{
  "id": "1109.5724",
  "version": "v2",
  "published": "2011-09-26T20:52:19.000Z",
  "updated": "2012-09-04T13:51:20.000Z",
  "title": "On the Spectrum of Field Quadratures for a Finite Number of Photons",
  "authors": [
    "Emilio Pisanty",
    "Eduardo Nahmad-Achar"
  ],
  "comment": "16 pages, 11 figures",
  "journal": "2012 J. Phys. A: Math. Theor. 45 395303",
  "doi": "10.1088/1751-8113/45/39/395303",
  "categories": [
    "quant-ph"
  ],
  "abstract": "The spectrum and eigenstates of any field quadrature operator restricted to a finite number $N$ of photons are studied, in terms of the Hermite polynomials. By (naturally) defining \\textit{approximate} eigenstates, which represent highly localized wavefunctions with up to $N$ photons, one can arrive at an appropriate notion of limit for the spectrum of the quadrature as $N$ goes to infinity, in the sense that the limit coincides with the spectrum of the infinite-dimensional quadrature operator. In particular, this notion allows the spectra of truncated phase operators to tend to the complete unit circle, as one would expect. A regular structure for the zeros of the Christoffel-Darboux kernel is also shown.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-09-04T13:51:20.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite number",
      "complete unit circle",
      "infinite-dimensional quadrature operator",
      "field quadrature operator",
      "regular structure"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Journal of Physics A Mathematical General",
      "year": 2012,
      "month": "Oct",
      "volume": 45,
      "number": 39,
      "pages": 395303
    },
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012JPhA...45M5303P"
    }
  }
}