{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,26]],"date-time":"2026-08-26T18:21:46Z","timestamp":1787768506120,"version":"build-2784847793"},"reference-count":55,"publisher":"American Association for the Advancement of Science (AAAS)","issue":"35","funder":[{"DOI":"10.13039\/501100000781","name":"European Research Council","doi-asserted-by":"publisher","award":["101040409"],"award-info":[{"award-number":["101040409"]}],"id":[{"id":"10.13039\/501100000781","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["277625399"],"award-info":[{"award-number":["277625399"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["EXC 2004\/1\u2013390534769"],"award-info":[{"award-number":["EXC 2004\/1\u2013390534769"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["EXC 2004\/1\u2013390534769"],"award-info":[{"award-number":["EXC 2004\/1\u2013390534769"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["277625399"],"award-info":[{"award-number":["277625399"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]},{"name":"UNAM-PAPIIT","award":["IN-117623"],"award-info":[{"award-number":["IN-117623"]}]},{"name":"UNAM-PAPIIT","award":["IA-101325"],"award-info":[{"award-number":["IA-101325"]}]},{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["EXC 2181 390900948"],"award-info":[{"award-number":["EXC 2181 390900948"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]},{"name":"UNAM-PAPIIT","award":["IN-117623"],"award-info":[{"award-number":["IN-117623"]}]}],"content-domain":{"domain":["www.science.org"],"crossmark-restriction":true},"short-container-title":["Sci. Adv."],"published-print":{"date-parts":[[2026,8,28]]},"abstract":"<jats:p>Critical exponents characterize the divergent scaling of thermodynamic quantities near phase transitions and allow for the classification of physical systems into universality classes. While quantum gases thermalizing by interparticle interactions fall into the XY model universality class, the ideal Bose gas has been predicted to form a distinct universality class whose signatures have not yet been revealed experimentally. Here, we report the observation of critical scaling in a two-dimensional trapped quantum gas of essentially noninteracting photons, which thermalize by radiative contact to a reservoir of molecules inside a microcavity. By measuring the spatial correlations near the condensation transition, we determine the critical exponent for the correlation length to be \u03bd\u00a0=\u00a00.52\u00a0\u00b1\u00a00.04. Our results constitute an experimental test of the long-standing scaling predictions for the Bose gas universality class.<\/jats:p>","DOI":"10.1126\/sciadv.aee2942","type":"journal-article","created":{"date-parts":[[2026,8,26]],"date-time":"2026-08-26T17:59:39Z","timestamp":1787767179000},"update-policy":"https:\/\/doi.org\/10.34133\/aaas_crossmark","source":"Crossref","is-referenced-by-count":0,"title":["Observation of critical scaling in the Bose gas universality class"],"prefix":"10.1126","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7460-3387","authenticated-orcid":true,"given":"Leon","family":"Kleebank","sequence":"first","affiliation":[{"name":"Institut f\u00fcr Angewandte Physik, Universit\u00e4t Bonn, Bonn 53115, Germany."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7818-2981","authenticated-orcid":true,"given":"Frank","family":"Vewinger","sequence":"additional","affiliation":[{"name":"Institut f\u00fcr Angewandte Physik, Universit\u00e4t Bonn, Bonn 53115, Germany."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5161-5468","authenticated-orcid":true,"given":"Arturo","family":"Camacho-Guardian","sequence":"additional","affiliation":[{"name":"Instituto de F\u00edsica, Universidad Nacional Aut\u00f3noma de M\u00e9xico, Apdo. Postal 20-364, 01000 Cd. M\u00e9xico, Mexico."