{
  "abstract": "Higher-order squeezing captures non-Gaussian features of quantum light by probing moments of the field beyond the variance, and is associated with operators involving nonlinear combinations of creation and annihilation operators. Here we study a class of operators of the form ξ ( a † ) k a l + ξ ∗ ( a † ) l a k + f ( a † a ) , which arise naturally in the analysis of higher-order quantum fluctuations. The operators are defined on the linear span of Fock states. We show that the essential self-adjointness of these operators depends on the asymptotics of the real-valued function f ( n ) at infinity. In particular, pure higher-order squeezing operators ( k ⩾ 3 , l = 0 , and f ( n ) = 0 ) are not essentially self-adjoint, but adding a properly chosen term f ( a † a ) , like a Kerr term, can have a regularizing effect and restore essential self-adjointness. In the non-self-adjoint regime, we compute the deficiency indices and classify all self-adjoint extensions. Our results provide a rigorous operator-theoretic foundation for modeling and interpreting higher-order squeezing in quantum optics, and reveal interesting connections with the Birkhoff–Trjitzinsky theory of asymptotic expansions for recurrence relations.",
  "abstract_shown": true,
  "affiliations": [
    "Friedrich-Alexander-Universität Erlangen-Nürnberg"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 3,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Felix Fischer",
      "orcid": "0009-0001-3040-8184"
    },
    {
      "affs": [
        0
      ],
      "name": "Daniel Klaus Burgarth",
      "orcid": "0000-0003-4063-1264"
    },
    {
      "affs": [
        0
      ],
      "name": "Davide Lonigro",
      "orcid": "0000-0002-0792-8122"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a56ag2w5meab9.bib",
  "cited_by": 10,
  "doi": "10.1088/1751-8121/ae7acb",
  "fulltext_url": null,
  "id": "a56ag2w5meab9",
  "issns": [
    "1751-8113",
    "1751-8121"
  ],
  "landing_url": "https://doi.org/10.1088/1751-8121/ae7acb",
  "language": "en",
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "2610|Spectral Theory in Mathematical Physics"
    ]
  ],
  "openalex": "W4416244018",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-06-09",
  "publisher": "Institute of Physics",
  "ris": "https://research.draconitic.com/paper/a56ag2w5meab9.ris",
  "sources": [
    {
      "first_seen": "2026-11-07T13:20:42Z",
      "native_id": "W4416244018",
      "source": "openalex",
      "url": "https://doi.org/10.1088/1751-8121/ae7acb"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2610|Spectral Theory in Mathematical Physics",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Self-adjoint realizations of higher-order squeezing operators",
  "title_text": "Self-adjoint realizations of higher-order squeezing operators",
  "type": "peer-reviewed",
  "updated_at": "2026-11-07T13:20:42Z",
  "url": "https://research.draconitic.com/paper/a56ag2w5meab9",
  "venue": "Journal of Physics A Mathematical and Theoretical",
  "versions": []
}