{
  "id": "1204.2780",
  "version": "v3",
  "published": "2012-04-12T17:37:49.000Z",
  "updated": "2012-10-02T11:36:55.000Z",
  "title": "Electron vortex beams in a magnetic field: A new twist on Landau levels and Aharonov-Bohm states",
  "authors": [
    "Konstantin Y. Bliokh",
    "Peter Schattschneider",
    "Jo Verbeeck",
    "Franco Nori"
  ],
  "comment": "21 pages, 10 figures, 1 table, to appear in Phys. Rev. X",
  "journal": "Phys. Rev. X 2, 041011 (2012)",
  "doi": "10.1103/PhysRevX.2.041011",
  "categories": [
    "quant-ph",
    "cond-mat.str-el",
    "physics.optics"
  ],
  "abstract": "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 (i) Larmor, (ii) cyclotron (double-Larmor), or (iii) zero frequency. At the same time, its centroid always follows the classical cyclotron trajectory, in agreement with the Ehrenfest theorem. Remarkably, the non-rotating superpositions reproduce stable multi-vortex configurations that appear in rotating superfluids. Our results open up an avenue for the direct electron-microscopy observation of fundamental properties of free quantum electron states in magnetic fields.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2012-10-02T11:36:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "41.85.-p",
      "42.50.Tx",
      "03.65.Ta"
    ],
    "keywords": [
      "magnetic field",
      "electron vortex beams",
      "modes represent bessel beams",
      "aharonov-bohm states",
      "landau levels"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Physical Review X",
      "year": 2012,
      "month": "Oct",
      "volume": 2,
      "number": 4,
      "pages": "041011"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012PhRvX...2d1011B"
    }
  }
}