{
  "abstract": "After truncating the matter Hilbert space of a single-mode light-matter model, gauge transformations leave the spectrum invariant whereas the ground-state photon number is gauge dependent, hence, its meaning remains disputed. We show that this gauge dependence obeys an exact algebraic law whenever the gauge transformation acts as a displacement of the field coupled to a matter operator $G$. Namely, the ground-state photon number is a quadratic polynomial in the gauge parameter $λ$, $\\langle a^{\\dagger} a\\rangle_λ$ $=$ $\\langle a^{\\dagger} a\\rangle_{0}$ $+$ $Cλ$ $+$ $Qλ^2$. Here the coefficients are the correlator $C=\\langle G\\,p\\rangle$ of $G$ and the field momentum $p$, and $Q=\\langle G^2\\rangle$. Its minimum over all gauges is naturally gauge-invariant, and for the quantum Rabi model it is determined by the ground-state energy alone. We show that it is strictly positive for the quantum Rabi and Dicke models with level splitting, so that a residual photon content survives in every gauge. At weak coupling the gauge of minimal photon number is the Jaynes-Cummings gauge, and for the Dicke model it remains so at all couplings in the thermodynamic limit.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.40446",
  "author_total": 2,
  "authors": [
    {
      "name": "Arka Dutta"
    },
    {
      "name": "Marcus Kollar"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/096a1nfxz1vxe.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.40446",
  "fulltext_url": null,
  "id": "096a1nfxz1vxe",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.40446",
  "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",
      "quant-ph"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.40446",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/096a1nfxz1vxe.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:28Z",
      "native_id": "2610.40446",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.40446"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "A universal gauge structure in the photon content of light-matter systems",
  "title_text": "A universal gauge structure in the photon content of light-matter systems",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:47Z",
  "url": "https://research.draconitic.com/paper/096a1nfxz1vxe",
  "venue": "arXiv",
  "versions": []
}