Generation of electron beams carrying orbital angular momentum

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Abstract

All forms of waves can contain phase singularities. In the case of optical waves, a light beam with a phase singularity carries orbital angular momentum, and such beams have found a range of applications in optical manipulation, quantum information and astronomy. Here we report the generation of an electron beam with a phase singularity propagating in free space, which we achieve by passing a plane electron wave through a spiral phase plate constructed naturally from a stack of graphite thin films. The interference pattern between the final beam and a plane electron wave in a transmission electron microscope shows the 'Y'-like defect pattern characteristic of a beam carrying a phase singularity with a topological charge equal to one. This fundamentally new electron degree of freedom could find application in a number of research areas, as is the case for polarized electron beams.

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Entanglement of the orbital angular momentum states of photons.

A Mair, A. Vaziri, G. Weihs … (2001)

Entangled quantum states are not separable, regardless of the spatial separation of their components. This is a manifestation of an aspect of quantum mechanics known as quantum non-locality. An important consequence of this is that the measurement of the state of one particle in a two-particle entangled state defines the state of the second particle instantaneously, whereas neither particle possesses its own well-defined state before the measurement. Experimental realizations of entanglement have hitherto been restricted to two-state quantum systems, involving, for example, the two orthogonal polarization states of photons. Here we demonstrate entanglement involving the spatial modes of the electromagnetic field carrying orbital angular momentum. As these modes can be used to define an infinitely dimensional discrete Hilbert space, this approach provides a practical route to entanglement that involves many orthogonal quantum states, rather than just two Multi-dimensional entangled states could be of considerable importance in the field of quantum information, enabling, for example, more efficient use of communication channels in quantum cryptography.