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Physical Review A

Determination of the Landé g J factor and Zeeman coefficients in ground-state 171 Yb + and their applications to quantum frequency standards

J. Z. Han, Benquan Lu, Yanmei Yu, Jiguang Li, Zhiguo Huang, Jingwei Wen, Ling Qian, Lijun Wang

Published Jan 17, 2025• 3 citations
Publisher

Abstract

We report the determination of the Land\'e ${g}_{J}$ factor and Zeeman coefficients for the ground-state of ${}^{171}{\mathrm{Yb}}^{+}$, relevant to microwave quantum frequency standards (QFSs). The ${g}_{J}$ factor is obtained by using two independent methods, the multiconfiguration Dirac-Hartree-Fock and multireference configuration-interaction methods, yielding a consistent value of $2.002\phantom{\rule{0.16em}{0ex}}615(70)$. The first- and second-order Zeeman coefficients are determined as $14\phantom{\rule{0.16em}{0ex}}010.78(49)\phantom{\rule{4pt}{0ex}}\mathrm{Hz}/\textmu{}\mathrm{T}$ and $31.0869(22)\phantom{\rule{4pt}{0ex}}\mathrm{mHz}/\textmu{}{\mathrm{T}}^{2}$, respectively, based on the calculated ${g}_{J}$ factor. These coefficients enable reduced magnetic-field-induced uncertainties, improving the accuracy of the ${}^{171}{\mathrm{Yb}}^{+}$ microwave QFSs. The results reported in this work also offer potential for improved constraints on variations in fundamental constants through frequency comparisons and advancing trapped-ion quantum computers based on the ground-state hyperfine splitting of ${}^{171}{\mathrm{Yb}}^{+}$.

DOI
10.1103/physreva.111.012814

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Determination of Landé gJg_JgJ​ factor and Zeeman coefficients in ground-state 171^{171}171Yb+^++ and their applications to quantum frequency standards
We report the determination of the Landé gJg_JgJ​ factor and Zeeman coefficients for the ground-state of 171^{171}171Yb+^++, relevant to microwave quantum frequency standards (QFSs). The gJg_JgJ​ factor is obtained by using two independent methods: multiconfiguration Dirac-Hartree-Fock and multireference configuration interaction, yielding a consistent value of 2.002615(70). The first- and second-order Zeeman coefficients are determined as 14,010.78(49) Hz/μμμT and 31.0869(22) mHz/μμμT2^22, respectively, based on the calculated gJg_JgJ​ factor. These coefficients enable reduced magnetic-field-induced uncertainties, improving the accuracy of the 171^{171}171Yb+^++ microwave QFSs. The results reported in this work also offer potential for improved constraints on variations in fundamental constants through frequency comparisons, and advancing trapped-ion quantum computers based on the ground-state hyperfine splitting of 171^{171}171Yb+^++.
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We report measurements of the branching fraction, hyperfine constant, and second-order Zeeman coefficient of the D5/2{D}_{5/2}D5/2​ level in 171Yb+^{171}\mathrm{Yb}^{+}171Yb+ with up to a two-orders-of-magnitude reduction in uncertainty compared to previously reported values. We estimate the electric quadrupole reduced matrix element of the ${S}_{1/2}\phantom{\rule{4pt}{0ex}}\ensuremath{\leftrightarrow}\phantom{\rule{4pt}{0ex}}{D}_{5/2}$ transition to be 12.5(4) ea02e{a}_{0}^{2}ea02​. Furthermore, we determine the transition frequency of the ${F}_{7/2}\phantom{\rule{4pt}{0ex}}\ensuremath{\leftrightarrow}{\phantom{\rule{4pt}{0ex}}}^{1}D{[3/2]}_{3/2}$ at 760 nm with a $\ensuremath{\sim}$25-fold improvement in uncertainty. These measurements provide benchmarks for quantum-many-body atomic-physics calculations and provide valuable data for efforts to improve quantum information processors based on 171Yb+{}^{171}{\text{Yb}}^{+}171Yb+.
We present the determination of the ground-state hyperfine splitting (νHFS) in laser-cooled 171Yb+ ions using our microwave quantum frequency standard (QFS). Employing Ramsey spectroscopy in a closed-loop measurement configuration, we have achieved a νHFS value of 12 642 812 118 469.0(8) mHz with a fractional uncertainty of 6.6×10−14. This result aligns with previously reported values and represents the highest accuracy reported to date for such measurements conducted in a single-shot closed-loop configuration, without averaging over multiple dates. The development of this accurate 171Yb+ microwave QFS holds promise as a transportable time-frequency reference for satellite navigation systems.
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