{
  "annotation_id": "ab8833a3-1c15-4747-acf3-b4a2767ca76c",
  "date_created": "2026-03-02T18:02:45.137000Z",
  "date_modified": "2026-03-02T18:02:45.137000Z",
  "file_hash": "af489a868b4051bbecfe844ee60db515a4afdffe47707d4ea09b049c476569f2",
  "private": false,
  "record": {
    "abstract": "We analyze the long-time quantum dynamics of degenerate parametric\ndown-conversion from an initial sub-harmonic vacuum (spontaenous\ndown-conversion). Standard linearization of the Heisenberg equations of motions\nfails in this case, since it is based on an expansion around an unstable\nclassical solution and neglects pump depletion. Introducing a mean-field\napproximation we find a periodic exchange of energy between the pump and\nsubharmonic mode goverened by an anharmonic pendulum equation. From this\nequation the optimum interaction time or crystal length for maximum conversion\ncan be determined. A numerical integration of the 2-mode Schr\"odinger equation\nusing a dynamically optimized basis of displaced and squeezed number states\nverifies the characteristic times predicted by the mean-field approximation. In\ncontrast to semiclassical and mean-field predictions it is found that quantum\nfluctuations of the pump mode lead to a substantial limitation of the\nefficiency of parametric down-conversion.",
    "arxiv_id": "quant-ph/9809089",
    "authors": [
      "Michael Fleischhauer",
      "Oliver Veits"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1515/zna-1999-0108",
    "title": "Long-time dynamics of spontaneous parametric down-conversion and quantum   limitations of conversion efficiency",
    "url": "https://arxiv.org/abs/quant-ph/9809089"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "cc9c66a5-0fda-4992-a426-4503eb154929",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}