Item

Abstract

This thesis describes the ultra-precise determination of the g-factor of the electron bound to hydrogenlike ²⁸Si¹³⁺. The experiment is based on the simultaneous determination of the cyclotron- and Larmor frequency of a single ion, which is stored in a triple Penning-trap setup. The continuous Stern-Gerlach effect is used to couple the spin of the bound electron to the motional frequencies of the ion via a magnetic bottle, which allows the non-destructive determination of the spin state. To this end, a highly sensitive, cryogenic detection system was developed, which allowed the direct, non-destructive detection of the eigenfrequencies with the required precision. The development of a novel, phase sensitive detection technique finally allowed the determination of the g-factor with a relative accuracy of 4 • 10⁻¹¹, which was previously inconceivable. The comparison of the hereby determined value with the value predicted by quantumelectrodynamics (QED) allows the verification of the validity of this fundamental theory under the extreme conditions of the strong binding potential of a highly charged ion. The exact agreement of theory and experiment is an impressive demonstration of the exactness of QED. The experimental possibilities created in this work will allow in the near future not only further tests of theory, but also the determination of the mass of the electron with a precision that exceeds the current literature value by more than an order of magnitude.