Observation of the Continuous Stern-Gerlach Effect on an Electron Bound in an Atomic Ion

We report on the first observation of the continuous Stern-Gerlach effect on an electron bound in an atomic ion. The measurement was performed on a single hydrogenlike ion ( ${}^{12}{\mathrm{C}}^{5+}$) in a Penning trap. The measured $g$ factor of the bound electron, $g=2.001\mathrm{}042\left(2\right)$, is in excellent agreement with the theoretical value, confirming the relativistic correction at a level of $0.1\%$. This proves the possibility of $g$-factor determinations on atomic ions to high precision by using the continuous Stern-Gerlach effect. The result demonstrates the feasibility of conducting experiments on single heavy highly charged ions to test quantum electrodynamics in the strong electric field of the nucleus.