Direct bound-electron g-factor difference measurement of coupled ions at ALPHATRAP

The ALPHATRAP experiment is a cryogenic Penning-trap setup with the main objective to determine the g factor of the electron bound to heavy nuclei. Within this thesis, the results of several such measurements are presented. Among these, the measurement of the g factor of ${}^{20}$Ne${}^{9+}$ exhibits a 3σ discrepancy between theory and experimental value, which has been attributed to the required input parameter of the atomic mass of ${}^{20}$Ne. An independent measurement has recently confirmed the deviation of the mass, fully resolving the discrepancy. Furthermore, a measurement of ${}^{22}$Ne${}^{9+}$ can be used to improve the precision of the atomic mass of ${}^{22}$Ne by a factor 8 compared to the literature value, when using the theoretically predicted g factor as an input. However, the main focus of this thesis is the development of a novel technique, which, based upon the coupling of two ions as an ion crystal, enables the most precise determination of a g-factor difference to date. This difference, determined for the isotopes ${}^{20}$Ne${}^{9+}$ and ${}^{22}$Ne${}^{9+}$ with a relative precision of 5.6 × 10${}^{-13}$ with respect to the g factor, improves the precision for isotopic shifts of g factors by about two orders of magnitude. Based upon the agreement with theory, the quantum electrodynamic contribution to the nuclear recoil can be confirmed. Alternatively, the result can be applied to improve the precision of the charge radius difference of the isotopes by about one order of magnitude or to constrain new physics by limiting a potential fifth-force of the Higgs-portal mechanism.