Physics – Quantum Physics
Scientific paper
2012-04-12
Physics
Quantum Physics
19 pages, 8 figures, 1 table
Scientific paper
We examine the propagation of the recently-discovered electron vortex beams in a longitudinal magnetic field. We consider both the Aharonov-Bohm configuration with a single flux line and the Landau case of a uniform magnetic field. While stationary Aharonov-Bohm modes represent Bessel beams with flux- and vortex-dependent probability 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. At the same time, its centroid always follows the classical trajectory, in agreement with the Ehrenfest theorem. Our results open up an avenue for the direct electron-microscopy observation of fundamental properties of free quantum electron states in magnetic fields.
Bliokh Konstantin Y.
Nori Franco
Schattschneider Peter
Verbeeck Johan
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