{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,31]],"date-time":"2026-03-31T20:59:17Z","timestamp":1774990757874,"version":"3.50.1"},"reference-count":56,"publisher":"MDPI AG","issue":"15","license":[{"start":{"date-parts":[[2020,7,30]],"date-time":"2020-07-30T00:00:00Z","timestamp":1596067200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"the National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["No. 61571018"],"award-info":[{"award-number":["No. 61571018"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"the National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["No. 61531003"],"award-info":[{"award-number":["No. 61531003"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"the National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["No. 91436210"],"award-info":[{"award-number":["No. 91436210"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"the National Science Fund for Distinguished Young Scholars of China","award":["No. 61225003"],"award-info":[{"award-number":["No. 61225003"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>A magnetically-quiet environment is important for detecting faint magnetic-field signals or nonmagnetic spin-dependent interactions. Passive magnetic shielding using layers of large magnetic-permeability materials is widely used to reduce the magnetic-field noise. The magnetic-field noise can also be actively monitored with magnetometers and then compensated, acting as a complementary method to the passive shielding. We present here a general model to quantitatively depict and optimize the performance of active magnetic-field stabilization and experimentally verify our model using optically-pumped atomic magnetometers. We experimentally demonstrate a magnetic-field noise rejection ratio of larger than \u223c800 at low frequencies and an environment with a magnetic-field noise floor of \u223c40 fT\/Hz1\/2 in unshielded Earth\u2019s field. The proposed model provides a general guidance on analyzing and improving the performance of active magnetic-field stabilization with magnetometers. This work offers the possibility of sensitive detections of magnetic-field signals in a variety of unshielded natural environments.<\/jats:p>","DOI":"10.3390\/s20154241","type":"journal-article","created":{"date-parts":[[2020,7,30]],"date-time":"2020-07-30T12:15:38Z","timestamp":1596111338000},"page":"4241","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":29,"title":["Active Magnetic-Field Stabilization with Atomic Magnetometer"],"prefix":"10.3390","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0512-3280","authenticated-orcid":false,"given":"Rui","family":"Zhang","sequence":"first","affiliation":[{"name":"College of Liberal Arts and Sciences, and Interdisciplinary Center for Quantum Information, National University of Defense Technology, Changsha 410073, China"},{"name":"State Key Laboratory of Advanced Optical Communication Systems and Networks, Department of Electronics, and Center for Quantum Information Technology, Peking University, Beijing 100871, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8525-7312","authenticated-orcid":false,"given":"Yudong","family":"Ding","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Advanced Optical Communication Systems and Networks, Department of Electronics, and Center for Quantum Information Technology, Peking University, Beijing 100871, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4568-3450","authenticated-orcid":false,"given":"Yucheng","family":"Yang","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Advanced Optical Communication Systems and Networks, Department of Electronics, and Center for Quantum Information Technology, Peking University, Beijing 100871, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1109-2049","authenticated-orcid":false,"given":"Zhaoyu","family":"Zheng","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Advanced Optical Communication Systems and Networks, Department of Electronics, and Center for Quantum Information Technology, Peking University, Beijing 100871, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9802-4577","authenticated-orcid":false,"given":"Jingbiao","family":"Chen","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Advanced Optical Communication Systems and Networks, Department of Electronics, and Center for Quantum Information Technology, Peking University, Beijing 100871, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0815-5122","authenticated-orcid":false,"given":"Xiang","family":"Peng","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Advanced Optical Communication Systems and Networks, Department of Electronics, and Center for Quantum Information Technology, Peking University, Beijing 100871, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7707-7474","authenticated-orcid":false,"given":"Teng","family":"Wu","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Advanced Optical Communication Systems and Networks, Department of Electronics, and Center for Quantum Information Technology, Peking University, Beijing 100871, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0644-6698","authenticated-orcid":false,"given":"Hong","family":"Guo","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Advanced Optical Communication Systems and Networks, Department of Electronics, and Center for Quantum Information Technology, Peking University, Beijing 100871, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,7,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"664","DOI":"10.1126\/science.175.4022.664","article-title":"Magnetoencephalography: Detection of the brain\u2019s electrical activity with a superconducting magnetometer","volume":"175","author":"Cohen","year":"1972","journal-title":"Science"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"211104","DOI":"10.1063\/1.2392722","article-title":"Magnetoencephalography with an atomic magnetometer","volume":"89","author":"Xia","year":"2006","journal-title":"Appl. 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