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

## TL;DR

This paper reports precise measurements of magnetic constants for $^{27}$Al$^{+}$ and $^{25}$Mg$^{+}$ ions, improving the accuracy of ion clock systematic uncertainties and aiding in the development of more precise optical clocks.

## Contribution

The paper provides improved measurements of the quadratic Zeeman coefficient and hyperfine splitting, refining the parameters used in $^{27}$Al$^{+}$ quantum-logic clock evaluations.

## Key findings

- Measured $C_2$ with improved uncertainty, consistent with previous data.
- Determined $ riangle W$ with better precision, aligning with recent measurements.
- Derived an updated nuclear g-factor and quadratic Zeeman shift for the clock.

## 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, $\Delta W / h = 1~788~762~752.85(13)$~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 $g_{I}/g_{J} = 9.299 ~308 ~313(60) \times 10^{-5}$ and the nuclear g-factor for the $^{25}$Mg nucleus $g_{I} = 1.861 ~957 ~82(28) \times 10^{-4}$. 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.