Measurements of ${}^{27}$Al${}^{+}$ and ${}^{25}$Mg${}^{+}$ magnetic constants for improved ion clock accuracy

Abstract

We have measured the quadratic Zeeman coefficient for the ${}^1{S}_0\leftrightarrow {}^3{P}_0$ optical clock transition in ${}^{27}$Al${}^{+}$, $C_2=-71.944(24)$~MHz/T${}^2$, and the unperturbed hyperfine splitting of the ${}^{25}$Mg${}^{+}$ ${}^2{S}_{1/2}$ ground electronic state, $\Delta W/h=1788762752.85(13)$~Hz, with improved uncertainties. Both constants are relevant to the evaluation of the ${}^{27}$Al${}^{+}$ quantum-logic clock systematic uncertainty. The measurement of $C_2$ is in agreement with a previous measurement and a new calculation at the $1\sigma$ level. The measurement of $\Delta W$ is in good agreement with a recent measurement and differs from a previously published result by approximately $2\sigma$. With the improved value for $\Delta W$, we deduce an improved value for the nuclear-to-electronic g-factor ratio $g_I/g_J=9.299308313(60)\times 10^{-5}$ and the nuclear g-factor for the ${}^{25}$Mg nucleus $g_I=1.86195782(28)\times 10^{-4}$. Using the values of $C_2$ and $\Delta W$ presented here, we derive a quadratic Zeeman shift of the ${}^{27}$Al${}^{+}$ quantum-logic clock of $\Delta \nu /\nu =-(9241.8\pm 3.7)\times 10^{-19}$, for a bias magnetic field of $B\approx 0.12$~mT.

7 pages, 5 figures, updated

References in corpus (5)

• An ${}^{27}$Al${}^{+}$ quantum-logic clock with systematic uncertainty below $10^{-18}$
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