{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,11]],"date-time":"2025-11-11T05:27:43Z","timestamp":1762838863336,"version":"build-2065373602"},"reference-count":36,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2025,11,9]],"date-time":"2025-11-09T00:00:00Z","timestamp":1762646400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["12574301"],"award-info":[{"award-number":["12574301"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100004731","name":"Zhejiang Provincial Natural Science Foundation","doi-asserted-by":"crossref","award":["Grant No. LZ25A040004"],"award-info":[{"award-number":["Grant No. LZ25A040004"]}],"id":[{"id":"10.13039\/501100004731","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Motivated by recent efforts in simulating nonequilibrium scenarios of the Dicke model in quantum-gas cavity QED, we investigate direct probing of the normal-to-superradiant quantum phase transition via Quantum Fisher Information (QFI). This transition represents a paradigmatic example of spontaneous symmetry breaking in quantum optics, where the system\u2019s Z2 symmetry is broken in the superradiant phase. At zero temperature, we derive analytical expressions for the QFI in the limit where the atomic transition frequency\u2014scaled by the cavity frequency\u2014tends to infinity. Furthermore, we analyze the impact of finite temperature on the QFI in both the thermodynamic limit and the regime of a finite but large number of atoms. All results demonstrate that the QFI exhibits a singularity as the coupling crosses the critical point\u2014a clear signature of quantum criticality associated with spontaneous symmetry breaking. The divergent behavior of the QFI across the quantum phase transition directly relates to measuring dynamic susceptibilities using experimentally accessible Bragg spectroscopy tools and resources.<\/jats:p>","DOI":"10.3390\/sym17111918","type":"journal-article","created":{"date-parts":[[2025,11,10]],"date-time":"2025-11-10T10:35:31Z","timestamp":1762770931000},"page":"1918","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Quantum Fisher Information Probing a Quantum-Gas Cavity QED"],"prefix":"10.3390","volume":"17","author":[{"given":"Lehan","family":"Zhu","sequence":"first","affiliation":[{"name":"Department of Physics, Fudan University, Shanghai 200438, China"}]},{"given":"Qian","family":"Wang","sequence":"additional","affiliation":[{"name":"Department of Physics, Zhejiang Normal University, Jinhua 321004, China"}]},{"given":"Zhaoxin","family":"Liang","sequence":"additional","affiliation":[{"name":"Department of Physics, Zhejiang Normal University, Jinhua 321004, China"}]}],"member":"1968","published-online":{"date-parts":[[2025,11,9]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1041","DOI":"10.1103\/RevModPhys.82.1041","article-title":"Quantum interface between light and atomic ensembles","volume":"82","author":"Hammerer","year":"2010","journal-title":"Rev. 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