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physica status solidi (b)

Photons, Orbital Angular Momentum, and Neutrons

R. L. Cappelletti, John Vinson

Published Sep 5, 2020• 8 citations
Publisher

Abstract

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.

DOI
10.1002/pssb.202000257

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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.
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.
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.
The identification of orbital angular momentum (OAM) as a fundamental property of a beam of light nearly 25 years ago has led to an extensive body of research around this topic. The possibility that single photons can carry OAM has made this degree of freedom an ideal candidate for the investigation of complex quantum phenomena and their applications. Research in this direction has ranged from experiments on complex forms of quantum entanglement to the interaction between light and quantum states of matter. Furthermore, the use of OAM in quantum information has generated a lot of excitement, as it allows for encoding large amounts of information on a single photon. Here, we explain the intuition that led to the first quantum experiment with OAM 15 years ago. We continue by reviewing some key experiments investigating fundamental questions on photonic OAM and the first steps to applying these properties in novel quantum protocols. At the end, we identify several interesting open questions that could form the subject of future investigations with OAM.This article is part of the themed issue 'Optical orbital angular momentum'.
A photon can be considered both a particle and a wave in quantum mechanics. Quantum optics deals with such quantum mechanical properties of a photon. One such property that has been of particular interest recently is that of light’s momentum, specifically its linear momentum and orbital angular momentum (OAM). Light carrying both types of momentum are of particular utility to the life sciences. Linear momentum (LM) photons have the ability to directly manipulate particles. For example, photons with these properties can be used to separate one specific particle from a group. One can then more closely observe its properties. OAM photons have the potential to unravel DNA strands using the torque of the photons to further observe certain specific physical properties. Light carrying OAM has also shown promise in the field of information technology as a new means of sending large amounts of data over long distances securely and extremely quickly. Because photons behave quantum mechanically, the encryptions are much more difficult to decode, and since the information is being sent as light it clearly travels at the speed of light. This paper will provide background on the quantum optics of particle manipulation and the results from experimental studies performed on this topic. The results show evidence of light with both types of momentum being created and used to manipulate particles. We generated light with both types of momentum, trapped particles with optical tweezers, and measured the force on the particles with a high speed video camera, optical tweezers, and computer programs that we used to track the particles.