Precision spectroscopy of the 2S-nP transitions in atomic hydrogen

Precision measurements of atomic hydrogen (H) have long been used to extract fundamental constants and to test bound-state quantum electrodynamics. Both Rydberg constant $R_\infty$ and proton RMS charge radius $r_p$ are determined significantly by H spectroscopy, requiring the measurement of at least two transitions. With the very precisely known 1S-2S transition frequency (C.\,G.\,Parthey et al., PRL 107, 203001 (2011)) as a corner stone, the limitation of this extraction is the measurement precision of other H transitions. Moreover, $r_p$ extracted from the H spectroscopy disagrees by 4 standard deviations with the value extracted from muonic hydrogen ($\mu$p) spectroscopy (A.\,Antognini et al., Science 339, 417 (2013)). Using a cryogenic beam of H atoms optically excited to the 2S state, we measured the 2S-4P transition with a relative uncertainty of 4 parts in $10^{12}$ (A.\,Beyer et al., Science 358, 79 (2017)). Combining our result with the 1S-2S result yields $R_\infty = 10973731.568076(96)$\,m$^{-1}$ and $r_p = 0.8335(95)$\,fm. Our $r_p$ value is 3.3 combined standard deviations smaller than the previous H world data, but in good agreement with the $\mu$p value. To further improve on this result, we are working on a measurement of the 2S-6P transition in H and deuterium.