Precision measurements in exotic atoms

Bound exotic systems offer unique opportunities to test our understanding of the tenets of modern physics and determine fundamental constants. By comparing measured transitions between antihydrogen and hydrogen, we can search for CPT violation, which may explain the observed baryon asymmetry in the universe while respecting the stringent bounds on CP violation within the standard model. The comparison of the energy levels of muonium (M) with their clean theoretical prediction searches for new physics in a multitude of scenarios, including new bosons coupled to leptons. Such particles are motivated by the persistent discrepancy between the recently remeasured anomalous magnetic moment of the muon and its theoretical prediction, arguably the most promising hint to new physics in decades. In this talk I will review ongoing work for antihydrogen and M spectroscopy at CERN and PSI, and present our recent measurement of the Lamb-Shift in M, comprising an order of magnitude of improvement upon the state of the art and the first improvement to M energy levels in 20 years. I will conclude by showing that pushing M spectroscopy to its limits would independently determine the g-2 with enough accuracy to shed light on the puzzle.