Determination of hyperfine splittings and Landé $g_J$ factors of $5s~^2S_{1/2}$ and $5p~^2P_{1/2,3/2}$ states of $^{111,113}$Cd$^+$ for a microwave frequency standard
J. Z. Han, R. Si, H. R. Qin, N. C. Xin, Y. T. Chen, S. N. Miao, C. Y. Chen, J. W. Zhang, L. J. Wang
关于捕获离子微波频率标准，我们报告的超精细分裂和Landé $g_J$因素的测定$^{111,113}$镉$^+$。用激光诱导荧光光谱测量了$^{111,113}$ Cd $^+$离子的$5p~^2P_{3/2}$态的超精细分裂。Cd $^+$离子被限制在线性Paul阱中，并被Ca $^+$离子共振冷却。此外，用多组态Dirac-Hartree-Fock方法更精确地计算了$^{111,113}$ Cd $^+$的$5s~^2S_{1/2}$和$5p~^2P_{1/2,3/2}$能级的超精细分裂和Landé $g_J$因子.通过对超精细分裂的测量值与Dirac-Hartree-Fock的计算值进行了交叉检验，进一步保证了结果的可靠性。本文的研究结果可以提高时钟跃迁的信噪比和二阶塞曼位移校正的精度，从而提高基于Cd $^+$离子的微波频率标准的稳定性和准确性。
英文摘要：
Regarding trapped-ion microwave-frequency standards, we report on the determination of hyperfine splittings and Landé $g_J$ factors of $^{111,113}$Cd$^+$. The hyperfine splittings of the $5p~^2P_{3/2}$ state of $^{111,113}$Cd$^+$ ions were measured using laser-induced fluorescence spectroscopy. The Cd$^+$ ions were confined in a linear Paul trap and sympathetically cooled by Ca$^+$ ions. Furthermore, the hyperfine splittings and Landé $g_J$ factors of the $5s~^2S_{1/2}$ and $5p~^2P_{1/2,3/2}$ levels of $^{111,113}$Cd$^+$ were calculated with greater accuracy using the multiconfiguration Dirac--Hartree--Fock scheme. The measured hyperfine splittings and the Dirac--Hartree--Fock calculation values were cross-checked, thereby further guaranteeing the reliability of our results. The results provided in this work can improve the signal-to-noise ratio of the clock transition and the accuracy of the second-order Zeeman shift correction, and subsequently the stability and accuracy of the microwave frequency standard based on trapped Cd$^+$ ions.
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