{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,30]],"date-time":"2026-07-30T11:23:16Z","timestamp":1785410596812,"version":"3.56.0"},"reference-count":42,"publisher":"Optica Publishing Group","issue":"5","license":[{"start":{"date-parts":[[2023,2,21]],"date-time":"2023-02-21T00:00:00Z","timestamp":1676937600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/doi.org\/10.1364\/OA_License_v2#VOR-OA"},{"start":{"date-parts":[[2023,2,21]],"date-time":"2023-02-21T00:00:00Z","timestamp":1676937600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/opg.optica.org\/policies\/opg-tdm-policy.json"}],"funder":[{"name":"Space Application System of China Manned Space Program"},{"name":"Science and Technology Major Project of Shanxi","award":["202101030201022"],"award-info":[{"award-number":["202101030201022"]}]},{"DOI":"10.13039\/501100012166","name":"National Key Research and Development Program of China","doi-asserted-by":"publisher","award":["2021YFA1400900"],"award-info":[{"award-number":["2021YFA1400900"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012166","name":"National Key Research and Development Program of China","doi-asserted-by":"publisher","award":["2021YFA0718300"],"award-info":[{"award-number":["2021YFA0718300"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11920101004"],"award-info":[{"award-number":["11920101004"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11934002"],"award-info":[{"award-number":["11934002"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11905245"],"award-info":[{"award-number":["11905245"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["91736208"],"award-info":[{"award-number":["91736208"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61727819"],"award-info":[{"award-number":["61727819"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["opg.optica.org"],"crossmark-restriction":false},"short-container-title":["Opt. Express"],"published-print":{"date-parts":[[2023,2,27]]},"abstract":"<jats:p>We investigated the optomechanical dynamics and explored the quantum phase of a Bose-Einstein condensate in a ring cavity. The interaction between the atoms and the cavity field in the running wave mode induces a semiquantized spin-orbit coupling (SOC) for the atoms. We found that the evolution of the magnetic excitations of the matter field resembles that of an optomechanical oscillator moving in a viscous optical medium, with very good integrability and traceability, regardless of the atomic interaction. Moreover, the light-atom coupling induces a sign-changeable long-range interatomic interaction, which reshapes the typical energy spectrum of the system in a drastic manner. As a result, a new quantum phase featuring a high quantum degeneracy was found in the transitional area for SOC. Our scheme is immediately realizable and the results are measurable in experiments.<\/jats:p>","DOI":"10.1364\/oe.477780","type":"journal-article","created":{"date-parts":[[2023,2,1]],"date-time":"2023-02-01T09:00:08Z","timestamp":1675242008000},"page":"8240","update-policy":"https:\/\/doi.org\/10.1364\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Optomechanics and quantum phase of the Bose-Einstein condensate with the cavity mediated spin-orbit coupling"],"prefix":"10.1364","volume":"31","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6025-6444","authenticated-orcid":true,"given":"Peng","family":"Zhang","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/00655qp86","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Pengju","family":"Tang","sequence":"additional","affiliation":[{"name":"Peking University"},{"name":"China Academy of Electronics and Information Technology"},{"name":"Yangtze Delta Region Industrial Innovation Center of Quantum and Information Technology"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ruizhi","family":"Pan","sequence":"additional","affiliation":[{"name":"Peking University"},{"name":"NIST\/University of Maryland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xuzong","family":"Chen","sequence":"additional","affiliation":[{"name":"Peking University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiaoji","family":"Zhou","sequence":"additional","affiliation":[{"name":"Peking University"},{"name":"Shanxi University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shougang","family":"Zhang","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/00655qp86","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"285","published-online":{"date-parts":[[2023,2,21]]},"reference":[{"key":"oe-31-5-8240-R1","doi-asserted-by":"publisher","first-page":"268","DOI":"10.1038\/nature06120","volume":"450","author":"Brennecke","year":"2007","journal-title":"Nature"},{"key":"oe-31-5-8240-R2","doi-asserted-by":"publisher","first-page":"011602","DOI":"10.1103\/PhysRevA.89.011602","volume":"89","author":"Dong","year":"2014","journal-title":"Phys. Rev. A"},{"key":"oe-31-5-8240-R3","doi-asserted-by":"publisher","first-page":"1391","DOI":"10.1103\/RevModPhys.86.1391","volume":"86","author":"Aspelmeyer","year":"2014","journal-title":"Rev. Mod. Phys."