Precision spectroscopy of the 2S-4P transition in atomic hydrogen

A precision measurement of the 2S-4P transition in atomic hydrogen, when combined with the precisely known 1S-2S transition frequency\footnote{C.$\,$G. Parthey et al., PRL 107, 203001 (2011)}, can be used to determine the value of the r.m.s.$\,$proton charge radius $r_p$. We report on our progress towards an absolute frequency measurement, using a cryogenic beam of atoms optically excited to the metastable 2S state\footnote{A. Beyer et al., Ann.$\,$Phys.$\,$525, 671 (2013)}. This strongly suppresses the first order Doppler shift, which is further reduced using actively stabilized counter-propagating laser beams for the 2S-4P (one-photon) excitation. We experimentally verify this suppression using time-of-flight resolved detection. We present a theoretical and experimental study of interference effects due to spontaneous emission\footnote{M. Horbatsch and E.$\,$A. Hessels, PRA 82, 052519 (2010)} and the corresponding line center shifts, using a segmented detector to spatially resolved the emission pattern. An experimental scheme to suppress this systematic shift and extract the unperturbed transition frequency is shown and future measurements of transitions to higher $nL$ states are discussed.