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Details of Grant 

EPSRC Reference: EP/R008264/1
Title: Relativistic Electron Vortices
Principal Investigator: Barnett, Professor S
Other Investigators:
Researcher Co-Investigators:
Project Partners:
Department: School of Physics and Astronomy
Organisation: University of Glasgow
Scheme: Standard Research
Starts: 01 December 2017 Ends: 30 April 2021 Value (£): 204,146
EPSRC Research Topic Classifications:
Quantum Optics & Information
EPSRC Industrial Sector Classifications:
No relevance to Underpinning Sectors
Related Grants:
Panel History:
Panel DatePanel NameOutcome
15 Jun 2017 EPSRC Physical Sciences – June 2017 Announced
Summary on Grant Application Form
Vortices are ubiquitous whenever we have a fluid in motion or a field. For the electromagnetic field these take the form of a line in space around which the phase accumulates an integer multiple, l, of 2 pi, analogous to the manner in which the height changes as we climb a spiral staircase. It is well-established that this phenomenon is associated with an orbital angular momentum for the light in which each photon carries l times h-bar units of orbital angular momentum.

Recent developments have demonstrated, beyond reasonable doubt, that propagating electrons can also be prepared with an on-axis vortex corresponding to a phase-singularity in the wave function. As with light, we can associate this with an orbital angular momentum.

While the phenomenon of electron vortices and the associated orbital angular momentum may be said to be well understood in the non-relativistic, Schroedinger, domain the same cannot be said to be true for relativistic electrons governed by the Dirac equation. In the Dirac theory, for example, the local velocity of an electron is not proportional to the gradient of the phase of the wave function and for this reason the appealing link between the existence of vortices and electron angular momentum is brought into question.

There are three reasons why this problem is important: one practical and two fundamental. The first derives from the requirement to be able to describe, as simply as possible, experiments with shaped electron beams as they move towards higher energies. The second is the question of whether electron vortices are real and what happens to these topological features as we move into the relativistic regime. Finally, we know that the spin and orbital parts of the electron angular momentum are not separately conserved so we need to know how to interpret the mechanical consequences of relativistic electron vortices. We note that analogous difficulties arose in the study of optical angular momentum but have been resolved. This encourages us to apply similar methods to electrons and we shall do so by writing Maxwell's equations for light and the Dirac equation for the electron in similar forms. This should allow us to apply insights and practical techniques devised and tested in optics to electrons.
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