with respect to its transverse extent normal to its mean direction of propagation. One such case involves the creation of orbital angular momentum (OAM) states in a neutron via interaction with a material device of a given size. It is shown in the work reported here that there exist two distinct measures of coherence of special significance and utility for describing neutron beams in scattering studies of materials in general. One measure corresponds to the coherent superposition of basis functions and their wavevectors which constitute each individual neutron packet state function whereas the other measure can be associated with an incoherent distribution of mean wavevectors of the individual neutron packets in a beam. Both the distribution of the mean wavevectors of individual packets in the beam as well as the wavevector components of the superposition of basis functions within an individual packet can contribute to the conventional notion of instrumental resolution. However, it is the transverse spatial extent of packet wavefronts alone that determines the area within which a coherent scattering process can occur in the first place. This picture is shown to be consistent with standard quantum theory. It is also demonstrated that these two measures of coherence can be distinguished from one another experimentally.

DOI
10.48550/arxiv.1911.07974

Related papers

Probing Single-Particle Spatial Extent With Helical Neutron Wavefronts

D. Sarenac, O. Lailey, C. W. Clark +8 more

Distinguishing transverse coherence length from single-particle wavepacket extent is fundamentally challenging, as both manifest through spatial broadening of observed intensity profiles in conventional experiments. Here we introduce a method based on helical neutron wavefronts that enables this separation. Helical neutron states produce annular intensity profiles whose peak radius depends on the transverse wavepacket extent, while coherence length only contributes to profile broadening. In our experimental geometry we measure a beam divergence of ~1.1 mrad, corresponding to a transverse coherence length of ~180 nm. In contrast, the same measurement places a lower bound of >= 2 um on the spatial extent of the individual neutron wavepackets, more than an order of magnitude larger than the coherence length. These results provide direct experimental evidence that transverse coherence length and single-particle wavepacket extent are distinct physical quantities, resolving a longstanding source of confusion in the neutron literature.

quant-pharXiv:2606.22292•Jun 23, 2026•0 citations

Photons, Orbital Angular Momentum, and Neutrons

R. L. Cappelletti, John Vinson

A traveling wave or wave packet may possess orbital angular momentum (OAM) in the form of a phase vortex about its propagation axis. These OAM states are a general wave property and exist in single‐particle wave packets, in a beam of unstructured wave packets of particles or in a mixture. OAM states of photons were first created almost 30 years ago. Recently work has been done to create these states with massive particles: electrons and neutrons. OAM waves can be generated by passing an unstructured wave through a vortex phase plate. This technique is reliant on each particle adequately sampling the area of the vortex plate. While laser sources provide sufficient transverse coherence, beams of massive particles are more challenging. If incident wave packets do not interrogate the discontinuity at the center of the vortex phase plate, the probability of detecting a single particle having a unit of OAM about the packet center decreases substantially and the expectation value of the OAM about that center vanishes. Herein, using laser light, we restrict the transverse size of a beam to either illuminate the discontinuity or not and consider the implications for producing OAM in individual neutrons.

physica status solidi (b)•Sep 5, 2020•8 citations

Measurement and characterization of the three-dimensional coherence function in neutron interferometry

H. Rauch, H. Wölwitsch, Helmut Kaiser +2 more

The spatial coherence function in all three orthogonal directions has been measured by means of perfect crystal neutron interferometry. It has been demonstrated that the coherence function is given by the Fourier transform of the related momentum distribution, which in turn is determined by the collimation and monochromatization of the beam incident upon and traversing the interferometer. Thus, a measurement of the coherence function can replace a measurement of the momentum distribution in certain cases. Retrieval of the coherence can be accomplished by phase echo and/or postselection methods. A complete retrieval of the coherence is impossible in principle due to unavoidable loss factors.

Physical Review A•Feb 1, 1996•67 citations

Quantum Beam Scattering—Beam’s Coherence Length, Which-Path Information and Weak Values

C. A. Chatzidimitriou‐Dreismann

The conventional theory of neutron beams interacting with many-body systems treats the beam as a classical system, i.e. with its dynamical variables appearing in the quantum dynamics of the scattering process not as operators but only as c-numbers. Moreover, neutrons are described with plane waves, i.e. the concept of neutron's (finite) coherence length is here irrelevant. The same holds for electron, atom or X-ray scattering. This simplification results in the full decoupling of the probe particle's dynamics from the quantum dynamics of the scatterer---a well-known fact also reflected in the standard formalism of time-correlation functions (see textbooks). Making contact with modern quantum theoretical approaches (e.g., quantum entanglement, 'which-path detection' versus interference, von Neumann measurement, Week Values, etc.) new observable effects may be exposed and/or predicted, for instance, a momentum-transfer deficit and an intensity deficit in neutron scattering from protons of hydrogen-containing samples. 7

Quantum Beam Science•Aug 15, 2023•1 citation

Coherence and spectral filtering in neutron interferometry

Helmut Kaiser, R. Clothier, S. A. Werner +2 more

The coherence length of a neutron wave packet depends on the spectral width of the distribution of wave vectors that make up the packet. The coherent overlap of the wave packets traversing the two beam paths in a perfect-silicon-crystal neutron interferometer (NI) is altered by placing a material with a neutron-nuclear optical potential in one of the beam paths in the NI. If the optical potential is positive, it causes a delay of the wave packet and a loss of fringe visibility. By use of an analyzer crystal, we narrow the spectral distribution after the mixing and interference has occurred in the last crystal slab of the NI. This increases the coherence length and restores some of the fringe visibility.

