Fundamental Constants and Tests with Simple Atoms

Precise measurements with simple atoms provide stringent tests of physical laws, improving the accuracy of fundamental constants---a set of which will be selected to fully define the proposed New International System of Units. This talk focuses on the atomic constants (namely, the Rydberg constant, the fine-structure constant, and the proton charge radius), discussing the impact of the proton radius obtained from the Lamb-shift measurements in muonic hydrogen [A. Antognini, \textit{et al}., Science \textbf{339}, 417 (2013)]. Significant discrepancies persist despite years of careful examination: the slightly smaller proton radius obtained from muonic hydrogen requires the Rydberg constant and the fine-structure constant to have values that disagree significantly with the CODATA recommendations. After giving a general overview, I will discuss our effort to produce one-electron ions in Rydberg states, to enable a different test of theory and measurement of the Rydberg constant.