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

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 $4\times 10^{-6}$. 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 $m_J=0\to m_{J^{\prime }}=0$ transition, we obtain $C_2=0.39\pm 0.04{\text{HzmT}}^{-2}$, 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.