High-Accuracy Measurement of the Magnetic Moment Anomaly of the Electron Bound in Hydrogenlike Carbon

We present a new experimental value for the magnetic moment of the electron bound in hydrogenlike carbon $\left({}^{12}\mathrm{C}{}^{5+}\right)$: $g_{\exp }=2.001\mathrm{}041596\left(5\right)$. This is the most precise determination of an atomic $g_J$ factor so far. The experiment was carried out on a single ${}^{12}\mathrm{C}{}^{5+}$ ion stored in a Penning trap. The high accuracy was made possible by spatially separating the induction of spin flips and the analysis of the spin direction. The current theoretical value amounts to $g_{\mathrm{th}}=2.001\mathrm{}041591\left(7\right)$. Together experiment and theory test the bound-state QED contributions to the $g_J$ factor of a bound electron to a precision of $1\%$.