},{"key":"oe-31-5-8240-R4","doi-asserted-by":"publisher","first-page":"7786","DOI":"10.1364\/OE.23.007786","volume":"23","author":"Asjad","year":"2015","journal-title":"Opt. Express"},{"key":"oe-31-5-8240-R5","doi-asserted-by":"publisher","first-page":"42306","DOI":"10.1364\/OE.446744","volume":"29","author":"Abbas","year":"2021","journal-title":"Opt. Express"},{"key":"oe-31-5-8240-R6","doi-asserted-by":"publisher","first-page":"095301","DOI":"10.1103\/PhysRevLett.109.095301","volume":"109","author":"Wang","year":"2012","journal-title":"Phys. Rev. Lett."},{"key":"oe-31-5-8240-R7","doi-asserted-by":"publisher","first-page":"83","DOI":"10.1038\/nature09887","volume":"471","author":"-J. Lin","year":"2011","journal-title":"Nature"},{"key":"oe-31-5-8240-R8","doi-asserted-by":"publisher","first-page":"83","DOI":"10.1126\/science.aaf6689","volume":"354","author":"Wu","year":"2016","journal-title":"Science"},{"key":"oe-31-5-8240-R9","doi-asserted-by":"publisher","first-page":"59","DOI":"10.1126\/science.aaz3071","volume":"367","author":"Dutt","year":"2019","journal-title":"Science"},{"key":"oe-31-5-8240-R10","doi-asserted-by":"publisher","first-page":"2080","DOI":"10.1016\/j.scib.2020.09.036","volume":"65","author":"Lu","year":"2020","journal-title":"Sci. Bull."},{"key":"oe-31-5-8240-R11","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1103\/PhysRevA.103.053318","volume":"103","author":"Lei","year":"2021","journal-title":"Sci. Bull."},{"key":"oe-31-5-8240-R12","doi-asserted-by":"publisher","first-page":"87","DOI":"10.1038\/nature03804","volume":"436","author":"Birnbaum","year":"2005","journal-title":"Nature"},{"key":"oe-31-5-8240-R13","doi-asserted-by":"publisher","first-page":"272","DOI":"10.1038\/nature06331","volume":"450","author":"Colombe","year":"2007","journal-title":"Nature"},{"key":"oe-31-5-8240-R14","doi-asserted-by":"publisher","first-page":"235","DOI":"10.1126\/science.1163218","volume":"322","author":"Brennecke","year":"2008","journal-title":"Science"},{"key":"oe-31-5-8240-R15","doi-asserted-by":"publisher","first-page":"013614","DOI":"10.1103\/PhysRevA.84.013614","volume":"84","author":"Zhang","year":"2011","journal-title":"Phys. Rev. A"},{"key":"oe-31-5-8240-R16","doi-asserted-by":"publisher","first-page":"602","DOI":"10.1038\/s41586-020-2224-x","volume":"580","author":"Muniz","year":"2020","journal-title":"Nature"},{"key":"oe-31-5-8240-R17","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1103\/PhysRevLett.128.080601","volume":"128","author":"Lozano-M\u00e9ndez","year":"2022","journal-title":"Phys. Rev. Lett."},{"key":"oe-31-5-8240-R18","doi-asserted-by":"publisher","first-page":"1359","DOI":"10.1126\/science.abd4385","volume":"373","author":"Zhang","year":"2021","journal-title":"Science"},{"key":"oe-31-5-8240-R19","doi-asserted-by":"publisher","first-page":"053621","DOI":"10.1103\/PhysRevA.94.053621","volume":"94","author":"Zhu","year":"2016","journal-title":"Phys. Rev. A"},{"key":"oe-31-5-8240-R20","doi-asserted-by":"publisher","first-page":"213601","DOI":"10.1103\/PhysRevLett.99.213601","volume":"99","author":"Gupta","year":"2007","journal-title":"Phys. Rev. Lett."},{"key":"oe-31-5-8240-R21","doi-asserted-by":"publisher","first-page":"143007","DOI":"10.1103\/PhysRevLett.112.143007","volume":"112","author":"Deng","year":"2014","journal-title":"Phys. Rev. Lett."},{"key":"oe-31-5-8240-R22","doi-asserted-by":"publisher","first-page":"115302","DOI":"10.1103\/PhysRevLett.112.115302","volume":"112","author":"Schmidt","year":"2014","journal-title":"Phys. Rev. Lett."},{"key":"oe-31-5-8240-R23","doi-asserted-by":"publisher","first-page":"073003","DOI":"10.1103\/PhysRevLett.113.073003","volume":"113","author":"Goldwin","year":"2014","journal-title":"Phys. Rev. Lett."},{"key":"oe-31-5-8240-R24","doi-asserted-by":"publisher","first-page":"033601","DOI":"10.1103\/PhysRevLett.124.033601","volume":"124","author":"Ostermann","year":"2020","journal-title":"Phys. Rev. Lett."},{"key":"oe-31-5-8240-R25","doi-asserted-by":"publisher","first-page":"163601","DOI":"10.1103\/PhysRevLett.121.163601","volume":"121","author":"Kroeze","year":"2018","journal-title":"Phys. Rev. Lett."},{"key":"oe-31-5-8240-R26","doi-asserted-by":"publisher","first-page":"160404","DOI":"10.1103\/PhysRevLett.123.160404","volume":"123","author":"Kroeze","year":"2019","journal-title":"Phys. Rev. Lett."