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4987-1600","authenticated-orcid":true,"given":"Victor","family":"Romero-Roch\u00edn","sequence":"additional","affiliation":[{"name":"Instituto de F\u00edsica, Universidad Nacional Aut\u00f3noma de M\u00e9xico, Apdo. Postal 20-364, 01000 Cd. M\u00e9xico, Mexico."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8855-606X","authenticated-orcid":true,"given":"Rosario","family":"Paredes","sequence":"additional","affiliation":[{"name":"Instituto de F\u00edsica, Universidad Nacional Aut\u00f3noma de M\u00e9xico, Apdo. Postal 20-364, 01000 Cd. M\u00e9xico, Mexico."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4236-318X","authenticated-orcid":true,"given":"Martin","family":"Weitz","sequence":"additional","affiliation":[{"name":"Institut f\u00fcr Angewandte Physik, Universit\u00e4t Bonn, Bonn 53115, Germany."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0002-3777","authenticated-orcid":true,"given":"Julian","family":"Schmitt","sequence":"additional","affiliation":[{"name":"Institut f\u00fcr Angewandte Physik, Universit\u00e4t Bonn, Bonn 53115, Germany."},{"name":"Kirchhoff-Institut f\u00fcr Physik, Universit\u00e4t Heidelberg, Heidelberg 69120, Germany."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"221","reference":[{"key":"e_1_3_1_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ppnp.2003.09.002"},{"key":"e_1_3_1_3_2","doi-asserted-by":"publisher","DOI":"10.1088\/0034-4885\/66\/12\/R01"},{"key":"e_1_3_1_4_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.44.631"},{"key":"e_1_3_1_5_2","doi-asserted-by":"publisher","DOI":"10.1070\/PU1988v031n04ABEH005749"},{"key":"e_1_3_1_6_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.68.174518"},{"key":"e_1_3_1_7_2","doi-asserted-by":"publisher","DOI":"10.1134\/S0021364007130097"},{"key":"e_1_3_1_8_2","doi-asserted-by":"publisher","DOI":"10.1038\/nature09722"},{"key":"e_1_3_1_9_2","doi-asserted-by":"publisher","DOI":"10.1126\/science.1214987"},{"key":"e_1_3_1_10_2","doi-asserted-by":"publisher","DOI":"10.1126\/science.1138807"},{"key":"e_1_3_1_11_2","doi-asserted-by":"publisher","DOI":"10.1126\/science.1258676"},{"key":"e_1_3_1_12_2","doi-asserted-by":"publisher","DOI":"10.1126\/sciadv.adi6762"},{"key":"e_1_3_1_13_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.24.1479"},{"key":"e_1_3_1_14_2","doi-asserted-by":"publisher","DOI":"10.1103\/RevModPhys.39.395"},{"key":"e_1_3_1_15_2","doi-asserted-by":"publisher","DOI":"10.1088\/0034-4885\/30\/2\/306"},{"key":"e_1_3_1_16_2","doi-asserted-by":"publisher","DOI":"10.1103\/RevModPhys.55.583"},{"key":"e_1_3_1_17_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.72.3238"},{"key":"e_1_3_1_18_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.63.214503"},{"key":"e_1_3_1_19_2","doi-asserted-by":"publisher","DOI":"10.1038\/s41586-022-05001-8"},{"key":"e_1_3_1_20_2","doi-asserted-by":"publisher","DOI":"10.1126\/science.aeb4154"},{"key":"e_1_3_1_21_2","doi-asserted-by":"crossref","unstructured":"A. Einstein \u201cQuantentheorie des einatomigen idealen Gases. Zweite Abhandlung \u201d in Albert Einstein: Akademie-Vortr\u00e4ge (Wiley 2005) pp. 245\u2013257.","DOI":"10.1002\/3527608958.ch28"},{"key":"e_1_3_1_22_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRev.166.152"},{"key":"e_1_3_1_23_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRev.188.522"},{"key":"e_1_3_1_24_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.90.033605"},{"key":"e_1_3_1_25_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.81.033615"},{"key":"e_1_3_1_26_2","doi-asserted-by":"publisher","DOI":"10.1088\/1751-8113\/47\/8\/085201"},{"key":"e_1_3_1_27_2","doi-asserted-by":"crossref","unstructured":"R. P. Smith \u201cEffects of Interactions on Bose-Einstein Condensation \u201d in Universal Themes of Bose-Einstein Condensation N. P. Proukakis D. W. Snoke P. B. Littlewood Eds. (Cambridge University Press 2017) pp. 99\u2013116.","DOI":"10.1017\/9781316084366.008"},{"key":"e_1_3_1_28_2","doi-asserted-by":"publisher","DOI":"10.1088\/1742-5468\/ab4984"},{"key":"e_1_3_1_29_2","first-page":"389","article-title":"Two-dimensional Bose fluids: An atomic physics perspective","volume":"34","author":"Hadzibabic Z.","year":"2011","unstructured":"Z. Hadzibabic, J. Dalibard, Two-dimensional Bose fluids: An atomic physics perspective. Riv. del Nuovo Cim. 34, 389 (2011).","journal-title":"Riv. del Nuovo Cim."