{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:37:49Z","timestamp":1760236669864,"version":"build-2065373602"},"reference-count":24,"publisher":"MDPI AG","issue":"24","license":[{"start":{"date-parts":[[2021,12,13]],"date-time":"2021-12-13T00:00:00Z","timestamp":1639353600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Key R&amp;D Program of China","award":["2016YFF0200202"],"award-info":[{"award-number":["2016YFF0200202"]}]},{"name":"the Foundation for Western Young Scholars, China","award":["XAB2018A06"],"award-info":[{"award-number":["XAB2018A06"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Second-order Zeeman frequency shift is one of the major systematic factors affecting the frequency uncertainty performance of cesium atomic fountain clock. Second-order Zeeman frequency shift is calculated by experimentally measuring the central frequency of the (1,1) or (\u22121,\u22121) magnetically sensitive Ramsey transition. The low-frequency transition method can be used to measure the magnetic field strength and to predict the central fringe of (1,1) or (\u22121,\u22121) magnetically sensitive Ramsey transition. In this paper, we deduce the formula for magnetic field measurement using the low-frequency transition method and measured the magnetic field distribution of 4 cm inside the Ramsey cavity and 32 cm along the flight region experimentally. The result shows that the magnetic field fluctuation is less than 1 nT. The influence of low-frequency pulse signal duration on the accuracy of magnetic field measurement is studied and the optimal low-frequency pulse signal duration is determined. The central fringe of (\u22121,\u22121) magnetically sensitive Ramsey transition can be predicted by using a numerical integrating of the magnetic field \u201cmap\u201d. Comparing the predicted central fringe with that identified by Ramsey method, the frequency difference between these two is, at most, a fringe width of 0.3. We apply the experimentally measured central frequency of the (\u22121,\u22121) Ramsey transition to the Breit-Rabi formula, and the second-order Zeeman frequency shift is calculated as 131.03 \u00d7 10\u221215, with the uncertainty of 0.10 \u00d7 10\u221215.<\/jats:p>","DOI":"10.3390\/s21248333","type":"journal-article","created":{"date-parts":[[2021,12,14]],"date-time":"2021-12-14T01:22:05Z","timestamp":1639444925000},"page":"8333","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["The Application of Low-Frequency Transition in the Assessment of the Second-Order Zeeman Frequency Shift"],"prefix":"10.3390","volume":"21","author":[{"given":"Yang","family":"Bai","sequence":"first","affiliation":[{"name":"National Time Service Center, Chinese Academy of Sciences, Shu Yuan Road, Xi\u2019an 710600, China"},{"name":"Key Laboratory of Time and Frequency Primary Standards, National Time Service Center, Chinese Academy of Sciences, Xi\u2019an 710600, China"},{"name":"University of Chinese Academy of Sciences, Yu Quan Road, Beijing 100049, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xinliang","family":"Wang","sequence":"additional","affiliation":[{"name":"National Time Service Center, Chinese Academy of Sciences, Shu Yuan Road, Xi\u2019an 710600, China"},{"name":"Key Laboratory of Time and Frequency Primary Standards, National Time Service Center, Chinese Academy of Sciences, Xi\u2019an 710600, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Junru","family":"Shi","sequence":"additional","affiliation":[{"name":"National Time Service Center, Chinese Academy of Sciences, Shu Yuan Road, Xi\u2019an 710600, China"},{"name":"Key Laboratory of Time and Frequency Primary Standards, National Time Service Center, Chinese Academy of Sciences, Xi\u2019an 710600, China"},{"name":"University of Chinese Academy of Sciences, Yu Quan Road, Beijing 100049, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fan","family":"Yang","sequence":"additional","affiliation":[{"name":"National Time Service Center, Chinese Academy of Sciences, Shu Yuan Road, Xi\u2019an 710600, China"},{"name":"Key Laboratory of Time and Frequency Primary Standards, National Time Service Center, Chinese Academy of Sciences, Xi\u2019an 710600, China"},{"name":"University of Chinese Academy of Sciences, Yu Quan Road, Beijing 100049, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jun","family":"Ruan","sequence":"additional","affiliation":[{"name":"National Time Service Center, Chinese Academy of Sciences, Shu Yuan Road, Xi\u2019an 710600, China"},{"name":"Key Laboratory of Time and Frequency Primary Standards, National Time Service Center, Chinese Academy of Sciences, Xi\u2019an 710600, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ruifang","family":"Dong","sequence":"additional","affiliation":[{"name":"National Time Service Center, Chinese Academy of Sciences, Shu Yuan Road, Xi\u2019an 710600, China"},{"name":"Key Laboratory of Time and Frequency Primary Standards, National Time Service Center, Chinese Academy of Sciences, Xi\u2019an 710600, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shougang","family":"Zhang","sequence":"additional","affiliation":[{"name":"National Time Service Center, Chinese Academy of Sciences, Shu Yuan Road, Xi\u2019an 710600, China"},{"name":"Key Laboratory of Time and Frequency Primary Standards, National Time Service Center, Chinese Academy of Sciences, Xi\u2019an 710600, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,12,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"108","DOI":"10.1088\/0026-1394\/51\/1\/108","article-title":"Contributing to TAI with a Secondary Representation of the SI Second","volume":"51","author":"Abgrall","year":"2014","journal-title":"Metrologia"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"070601","DOI":"10.1088\/1674-1056\/24\/7\/070601","article-title":"Recent improvements on the atomic fountain clock at SIOM Project supported by the National Natural Science Foundation of China (Grant Nos.61275204 and 91336105)","volume":"24","author":"Du","year":"2015","journal-title":"Chin. 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