{
  "abstract": "We combine the Briegel--Englert damping basis of a lossy cavity mode with the permutation-invariant Liouville basis of \\(N\\) identical, incoherently pumped two-level emitters. The resulting Liouvillian is exactly block tridiagonal in a single radial field index, with atomic blocks of dimension \\(\\binom{N+3}{3}\\). The stationary state follows from a matrix continued fraction whose asymptotic closure is a linear matrix equation that we prove to be uniquely solvable throughout the dissipative regime \\(A>0\\), and the same construction in the coherence-one sector yields the emission spectrum. The method is validated against direct diagonalization, weak-pump perturbation theory, and closed-system spectra, reaches \\(N=16\\) in tens of seconds in the few-quanta regime, and has a quantified precision limit at large photon number. We use it to derive an exact two-atom photon-balance identity that isolates the cavity-induced pair coherence and relates it to a singlet--triplet population difference; to establish an exact pump-order hierarchy of connected correlations for a zero-temperature cavity and a parity property of the minimal collective-spin sector; and to benchmark the second-order cumulant closure used in few-emitter laser theory, which we find to be semi-quantitative for the photon number but to predict the wrong sign of the inter-emitter coherence above inversion. In a good-cavity regime the exact solution shows near-Poissonian statistics and strong line narrowing for two and three emitters.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.17785",
  "author_total": 1,
  "authors": [
    {
      "name": "Stephan Hartmann"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/brczh6ftzbpv1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.17785",
  "fulltext_url": null,
  "id": "brczh6ftzbpv1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.17785",
  "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",
      "physics.atom-ph"
    ],
    [
      "arxiv",
      "physics.optics"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "3107|Quantum optics and atomic interactions"
    ]
  ],
  "openalex": "W7213563809",
  "pdf_url": "https://arxiv.org/pdf/2609.17785",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/brczh6ftzbpv1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:06Z",
      "native_id": "2609.17785",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.17785"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:physics.atom-ph",
      "subfield": "amo"
    },
    {
      "field": "physics",
      "origin": "arxiv:physics.optics",
      "subfield": "optics-photonics"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Exact damping-basis continued fractions for few-atom lasers: collective correlations beyond second-order cumulant closure",
  "title_text": "Exact damping-basis continued fractions for few-atom lasers: collective correlations beyond second-order cumulant closure",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:06Z",
  "url": "https://research.draconitic.com/paper/brczh6ftzbpv1",
  "venue": "arXiv",
  "versions": []
}