Our current understanding of physics suggests that matter and antimatter should be created and destroyed in equal amounts, but this seems inconsistent with the observation that our universe consists almost entirely of matter. Comparisons between matter and antimatter could reveal new physics which explains why the universe has formed with this apparent imbalance. The 1S-2S transition of hydrogen has been measured with incredible precision, and a similarly precise measurement of the 1S-2S transition of antihydrogen would constitute one of the best comparisons between matter and antimatter.

One of the best ways to study antimatter is to investigate antihydrogen, the bound state of an antiproton and a positron. Antihydrogen atoms do not exist naturally and must be synthesized in the lab by merging carefully-prepared plasmas of positrons and antiprotons. If the atoms are created in a magnetic trap like the one used by the ALPHA experiment at CERN, then a fraction of the coldest atoms remain trapped, while the rest escape and annihilate on the trap walls. The trapped atoms may then be probed using microwaves or lasers to make high-precision comparisons with hydrogen.

Antihydrogen is the simplest pure antimatter atomic system, and it allows for direct tests of CPT symmetry as well as the weak equivalence principle. Furthermore, the study of antihydrogen may provide clues to the matter- antimatter asymmetry observed in the universe - one of the major unanswered questions in modern physics. Since 2010, it has been possible to perform such tests on magnetically trapped antihydrogen, and this work reports on several recent studies.