},{"key":"e_1_3_1_30_2","doi-asserted-by":"publisher","DOI":"10.1038\/nature04851"},{"key":"e_1_3_1_31_2","doi-asserted-by":"publisher","DOI":"10.1088\/1742-5468\/2011\/02\/P02032"},{"key":"e_1_3_1_32_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.114.255302"},{"key":"e_1_3_1_33_2","doi-asserted-by":"publisher","DOI":"10.1038\/nature09567"},{"key":"e_1_3_1_34_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.91.033813"},{"key":"e_1_3_1_35_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.98.013810"},{"key":"e_1_3_1_36_2","doi-asserted-by":"publisher","DOI":"10.1126\/science.1140990"},{"key":"e_1_3_1_37_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.110.200406"},{"key":"e_1_3_1_38_2","doi-asserted-by":"publisher","DOI":"10.1126\/science.abm2543"},{"key":"e_1_3_1_39_2","doi-asserted-by":"publisher","DOI":"10.1038\/s42005-025-01977-7"},{"key":"e_1_3_1_40_2","doi-asserted-by":"publisher","DOI":"10.1209\/0295-5075\/130\/54001"},{"key":"e_1_3_1_41_2","doi-asserted-by":"publisher","DOI":"10.1002\/adom.202202820"},{"key":"e_1_3_1_42_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.92.011602"},{"key":"e_1_3_1_43_2","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6455\/aad409"},{"key":"e_1_3_1_44_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.111.100404"},{"key":"e_1_3_1_45_2","doi-asserted-by":"publisher","DOI":"10.1038\/nphoton.2017.139"},{"key":"e_1_3_1_46_2","doi-asserted-by":"publisher","DOI":"10.1038\/s41586-025-08616-9"},{"key":"e_1_3_1_47_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01331132"},{"key":"e_1_3_1_48_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.17.1273"},{"key":"e_1_3_1_49_2","doi-asserted-by":"publisher","DOI":"10.1016\/0030-4018(75)90081-4"},{"key":"e_1_3_1_50_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.106.230401"},{"key":"e_1_3_1_51_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevResearch.2.033018"},{"key":"e_1_3_1_52_2","first-page":"021052","article-title":"Universal phenomenology at critical exceptional points of nonequilibrium O(n) models","volume":"14","author":"Zelle C. P.","year":"2024","unstructured":"C. P. Zelle, R. Daviet, A. Rosch, S. Diehl, Universal phenomenology at critical exceptional points of nonequilibrium O(n) models. Phys. Rev. X 14, 021052 (2024).","journal-title":"Phys. Rev. X"},{"key":"e_1_3_1_53_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.114.061601"},{"key":"e_1_3_1_54_2","doi-asserted-by":"publisher","DOI":"10.1038\/nphys1680"},{"key":"e_1_3_1_55_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.59.4595"},{"key":"e_1_3_1_56_2","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6455\/ad2860"}],"container-title":["Science Advances"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.science.org\/doi\/pdf\/10.1126\/sciadv.aee2942","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,26]],"date-time":"2026-08-26T18:01:12Z","timestamp":1787767272000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.science.org\/doi\/10.1126\/sciadv.aee2942"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,8,28]]},"references-count":55,"journal-issue":{"issue":"35","published-print":{"date-parts":[[2026,8,28]]}},"alternative-id":["10.1126\/sciadv.aee2942"],"URL":"https:\/\/doi.org\/10.1126\/sciadv.aee2942","relation":{},"ISSN":["2375-2548"],"issn-type":[{"value":"2375-2548","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,8,28]]},"assertion":[{"value":"2025-11-27","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2026-07-16","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2026-08-26","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"eaee2942"}}