Microwave Spectroscopy of Magnetically Trapped Atomic Antihydrogen

We have every reason to believe that equal amounts of matter and antimatter were produced in the early universe. Moreover, theory predicts that the laws of physics make no distinction between the two. In this light, the fact that the observable universe is overwhelmingly dominated by matter is inexplicable. ALPHA is an international project located at CERN involving approximately 40 physicists from 15 different institutions in 7 countries. The primary goal of the collaboration is to study the antihydrogen atom at the highest level of precision possible, and thereby enable comparisons between hydrogen and antihydrogen. Through these comparisons it hopes to improve our understanding of the distinction between matter and antimatter, and perhaps shed some light on the puzzle of why we live in a matter dominated universe. The hyperfine energy intervals of ground-state hydrogen and antihydrogen represent an opportunity for a precision comparison. A discrepancy between the energy levels of these two atomic systems would indicate a major revolution in physics, and in our understanding of the universe. This thesis describes and interprets the first proof-of-principle spectroscopic measurements performed on magnetically trapped antihydrogen atoms. The experiments were performed by the ALPHA collaboration using microwave radiation tuned to induce transitions between hyperfine levels of ground state antihydrogen atoms. Our observations confirm that positron spin resonance transitions between hyperfine levels of ground state antihydrogen are consistent with expectations for hydrogen to within 4 parts in 10^3. The hyperfine splitting of ground state antihydrogen atoms is also constrained to 1420 +/- 85 MHz