Determination of Landé $g_J$ factor and Zeeman coefficients in ground-state $^{171}$Yb$^+$ and their applications to quantum frequency standards

Abstract: We report the determination of the Land\'{e} $g_J$ factor and Zeeman coefficients for the ground-state of $^{171}$Yb$^+$, relevant to microwave quantum frequency standards (QFSs). The $g_J$ 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/$\mu$T and 31.0869(22) mHz/$\mu$T$^2$, respectively, based on the calculated $g_J$ factor. These coefficients enable reduced magnetic-field-induced uncertainties, improving the accuracy of the $^{171}$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 $^{171}$Yb$^+$.