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Physical Review Letters

Intrinsic Orbital Angular Momentum States of Neutrons

R. L. Cappelletti, Terrence Jach, John Vinson

Published Mar 2, 2018• 35 citations
Publisher

Abstract

It has been shown that single-particle wave functions, of both photons and electrons, can be created with a phase vortex, i.e., an intrinsic orbital angular momentum (OAM). A recent experiment has claimed similar success using neutrons [C. W. Clark et al., Nature, 525, 504 (2015)NATUAS0028-083610.1038/nature15265]. We show that their results are insufficient to unambiguously demonstrate OAM, and they can be fully explained as phase contrast interference patterns. Furthermore, given the small transverse coherence length of the neutrons in the original experiment, the probability that any neutron was placed in an OAM state is vanishingly small. We highlight the importance of the relative size of the coherence length, which presents a unique challenge for neutron experiments compared to electron or photon work, and we suggest improvements for the creation of neutron OAM states.

DOI
10.1103/physrevlett.120.090402

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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.

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It has been shown that single-particle wave functions, of both photons and electrons, can be created with a phase vortex, i.e., an intrinsic orbital angular momentum (OAM). A recent experiment has claimed similar success using neutrons [C. W. Clark et al., Nature, 525, 504 (2015)NATUAS0028-083610.1038/nature15265]. We show that their results are insufficient to unambiguously demonstrate OAM, and they can be fully explained as phase contrast interference patterns. Furthermore, given the small transverse coherence length of the neutrons in the original experiment, the probability that any neutron was placed in an OAM state is vanishingly small. We highlight the importance of the relative size of the coherence length, which presents a unique challenge for neutron experiments compared to electron or photon work, and we suggest improvements for the creation of neutron OAM states.
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.
Abstract We present calculations of interferograms (interference patterns) of one or multiple spiral phase plates that would be observed with a perfect crystal neutron interferometer of Mach–Zehnder type. A spiral phase plate (SPP) in one of the two coherent beam paths produces a twist in the phase front and thus a vortex beam with intrinsic angular momentum, which in the case of neutrons should be observed as a characteristic interference pattern that appears complementary to each other in both detectors behind the interferometer. Adding additional SPPs in one beam path of the interferometer yield interference patterns similar to that of a single SPP but only due to the cumulative step height. All simulated interferograms have been calculated on the basis of dynamical neutron diffraction without any assumption of a neutron orbital angular momentum and show very convincing agreement with experimental results from the literature, see e.g. (C. W. Clark, R. Barankov, M. G. Huber, M. Arif, D. G. Cory, and D. A. Pushin, “Controlling neutron orbital angular momentum,” Nature, vol. 525, pp. 504–506, 2015). In particular, this clarifies, that the cited experiments do not give evidence of the quantization of interactions caused by a twist of the phase front of a neutron wave in the interferometer and thus no evidence for the effect of a neutron orbital angular momentum.
Angular momentum plays a central role in quantum mechanics, recurring in every length scale from the microscopic interactions of light and matter to the macroscopic behavior of superfluids. Vortex beams, carrying intrinsic orbital angular momentum (OAM), are now regularly generated with elementary particles such as photons and electrons. Thus far, the creation of a vortex beam of a nonelementary particle has never been demonstrated experimentally. We present vortex beams of atoms and molecules, formed by diffracting supersonic beams of helium atoms and dimers off transmission gratings. This method is general and could be applied to most atomic and molecular gases. Our results may open new frontiers in atomic physics, using the additional degree of freedom of OAM to probe collisions and alter fundamental interactions.
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.
This work presents a single-pass diffraction experiment that demonstrates that single photons in a vortex beam in passing through three slits arranged in an equilateral triangle can interfere with themselves and provide quantitative information of their total amount of orbital angular momentum (OAM) they carry. For the experiment presented the aperture has been reduced to a very thin triangular slit. A vortex beam is created by a diffractive optical element (DOE) and then it is made to pass through the slit. This work is considered as an extension to the Young double slit experiment.
The observation of the quantum nature of quasi-classical states is of utmost importance since these states are realistic sources of radiation and do not have any shortage in photon numbers. Therefore, they do not face the scalability problem as much as single-photon sources do, which makes them much more robust against photon loss. The physical dynamics of these states predict that the quantum aspects of a continuous source can be observed in the weak limit. Yet, since these states are superposition of different particle states of radiation, we need post-selection to achieve this result. Practically, even after the post-selection, this high photon rate has not been observed. In this manuscript, we attempt to demonstrate that quasi-classical states supplemented with orbital angular momentum (OAM) can deliver a significant high photon rate in producing quantum signature alluding to this fact that OAM is indeed an intrinsic property of light at the quantum level as well. Through our experiment, we realize two-photon bunching with the projection of OAM from a continuous wave source. We observe that this approach can produce the result from a single-photon source with the high accuracy after the post-selection. In fact, since there is no interaction with matter, the post-selected photon rate from this approach can be considered as an upper bound for the single-photon generation based on the input power. This work is a step forward toward a more diverse and practical use of quasi-classical states in the domain of quantum optics and quantum information.