Experimental Determination of the Landé $g$-Factors for 5$s^{2}$$^{1}\!S$ and $5s5p$$^{3}\!P$ States of the $^{87}$Sr Atom
Ben-quan Lu1,2,3, Yebing Wang1,2, Yang Guo1,2, Qinfang Xu1, Mojuan Yin1, Jiguang Li3, Hong Chang1,2**
1National Time Service Center, Xi'an 710000 2University of Chinese Academy of Sciences, Beijing 100049 3Institute of Applied Physics and Computational Mathematics, Beijing 100088
Abstract：We present an experimental determination on the Landé $g$-factors for the 5$s^{2}$ $^{1}\!S_{0}$ and $5s5p$ $^{3}\!P_{0}$ states in ultra-cold atomic systems, which is important for evaluating the Zeeman shift of the clock transition in the $^{87}$Sr optical lattice clock. The Zeeman shift of the $5s5p$ $^{3}\!P_{0}$–5$s^{2}$ $^{1}\!S_{0}$ forbidden transition is measured with the $\pi$-polarized and $\sigma^{\pm}$-polarized interrogations at different magnetic field strengths. Moreover, in the $g$-factor measurement with the $\sigma^{\pm}$-transition spectra, it is unnecessary to calibrate the external magnetic field. By this means, the ground state 5$s^{2}$ $^{1}\!S_{0}$ $g$-factor for the $^{87}$Sr atom is $-1.306(52)\times10^{-4}$, which is the first experimental determination to the best of our knowledge, and the result matches very well with the theoretical estimation. The differential $g$-factor $\delta g$ between the $5s5p$ $^{3}\!P_{0}$ state and the 5$s^{2}$ $^{1}\!S_{0}$ state of the $^{87}$Sr atoms is measured in the experiment as well, which are $-7.67(36)\times10^{-5}$ with $\pi$-transition spectra and $-7.72(43)\times10^{-5}$ with $\sigma^{\pm}$-transition spectra, in good agreement with the previous report [Phys. Rev. A 76 (2007) 022510]. This work can also be used for determining the differential $g$-factor of the clock states for the optical clocks based on other atoms.
. [J]. 中国物理快报, 2018, 35(4): 43203-.
Ben-quan Lu, Yebing Wang, Yang Guo, Qinfang Xu, Mojuan Yin, Jiguang Li, Hong Chang. Experimental Determination of the Landé $g$-Factors for 5$s^{2}$$^{1}\!S$ and $5s5p$$^{3}\!P$ States of the $^{87}$Sr Atom. Chin. Phys. Lett., 2018, 35(4): 43203-.
Turyshev S G 2009 From Quantum to Cosmos: Fundamental Physics Research in Space (Singapore: World Scientific) chap 3 p 57
[7]
Rosenb, T, Hume D B, Schmidt P O, Chou C W, Brusch A, Lorini L, Oskay W H, Drullinger R E, Fortier T M, Stalnaker J E, Diddams S A, Swann W C, Newbury N R, Itano W M, Winel, D J and Bergquist J C 2008 Science319 1808
Cairncross W B, Gresh D N, Grau M, Cossel K C, Roussy T S, Ni Y, Zhou Y, Ye J and Cornell E A 2017 Phys. Rev. Lett.119 153001
[10]
Major F G 2007 The Quantum Beat: Principles And Applications Of Atomic Clocks (New York: Springer) vol 2 chap 19 p 417
[11]
Grewal M S, Andrews A P and Bartone C G 2013 Global Navigation Satellite Systems, Inertial Navigation And Integration (New York: John Wiley & Sons) chap 2 p 9
Boyd M M, Zelevinsky T, Ludlow A D, Blatt S, Zanon-Willette T, Foreman S M and Ye J 2007 Phys. Rev. A 76 022510
[24]
Rosenb, T, Schmidt P O, Hume D B, Itano W M, Fortier T M, Stalnaker J E, Kim K, Diddams S A, Koelemeij J C J, Bergquist J C and Wineland D J 2007 Phys. Rev. Lett.98 220801
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