Towards an improved measurement of the proton size from precision spectroscopy of atomic hydrogen

Precision spectroscopy of atomic hydrogen has long been successfully used to provide stringent tests on fundamental theories and precisely determine physical constants. The current limit originates from the uncertainty in the value of the proton r.m.s.$\,$charge radius $r_p$. Moreover, the value of $r_p$ extracted from laser spectroscopy of muonic hydrogen\footnote{R. Pohl et al., Nature 466, 213 (2010)} is ten times more accurate than any other determination, but disagrees by 7$\sigma$ with the recommended CODATA 2010 value. Here, we report on our progress towards an improved absolute frequency measurement of the 2S-4P (one-photon) transition in atomic hydrogen, which combined with the much more precisely known 1S-2S transition frequency\footnote{C.\,G. Parthey et al., PRL 107, 203001 (2011)} allows a more precise extraction of $r_p$ from electronic hydrogen. To suppress the first order Doppler shift, we use a cryogenic beam of atoms optically excited to the 2S state and actively stabilized counter-propagating laser beams. Interference effects due to spontaneous emission\footnote{M. Horbatsch and E.$\,$A. Hessels, PRA 82, 052519 (2010)} were studied and we show how to experimentally suppress the corresponding line center shifts.