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Adv."],"published-print":{"date-parts":[[2026,9,25]]},"abstract":"<jats:p>Strengthening light-matter coupling has become a central challenge in cavity quantum electrodynamics (QED), enabling ultrafast gate operations, qubit protection, and deterministic nonlinear optics. As the coupling increases, even the simplest configuration\u2014an atom interacting with a quantized field\u2014requires careful treatment, as exemplified by ongoing debates on quantum Rabi models (QRMs). Here we propose a magnetic graph model for single-atom cavity QED that offers a unified description of quantum dynamics from the weak- to the ultrastrong-coupling regime via graph connectivity. We demonstrate that the generalized QRM maps onto a complex bipartite graph of identical sites under Floquet boundary conditions. This framework captures the crossover from weak to deep-strong coupling via a single metric\u2014the cost of disconnecting a nonmagnetic subgraph. We examine the mechanism underlying this connectivity transition, establishing the pivotal role of phase frustration. Scalable to many-body systems, this approach bridges graph theory and cavity QED, revealing complex-graph dynamics even in the simplest setting.<\/jats:p>","DOI":"10.1126\/sciadv.aee5566","type":"journal-article","created":{"date-parts":[[2026,9,25]],"date-time":"2026-09-25T17:58:53Z","timestamp":1790359133000},"update-policy":"https:\/\/doi.org\/10.34133\/aaas_crossmark","source":"Crossref","is-referenced-by-count":0,"title":["Magnetic graphs for cavity quantum electrodynamics"],"prefix":"10.1126","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8667-6404","authenticated-orcid":true,"given":"Sunkyu","family":"Yu","sequence":"first","affiliation":[{"name":"Intelligent Wave Systems Laboratory, Department of Electrical and Computer Engineering, Seoul National University, Seoul 08826, Korea."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0865-2903","authenticated-orcid":true,"given":"Xianji","family":"Piao","sequence":"additional","affiliation":[{"name":"Wave Engineering Laboratory, School of Electrical and Computer Engineering, University of Seoul, Seoul 02504, Korea."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0197-7633","authenticated-orcid":true,"given":"Namkyoo","family":"Park","sequence":"additional","affiliation":[{"name":"Photonic Systems Laboratory, Department of Electrical and Computer Engineering, Seoul National University, Seoul 08826, Korea."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"221","reference":[{"key":"e_1_3_2_2_2","doi-asserted-by":"publisher","DOI":"10.1038\/s41567-019-0534-4"},{"key":"e_1_3_2_3_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.126.153603"},{"key":"e_1_3_2_4_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.134.063602"},{"key":"e_1_3_2_5_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.132.106902"},{"key":"e_1_3_2_6_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.103.053703"},{"key":"e_1_3_2_7_2","doi-asserted-by":"publisher","DOI":"10.1038\/s41567-023-02155-8"},{"key":"e_1_3_2_8_2","doi-asserted-by":"publisher","DOI":"10.1038\/s41567-023-02178-1"},{"key":"e_1_3_2_9_2","doi-asserted-by":"publisher","DOI":"10.1038\/s42254-018-0006-2"},{"key":"e_1_3_2_10_2","doi-asserted-by":"publisher","DOI":"10.1103\/RevModPhys.91.025005"},{"key":"e_1_3_2_11_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.81.042311"},{"key":"e_1_3_2_12_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.96.023818"},{"key":"e_1_3_2_13_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.84.043832"},{"key":"e_1_3_2_14_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.96.013849"},{"key":"e_1_3_2_15_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.102.023718"},{"key":"e_1_3_2_16_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevResearch.3.023079"},{"key":"e_1_3_2_17_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevResearch.4.023048"},{"key":"e_1_3_2_18_2","doi-asserted-by":"publisher","DOI":"10.1038\/30918"},{"key":"e_1_3_2_19_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.116.220502"},{"key":"e_1_3_2_20_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.132.130601"},{"key":"e_1_3_2_21_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.108.033721"},{"key":"e_1_3_2_22_2","first-page":"2325611","article-title":"Quantum simulation in Fock-state lattices","volume":"9","author":"Yuan J.","year":"2024","unstructured":"J. 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