},{"key":"oe-31-5-8240-R27","doi-asserted-by":"publisher","first-page":"5202","DOI":"10.1103\/PhysRevLett.83.5202","volume":"83","author":"Moore","year":"1999","journal-title":"Phys. Rev. Lett."},{"key":"oe-31-5-8240-R28","doi-asserted-by":"publisher","first-page":"013804","DOI":"10.1103\/PhysRevA.75.013804","volume":"75","author":"Dimer","year":"2007","journal-title":"Phys. Rev. A"},{"key":"oe-31-5-8240-R29","doi-asserted-by":"publisher","first-page":"1301","DOI":"10.1038\/nature09009","volume":"464","author":"Baumann","year":"2010","journal-title":"Nature"},{"key":"oe-31-5-8240-R30","doi-asserted-by":"publisher","first-page":"14377","DOI":"10.1364\/OE.21.014377","volume":"21","author":"Wang","year":"2013","journal-title":"Opt. Express"},{"key":"oe-31-5-8240-R31","doi-asserted-by":"publisher","first-page":"053629","DOI":"10.1103\/PhysRevA.88.053629","volume":"88","author":"Zhai","year":"2013","journal-title":"Phys. Rev. A"},{"key":"oe-31-5-8240-R32","doi-asserted-by":"publisher","first-page":"033607","DOI":"10.1103\/PhysRevA.94.033607","volume":"94","author":"Niederle","year":"2016","journal-title":"Phys. Rev. A"},{"key":"oe-31-5-8240-R33","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1103\/PhysRevX.6.011032","volume":"6","author":"Aron","year":"2016","journal-title":"Phys. Rev. X"},{"key":"oe-31-5-8240-R34","doi-asserted-by":"publisher","first-page":"1570","DOI":"10.1126\/science.1220314","volume":"336","author":"Mottl","year":"2012","journal-title":"Science"},{"key":"oe-31-5-8240-R35","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1103\/PhysRevLett.102.130401","volume":"102","author":"-J. Lin","year":"2009","journal-title":"Phys. Rev. Lett."},{"key":"oe-31-5-8240-R36","doi-asserted-by":"publisher","first-page":"769","DOI":"10.1038\/nphys2789","volume":"9","author":"Parker","year":"2013","journal-title":"Nat. Phys."},{"key":"oe-31-5-8240-R38","doi-asserted-by":"publisher","first-page":"023621","DOI":"10.1103\/PhysRevA.91.023621","volume":"91","author":"Wilson","year":"2015","journal-title":"Phys. Rev. A"},{"key":"oe-31-5-8240-R39","doi-asserted-by":"publisher","first-page":"509","DOI":"10.1038\/nphys1304","volume":"5","author":"Schliesser","year":"2009","journal-title":"Nat. Phys."},{"key":"oe-31-5-8240-R40","doi-asserted-by":"publisher","first-page":"801","DOI":"10.1126\/science.1231282","volume":"339","author":"Purdy","year":"2013","journal-title":"Science"},{"key":"oe-31-5-8240-R41","doi-asserted-by":"publisher","first-page":"1043","DOI":"10.1126\/science.1196442","volume":"331","author":"Swallows","year":"2017","journal-title":"Science"},{"key":"oe-31-5-8240-R42","doi-asserted-by":"publisher","first-page":"38359","DOI":"10.1364\/OE.378632","volume":"27","author":"Elvin","year":"2019","journal-title":"Opt. Express"},{"key":"oe-31-5-8240-R43","doi-asserted-by":"publisher","first-page":"19593","DOI":"10.1364\/OE.389644","volume":"28","author":"Skljarow","year":"2020","journal-title":"Opt. Express"}],"container-title":["Optics Express"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/opg.optica.org\/viewmedia.cfm?URI=oe-31-5-8240&seq=0","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,6]],"date-time":"2024-08-06T15:32:26Z","timestamp":1722958346000},"score":1,"resource":{"primary":{"URL":"https:\/\/opg.optica.org\/abstract.cfm?URI=oe-31-5-8240"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,2,21]]},"references-count":42,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2023]]},"published-print":{"date-parts":[[2023]]}},"URL":"https:\/\/doi.org\/10.1364\/oe.477780","relation":{},"ISSN":["1094-4087"],"issn-type":[{"value":"1094-4087","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,2,21]]},"assertion":[{"value":"Optica Publishing Group","name":"publisher","label":"This article is maintained by"},{"value":"https:\/\/doi.org\/10.1364\/OE.477780","name":"articlelink","label":"Crossref DOI link to publisher maintained version"},{"value":"research-article","name":"content_type","label":"Article type"},{"value":"Screened by Similarity Check","name":"cross_check","label":"Similarity check"},{"value":"Yes","order":0,"name":"peer_reviewed","label":"Peer reviewed","group":{"name":"peer_review","label":"Peer review"}},{"value":"Single blind","order":1,"name":"review_process","label":"Review process","group":{"name":"peer_review","label":"Peer review"}},{"value":"24 October 2022","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"9 January 2023","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"21 February 2023","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}},{"value":"\u00a9 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement","name":"copyright","label":"Copyright"}]}}