Double-resonance $g$-factor measurements by quantum jump spectroscopy

With the advent of high-precision frequency combs that can bridge large frequency intervals, new possibilities have opened up for the laser spectroscopy of atomic transitions. Here, we show that laser spectroscopic techniques can also be used to determine the ground-state $g$ factor of a bound electron: Our proposal is based on a double-resonance experiment, where the spin state of a ground-state electron is constantly being read out by laser excitation to the atomic $L$ shell, while the spin flip transitions are being induced simultaneously by a resonant microwave field, leading to a detection of the quantum jumps between the ground-state Zeeman sublevels. The magnetic moments of electrons in light hydrogen-like ions could thus be measured with advanced laser technology. Corresponding theoretical predictions are also presented.