Excited-state magnetic properties of carbon-like $\text{Ca}^{14+}$

TL;DR

This study precisely measured the magnetic properties of excited states in highly charged calcium ions, confirming their low magnetic sensitivity and aligning experimental results with advanced theoretical calculations, highlighting their potential for optical clock applications.

Contribution

First experimental determination of the $g$-factor and second-order Zeeman coefficient in $ ext{Ca}^{14+}$, demonstrating low magnetic sensitivity and validating advanced theoretical models.

Findings

Measured $g$-factor with high precision ($1.499032(6)$).

Determined the smallest reported second-order Zeeman coefficient ($0.39 ext{HzmT}^{-2}$).

Confirmed theoretical predictions including QED effects and Breit contributions.

Abstract

We measured the $g$-factor of the excited state $^3\text{P}_1$ in $\text{Ca}^{14+}$ ion to be $g = 1.499032(6)$ with a relative uncertainty of $4\times10^{-6}$. The magnetic field magnitude is derived from the Zeeman splitting of a $\text{Be}^+$ ion, co-trapped in the same linear Paul trap as the highly charged $\text{Ca}^{14+}$ ion. Furthermore, we experimentally determined the second-order Zeeman coefficient $C_2$ of the $^3\text{P}_0$ - $^3\text{P}_1$ clock transition. For the $m_J=0\rightarrow m_{J'}=0$ transition, we obtain $C_2 = 0.39\pm0.04\text{HzmT}^{-2}$, which is to our knowledge the smallest reported for any atomic transition to date. This confirms the predicted low sensitivity of highly charged ions to higher-order Zeeman effects, making them ideal candidates for high-precision optical clocks. Comparison of the experimental results with our state-of-the art electronic structure calculations shows good agreement, and demonstrates the significance of the frequency-dependent Breit contribution, negative energy states and QED effects on magnetic moments.