Physical Review A•Jan 1, 1992•65 citations

Loss of wave-packet coherence in stationary scattering experiments

James M. Feagin, Leigh R. Hargreaves

We consider the cross section for a scattering reaction averaged over a statistical ensemble of incident beam wave packets. We generalize a result known from neutron diffraction that static experiments involving stationary scattering via conservative interactions and steady beam currents cannot distinguish the wave-packet nature of the incident beam. Thus we interpret the results of recent experiments on the loss of interference effects in proton scattering from molecular hydrogen as due to the weak collimation of the incident beam rather than alterations to beam wave packets.

Physical Review A•Sep 24, 2013•19 citations
In the analysis of neutron scattering measurements of condensed matter structure, it normally suffices to treat the incident and scattered neutron beams as if composed of incoherent distributions of plane waves with wavevectors of different magnitudes and directions which are taken to define an instrumental resolution. However, despite the wide-ranging applicability of this conventional treatment, there are cases in which the wave function of an individual neutron in the beam must be described more accurately by a spatially localized packet, in particular with respect to its transverse extent normal to its mean direction of propagation. One such case involves the creation of orbital angular momentum (OAM) states in a neutron via interaction with a material device of a given size. It is shown in the work reported here that there exist two distinct measures of coherence of special significance and utility for describing neutron beams in scattering studies of materials in general. One measure corresponds to the coherent superposition of basis functions and their wavevectors which constitute each individual neutron packet state function whereas the other measure can be associated with an incoherent distribution of mean wavevectors of the individual neutron packets in a beam. Both the distribution of the mean wavevectors of individual packets in the beam as well as the wavevector components of the superposition of basis functions within an individual packet can contribute to the conventional notion of instrumental resolution. However, it is the transverse spatial extent of packet wavefronts alone that determines the area within which a coherent scattering process can occur in the first place. This picture is shown to be consistent with standard quantum theory. It is also demonstrated that these two measures of coherence can be distinguished from one another experimentally.
Distinguishing transverse coherence length from single-particle wavepacket extent is fundamentally challenging, as both manifest through spatial broadening of observed intensity profiles in conventional experiments. Here we introduce a method based on helical neutron wavefronts that enables this separation. Helical neutron states produce annular intensity profiles whose peak radius depends on the transverse wavepacket extent, while coherence length only contributes to profile broadening. In our experimental geometry we measure a beam divergence of ~1.1 mrad, corresponding to a transverse coherence length of ~180 nm. In contrast, the same measurement places a lower bound of >= 2 um on the spatial extent of the individual neutron wavepackets, more than an order of magnitude larger than the coherence length. These results provide direct experimental evidence that transverse coherence length and single-particle wavepacket extent are distinct physical quantities, resolving a longstanding source of confusion in the neutron literature.
A traveling wave or wave packet may possess orbital angular momentum (OAM) in the form of a phase vortex about its propagation axis. These OAM states are a general wave property and exist in single‐particle wave packets, in a beam of unstructured wave packets of particles or in a mixture. OAM states of photons were first created almost 30 years ago. Recently work has been done to create these states with massive particles: electrons and neutrons. OAM waves can be generated by passing an unstructured wave through a vortex phase plate. This technique is reliant on each particle adequately sampling the area of the vortex plate. While laser sources provide sufficient transverse coherence, beams of massive particles are more challenging. If incident wave packets do not interrogate the discontinuity at the center of the vortex phase plate, the probability of detecting a single particle having a unit of OAM about the packet center decreases substantially and the expectation value of the OAM about that center vanishes. Herein, using laser light, we restrict the transverse size of a beam to either illuminate the discontinuity or not and consider the implications for producing OAM in individual neutrons.
The spatial coherence function in all three orthogonal directions has been measured by means of perfect crystal neutron interferometry. It has been demonstrated that the coherence function is given by the Fourier transform of the related momentum distribution, which in turn is determined by the collimation and monochromatization of the beam incident upon and traversing the interferometer. Thus, a measurement of the coherence function can replace a measurement of the momentum distribution in certain cases. Retrieval of the coherence can be accomplished by phase echo and/or postselection methods. A complete retrieval of the coherence is impossible in principle due to unavoidable loss factors.
The conventional theory of neutron beams interacting with many-body systems treats the beam as a classical system, i.e. with its dynamical variables appearing in the quantum dynamics of the scattering process not as operators but only as c-numbers. Moreover, neutrons are described with plane waves, i.e. the concept of neutron's (finite) coherence length is here irrelevant. The same holds for electron, atom or X-ray scattering. This simplification results in the full decoupling of the probe particle's dynamics from the quantum dynamics of the scatterer---a well-known fact also reflected in the standard formalism of time-correlation functions (see textbooks). Making contact with modern quantum theoretical approaches (e.g., quantum entanglement, 'which-path detection' versus interference, von Neumann measurement, Week Values, etc.) new observable effects may be exposed and/or predicted, for instance, a momentum-transfer deficit and an intensity deficit in neutron scattering from protons of hydrogen-containing samples. 7
The coherence length of a neutron wave packet depends on the spectral width of the distribution of wave vectors that make up the packet. The coherent overlap of the wave packets traversing the two beam paths in a perfect-silicon-crystal neutron interferometer (NI) is altered by placing a material with a neutron-nuclear optical potential in one of the beam paths in the NI. If the optical potential is positive, it causes a delay of the wave packet and a loss of fringe visibility. By use of an analyzer crystal, we narrow the spectral distribution after the mixing and interference has occurred in the last crystal slab of the NI. This increases the coherence length and restores some of the fringe visibility.
We consider the cross section for a scattering reaction averaged over a statistical ensemble of incident beam wave packets. We generalize a result known from neutron diffraction that static experiments involving stationary scattering via conservative interactions and steady beam currents cannot distinguish the wave-packet nature of the incident beam. Thus we interpret the results of recent experiments on the loss of interference effects in proton scattering from molecular hydrogen as due to the weak collimation of the incident beam rather than alterations to beam wave packets.