We present refined values of the hyperfine splitting frequencies of the ground $|g\rangle =|4f^{13}{(}^2{F}^o)6s^2,J=7/2\rangle$ and clock $|c\rangle =|4f^{13}{(}^2{F}^o)6s^2,J=5/2\rangle$ states of thulium atoms, $f_g^{\text{HFS}}=1496550658.23\left(3\right)$ Hz and $f_c^{\text{HFS}}=2113946873.08\left(9\right)$ Hz, respectively. The measurements are performed on an ultracold atomic ensemble in an optical lattice using combined microwave and optical transition spectroscopy. The achieved measurement accuracy of less than 0.1 ppb represents an improvement of 2 and 7 orders of magnitude for $f_g^{\text{HFS}}$ and $f_c^{\text{HFS}}$, respectively, compared to the previously published values. We also refine the value of the Landé $g$-factor of the clock level to $g_c=0.854786\left(12\right)$. The results of this work can be used in the frequency standards and quantum simulators based on thulium atoms being developed today, as well as in a number of fundamental studies that require precise knowledge of the hyperfine structure characteristics of various elements.

中文翻译：

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组合微波和光学光谱用于铥原子超精细结构分析


我们提出了超精细分裂的精确值 $g$ 地面频率 $|g\rangle =|4f^{13}{(}^2{F}^o)6s^2,J=7/2\rangle$ 和时钟 $|c\rangle =|4f^{13}{(}^2{F}^o)6s^2,J=5/2\rangle$ 铥原子的状态， $f_g^{\text{HFS}}=1496550658.23\left(3\right)$ 赫兹和 $f_c^{\text{HFS}}=2113946873.08\left(9\right)$ 分别为赫兹。使用组合微波和光学跃迁光谱对光学晶格中的超冷原子系综进行测量。所达到的低于 0.1 ppb 的测量精度代表了 2 和 7 个数量级的改进 $f_g^{\text{HFS}}$ 和 $f_c^{\text{HFS}}$ 分别与之前发布的值相比。我们还将时钟级别的 Landé g 因子值细化为 $g_c=0.854786\left(12\right)$ 。这项工作的结果可用于当今正在开发的基于铥原子的频率标准和量子模拟器，以及需要精确了解各种元素的超精细结构特征的许多基础研究。