{"paper":{"title":"Self-adjoint extensions of $k$-photon light-matter Hamiltonians","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"Daniel Burgarth, Davide Lonigro, Felix Fischer, Felix Knapp","submitted_at":"2026-07-24T15:04:35Z","abstract_excerpt":"Multiphoton light-matter interactions, in which a bosonic mode exchanges $k$ excitations at a time with a quantum system, are a source of genuine nonlinearity in quantum optics and are increasingly accessible experimentally. Here we study the class of operators $H = H_{\\rm mat}\\otimes I + I\\otimes\\omega a^\\ast a + \\Sigma\\otimes(a^\\ast)^k + \\Sigma^\\ast\\otimes a^k$ on $\\mathcal{H}\\otimes L^2(\\mathbb{R})$, coupling a single bosonic mode to an arbitrary matter system through a bounded operator $\\Sigma$. When $\\Sigma$ is normal and nonzero, we prove that $H$ is self-adjoint if and only if $k\\leq2$;"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.22378","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.22378/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}