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Chin. Phys. B, 2022, Vol. 31(4): 043101    DOI: 10.1088/1674-1056/ac29a6

Theoretical calculation of the quadratic Zeeman shift coefficient of the 3P0o clock state for strontium optical lattice clock

Benquan Lu(卢本全)1, Xiaotong Lu(卢晓同)1, Jiguang Li(李冀光)3, and Hong Chang(常宏)1,2,†
1 National Time Service Center, Xi'an 710000, China;
2 The University of Chinese Academy of Sciences, Beijing 100088, China;
3 Institute of Applied Physics and Computational Mathematics, Beijing 100088, China
Abstract  In the weak-magnetic-field approximation, we derived an expression of quadratic Zeeman shift coefficient of $^3P^{\rm o}_0$ clock state for $^{88}$Sr and $^{87}$Sr atoms. By using this formula and the multi-configuration Dirac-Hartree-Fock theory, the quadratic Zeeman shift coefficients were calculated. The calculated values $C_2$ = $-23.38(5)$ MHz/T$^2$ for $^{88}$Sr and the $^3P^{\rm o}_0$, $F = 9/2$, $M_F = \pm9/2$ clock states for $^{87}$Sr agree well with the other available theoretical and experimental values, especially the most accurate measurement recently. In addition, the calculated values of the $^3P^{\rm o}_0$, $F = 9/2$, $M_F = \pm9/2$ clock states were also determined in our $^{87}$Sr optical lattice clock. The consistency with measurements verifies the validation of our calculation model. Our theory is also useful to evaluate the second-order Zeeman shift of the clock transition, for example, the new proposed $^1S_0$, $F = 9/2$, $M_F = \pm5/2$-${}^3P^{\rm o}_0$, $F = 9/2$, $M_F = \pm3/2$ transitions.
Keywords:  optical lattice clock      quadratic Zeeman shift coefficient      strontium  
Received:  19 July 2021      Revised:  18 September 2021      Accepted manuscript online:  24 September 2021
PACS:  31.15.aj (Relativistic corrections, spin-orbit effects, fine structure; hyperfine structure)  
  31.15.vj (Electron correlation calculations for atoms and ions: excited states)  
  32.60.+i (Zeeman and Stark effects)  
  95.55.Sh (Auxiliary and recording instruments; clocks and frequency standards)  
Fund: Project supported by the National Natural Science Foundation of China (Grant No. 61775220), the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. XDB21030100), the Key Research Project of Frontier Science of the Chinese Academy of Sciences (Grant No. QYZDB-SSW-JSC004), and the West Light Foundation of the Chinese Academy of Sciences (Grant No. XAB2018B17).
Corresponding Authors:  Hong Chang     E-mail:

Cite this article: 

Benquan Lu(卢本全), Xiaotong Lu(卢晓同), Jiguang Li(李冀光), and Hong Chang(常宏) Theoretical calculation of the quadratic Zeeman shift coefficient of the 3P0o clock state for strontium optical lattice clock 2022 Chin. Phys. B 31 043101

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