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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.
