{
  "abstract": "We derive analytic expressions for observable dynamics under the fully quantized trilinear Hamiltonian, governing quantum three-wave mixing and parametric amplification. Starting from a coherent pump and vacuum signal and idler, the calculation reorganizes the Heisenberg expansion into resummed depletion and return profiles, yielding directly evaluable expressions for all 1st-, 2nd- and 3rd-order correlations. The construction uses no parametric approximation or fitted parameters. Representative numerical benchmarks show errors of order $10^{-12}$ throughout the entire pump depletion, and below $10^{-3}$ across dozens of depletion-and-back-conversion cycles, up to the first total collapse of the oscillation. The first-depletion treatment additionally provides 4th-order correlations, accommodates bright squeezed-pump inputs and reveals phenomena important to future optical quantum technologies. The framework can be extended to higher moments.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.39387",
  "author_total": 2,
  "authors": [
    {
      "name": "Wanli Xing"
    },
    {
      "name": "Timothy C. Ralph"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7tbabt1znwv8y.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.39387",
  "fulltext_url": null,
  "id": "7tbabt1znwv8y",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.39387",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "quant-ph"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.39387",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7tbabt1znwv8y.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:23Z",
      "native_id": "2610.39387",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.39387"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Analytic Solutions To Fully Quantized Parametric Amplification",
  "title_text": "Analytic Solutions To Fully Quantized Parametric Amplification",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:28Z",
  "url": "https://research.draconitic.com/paper/7tbabt1znwv8y",
  "venue": "arXiv",
  "versions": []
}