Precision spectroscopy of the 2S-6P transition in atomic hydrogen

Precision measurements of atomic hydrogen (H) have long been successfully used to extract fundamental constants and to test bound-state quantum electrodynamics. Both the Rydberg constant $R_\infty$ and the proton root mean square charge radius $r_p$ can be determined by H spectroscopy with high precision. We have previously measured the 2S-4P transition frequency to 4 parts in $10^{12}$ (A. Beyer et al., Science 358, 79 (2017)), finding good agreement in $r_p$ with the spectroscopy of muonic H (A. Antognini et al., Science 339, 417 (2013)). Recently, we have completed data-taking on the 2S-6P transition in H, which has a three times lower linewidth compared to the 2S-4P transition. This factor, together with an upgraded fluorescence detection, allows for a five-fold improvement in fractional precision. Here, we will discuss the ongoing data analysis and present preliminary results, focusing on a frequency shift from the light forces acting on the atoms.