Konstantin Y. Bliokh, Peter Schattschneider, Jo Verbeeck, Franco Nori
We examine the propagation of recently-discovered electron vortex beams in a longitudinal magnetic field. Both the Aharonov-Bohm configuration with a single flux line and the Landau case of a uniform magnetic field are considered. While stationary Aharonov-Bohm modes represent Bessel beams with field-dependent probability and current distributions, stationary Landau states manifest themselves as non-diffracting Laguerre-Gaussian beams. Furthermore, the Landau-state beams possess field- and vortex-dependent phases: (i) the Zeeman phase from coupling the quantized angular momentum to the magnetic field and (ii) the Gouy phase, known from optical Laguerre-Gaussian beams. Remarkably, together these phases determine the structure of Landau energy levels. This unified Zeeman-Landau-Gouy phase manifests itself in a nontrivial evolution of images formed by various superpositions of modes. We demonstrate that, depending on the chosen superposition, the image can rotate in a magnetic field with either Larmor, cyclotron, or zero frequency, whereas its centroid always follow the classical trajectory, in agreement with the Ehrenfest theorem. Our results open up an avenue for the direct experimental observation of fundamental internal properties of quantum electron states in magnetic fields.
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http://arxiv.org/abs/1204.2780
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