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Abstract

The high-precision measurement of the nuclear g-factor of a single ³He²⁺stored in
a Penning trap enables most accurate magnetometry using He nuclear magnetic
resonance probes. The g-factor measurement requires the detection of an axial
frequency shift caused by a spin flip. Due to the large mass and small magnetic
moment of ³He²⁺compared to the proton and electron, this frequency shift is
on the order of background frequency fluctuations, complicating the spin-state
determination. The signal-to-noise ratio can be enhanced by implementing two
upgrades to the Penning-trap setup. First, the electrode that generates the trap
potential must be supplied with an ultra-stable voltage source that must be tunable
in the range of a few hundred mV. At low electrode voltages (≤ 500mV),
the commercially available voltage source UM1-14 allows spin-flip detection with
99.2^+0,4_−2,7% fidelity. However, for larger electrode voltages the UM1-14 is no longer
suitable. Instead, a voltage source based on Josephson junctions was applied in
the context of this thesis and gives a spin-flip detection fidelity of 98⁺¹
_>−3%. Second,
the axial fluctuations are reduced by cooling the ion to low energies. This
is achieved by sympathetic laser cooling of ³He²⁺coupled to laser cooled ⁹Be⁺
After successful laser alignment, ⁹Be⁺was loaded into the trap and laser cooled.
An upper limit of the achieved ⁹Be⁺axial temperature is presently at 4.2K,
which is far above the Doppler cooling limit of 0.5mK.