Hyperfine Structure Measurements of Antiprotonic $^3$He using Microwave Spectroscopy

The goal of this project was to measure the hyperfine structure of $\overline{\text{p}}^3$He$^+$ using the technique of laser-microwave-laser spectroscopy. Antiprotonic helium ($\overline{\text{p}}$He$^+$) is a neutral exotic atom, consisting of a helium nucleus, an electron and an antiproton. The interactions of the angular momenta of its constituents cause a hyperfine splitting ({HFS}) within the energy states of this new atom. The 3\% of formed antiprotonic helium atoms which remain in a metastable, radiative decay-dominated state have a lifetime of about 1-3~$\mu$s. This time window is used to do spectroscopic studies. The hyperfine structure of $\overline{\text{p}}^4$He$^+$ was already extensively investigated before. From these measurements the spin magnetic moment of the antiproton can be determined. A comparison of the result to the proton magnetic moment provides a test of {CPT} invariance. Due to its higher complexity the new exotic three-body system of $\overline{\text{p}}^3$He$^+$ is a cross-check for the measurements with $\overline{\text{p}}^4$He$^+$ and a more stringent test of theoretical calculations and methods. The measurement principle is based on inducing a population asymmetry by laser-depopulation of one of two {HF} states. Subsequently, a microwave pulse stimulates population transfer between these substates, followed by a second laser pulse to measure the transferred population. For the microwave spectroscopy several cryogenic cavities were designed, built and tested. One major part of my work consisted of calculations and finite-element simulations as well as detailed preparation studies, diagnostics and calibration of these high frequency structures and the complete microwave apparatus. The main focus of my thesis was on the execution of the measurements at {CERN} (as well as the organization or the supervision of project students) and the related data analysis, including numerical simulations of the hyperfine transition processes. Two out of four measurable transition lines of the $(n,L)=(36,34)$ state of $\overline{\text{p}}^3$He$^+$ were observed for the first time and in good agreement with theoretical {QED} calculations. The final results for the two measured transition frequencies are $\nu_{\text{HF}}^{--} = 11.125 48(08)$~GHz and $\nu_{\text{HF}}^{-+} = 11.157 93(13)$~GHz.