One important contribution of atomic and molecular spectroscopy to fundamental physics comes in the determination of fundamental physical constants. In particular, spectroscopy of the hydrogen atom and subsequent comparison with the predictions of QED theory allows determining the Rydberg constant and the proton charge radius. A few years ago; spectroscopy of muonic hydrogen yielded a very precise value of the proton radius, which however was in strong disagreement with those obtained by other methods. This so-called « proton radius puzzle » has found no explanation so far. Experiments which may shed new light on this problem will be discussed, with emphasis on the spectroscopy of hydrogen molecular ions (H2+, HD+) which is studied both experimentally and theoretically in our team.
Another type of experiment consists in looking for tiny differential effects violating some symmetries assumed in the Standard Model. As an example, measuring the frequency of an atomic clock at a few years’ interval allows testing for a possible time variation of fundamental constants. Here again, the potential use of molecular spectroscopy will be addressed.