Chin. Phys. B, 2021, Vol. 30(7): 070601    DOI: 10.1088/1674-1056/abe375
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# Evaluation of second-order Zeeman frequency shift in NTSC-F2

Jun-Ru Shi(施俊如)1,2,3, Xin-Liang Wang(王心亮)1,2,†, Yang Bai(白杨)1,2,3, Fan Yang(杨帆)1,2,3, Yong Guan(管勇)1,2, Dan-Dan Liu(刘丹丹)1,2, Jun Ruan(阮军)1,2, and Shou-Gang Zhang(张首刚)1,2
1 National Time Service Center, Chinese Academy of Sciences, Xi'an 710600, China;
2 Key Laboratory of Time and Frequency Primary Standards, Chinese Academy of Sciences, Xi'an 710600, China;
3 University of Chinese Academy of Sciences, Beijing 100049, China
Abstract  Caesium atomic fountain clock is a primary frequency standard, which realizes the duration of second. Its performance is mostly dominated by the frequency accuracy, and the C-field induced second-order Zeeman frequency shift is the major effect, which limits the accuracy improvement. By applying a high-precision current supply and high-performance magnetic shieldings, the C-field stability has been improved significantly. In order to achieve a uniform C-field, this paper proposes a doubly wound C-field solenoid, which compensates the radial magnetic field along the atomic flight region generated by the lead-out single wire and improves the accuracy evaluation of second-order Zeeman frequency shift. Based on the stable and uniform C-field, we launch the selected atoms to different heights and record the magnetically sensitive Ramsey transition $|F = 3, m_{F} = -1\rangle \to |F = 4, m_{F} = -1\rangle$ central frequency, obtaining this frequency shift as 131.03$\times$10$^{-15}$ and constructing the C-field profile ($\sigma = 0.15$ nT). Meanwhile, during normal operation, we lock NTSC-F2 to the central frequency of the magnetically sensitive Ramsey transition $|F = 3, m_{F} = -1\rangle \to |F = 4, m_{F} = -1\rangle$ fringe for ten consecutive days and record this frequency fluctuation in time domain. The first evaluation of second-order Zeeman frequency shift uncertainty is 0.10$\times$10$^{-15}$. The total deviation of the frequency fluctuation on the clock transition induced by the C-field instability is less than 2.6$\times$10$^{-17}$. Compared with NTSC-F1, NTSC-F2, there appears a significant improvement.
Keywords:  caesium atomic fountain clock      second-order Zeeman frequency shift      C-field      magnetic shielding
Received:  02 December 2020      Revised:  22 January 2021      Accepted manuscript online:  05 February 2021
 PACS: 06.30.Ft (Time and frequency) 07.77.Gx (Atomic and molecular beam sources and detectors) 32.10.-f (Properties of atoms)
Fund: Project supported by the National Key R&D Program of China (Grant No. 2016YFF0200202), the Maintenance and Reformation Program for the Major Science and Technology Fundamental Devices of the Chinese Academy of Sciences (Grant No. DSS-WXGZ-2020-0005), and the Foundation for Western Young Scholars, China (Grant No. XAB2018A06).
Corresponding Authors:  Xin-Liang Wang     E-mail:  wangxl@ntsc.ac.cn