{
  "id": "2404.07905",
  "version": "v1",
  "published": "2024-04-11T16:45:52.000Z",
  "updated": "2024-04-11T16:45:52.000Z",
  "title": "Poincaré disk as a model of squeezed states of a harmonic oscillator",
  "authors": [
    "Ian Chi",
    "Martin Fraas",
    "Tina Tan"
  ],
  "comment": "16 pages, 5 figures",
  "categories": [
    "math-ph",
    "math.MP",
    "quant-ph"
  ],
  "abstract": "Single-mode squeezed states exhibit a direct correspondence with points on the Poincar\\'e disk. In this study, we delve into this correspondence and describe the motions of the disk generated by a quadratic Hamiltonian. This provides a geometric representation of squeezed states and their evolution. We discuss applications in bang-bang and adiabatic control problems involving squeezed states.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-04-11T16:45:52.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "harmonic oscillator",
      "adiabatic control problems",
      "poincare disk",
      "single-mode squeezed states",
      "quadratic hamiltonian"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}