100 years after its birth, testing quantum physics with ever-increasing precision: the cases of hydrogen and helium

The founding articles of quantum mechanics illustrated the new theory with first-principles predictions of the energy-level structure and the spectrum of simple, fundamental atoms and molecules such as the hydrogen atom (H), the helium atom (He), the hydrogen molecular ion (H2+), and the hydrogen molecule (H2). Over the years, large experimental efforts have been invested in verifying the predictions of quantum theory through measurements of the spectra of these fundamental few-body systems, at ever-increasing accuracy. On average, a factor of ten in the precision of both measurements and calculations is gained every ten years.

With the advent of frequency-metrology tools such as atomic clocks, frequency combs, and frequency-distribution networks, it is possible today to measure, in university research laboratories, transition frequencies in these systems with more than 12 significant digits and test the limits of theoretical predictions. Recent attempts to challenge the theory by comparing experiments and calculations in simple atoms have led to surprises and puzzles, the latest of which concern the size of the proton and the ionization energy of helium. This lecture will discuss recent precision measurements of the spectrum of the hydrogen and helium atoms carried out with the goals of resolving these puzzles, testing fundamental theory, and reducing the uncertainties of fundamental physical constants.