Precise measurement of $^{171}$Yb magnetic constants for $^{1}S_{0}\,-\,^{3}P_{0}$ clock transition

Abstract We present a precise measurement of $^{171}$Yb magnetic constants for $^{1}S_{0}\,-\,^{3}P_{0}$ clock transition. The background magnetic field is firstly compensated to $< 1\,\rm{mG}$ through measuring the splitting of two $ \pi $ transitins of $^{171}$Yb clock transition at different compensation coils currents. Then, the splitting ratios of the $ \pi $ and $ \sigma $ components of $^{171}$Yb clock transition at different bias magnetic fields are measured, and the first-order Zeeman coefficient is determined to be $\alpha = 199.44\,(5)\,\rm{Hz/G}$. The second-order Zeeman shifts at various bias magnetic fields are also measured through interleaved self-comparison in which the bias magnetic fields are modulated between high and low values. The second-order Zeeman coefficient is fitted to be $ \beta = -6.09\,(3)\,\rm{Hz/mT^{2}}$, which is consistent with the result of NIST.