{
  "annotation_id": "df426e73-4f9b-4af4-bdf0-139b310e4f12",
  "date_created": "2026-03-02T18:01:46.067000Z",
  "date_modified": "2026-03-02T18:01:46.067000Z",
  "file_hash": "701413c5e1570a0b399782508a3d3ea98a5c406a203157dc8ad680f5a03f32f3",
  "private": false,
  "record": {
    "abstract": "Field quantization in three dimensional unstable optical systems is treated\nby expanding the vector potential in terms of non-Hermitean (Fox-Li) modes in\nboth the cavity and external regions. The cavity non-Hermitean modes (NHM) are\ntreated using the paraxial and monochromaticity approximations. The NHM\nbi-orthogonality relationships are used in a standard canonical quantization\nprocedure based on introducing generalised coordinates and momenta for the\nelectromagnetic (EM) field. The quantum EM field is equivalent to a set of\nquantum harmonic oscillators (QHO), associated with either the cavity or the\nexternal region NHM. This confirms the validity of the photon model in unstable\noptical systems, though the annihilation and creation operators for each QHO\nare not Hermitean adjoints. The quantum Hamiltonian for the EM field is the sum\nof non-commuting cavity and external region contributions, each of which is sum\nof independent QHO Hamiltonians for each NHM, but the external field\nHamiltonian also includes a coupling term responsible for external NHM photon\nexchange processes. Cavity energy gain and loss processes is associated with\nthe non-commutativity of cavity and external region operators, given in terms\nof surface integrals involving cavity and external region NHM functions on the\ncavity-external region boundary. The spontaneous decay of a two-level atom\ninside an unstable cavity is treated using the essential states approach and\nthe rotating wave approximation. Atomic transitions leading to cavity NHM\nphoton absorption have a different coupling constant to those leading to photon\nemission, a feature resulting from the use of NHM functions. Under certain\nconditions the decay rate is enhanced by the Petermann factor.",
    "arxiv_id": "quant-ph/0107039",
    "authors": [
      "S. A. Brown",
      "B. J. Dalton"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1080/09500340110095625",
    "journal_ref": "Journal of Modern Optics, V49 (7), 1009-1041 (2002).",
    "title": "Field Quantization, Photons and Non-Hermitean Modes",
    "url": "https://arxiv.org/abs/quant-ph/0107039"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "d4c2b077-aa52-4ec7-ad35-42fc07ec272c",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}