{
  "abstract": "At atomic resonance the Jaynes--Cummings (JC) vertex of a single bosonic mode coupled to a two-level emitter is blind to $f=ω/λ$ at zero detuning and Kerr; the anti-Jaynes--Cummings (AJC) vertex is not. We show that the mean-rung excited population of the AJC block equals exactly $1/4$ at $f_\\star=\\sqrt{\\bar n+1}$, while the JC population at the same point is $1/2$. The Poisson-averaged packet value at $\\bar n=16$ is $0.24650$, within $3.5\\times 10^{-3}$ of the exact value, with the deviation reproduced by $-\\bar n/[16(\\bar n+1)^2]$. At $f_\\star$ the modulation depth of the AJC inversion is $1/2$ and the relative sensitivity of the continuum revival-time ratio $r=t_R^{\\rm AJC}/t_R^{\\rm JC}$ is maximal with value $1/(2\\sqrt{\\bar n+1})$. Full diagonalization on $2(n_{\\max}{+}1)$ states confirms the analytic values. The $1/4$ value can be generated by Floquet-engineered counter-rotating coupling provided that the static transverse rate satisfies $g_0\\ll g_1$. Parameter translations for an ideal trapped-ion blue sideband and a flux-tunable circuit-QED coupler are reported.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.14563",
  "author_total": 1,
  "authors": [
    {
      "name": "Onyango Stephen Okeyo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/aaqy186as6wha.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.14563",
  "fulltext_url": null,
  "id": "aaqy186as6wha",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.14563",
  "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",
      "3107|Quantum optics and atomic interactions"
    ]
  ],
  "openalex": "W7213268550",
  "pdf_url": "https://arxiv.org/pdf/2609.14563",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/aaqy186as6wha.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:25Z",
      "native_id": "2609.14563",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.14563"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Exact $1/4$ mean-rung population and $\\sqrt{2}$ continuum revival-time ratio in the anti-Jaynes--Cummings vertex at $f_\\star=\\sqrt{\\bar n+1}$",
  "title_text": "Exact 1/4 mean-rung population and √2 continuum revival-time ratio in the anti-Jaynes--Cummings vertex at f_⋆=√(n̅+1)",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:25Z",
  "url": "https://research.draconitic.com/paper/aaqy186as6wha",
  "venue": "arXiv",
  "versions": []
}