In the last two decades frequency combs became an essential tool for spectroscopy experiments around the world, allowing for simple and convenient referencing of lasers with diﬀerent wavelengths to each other and to radio frequency standards . A number of other interesting applications in applied spectroscopy, astronomy, quantum information and other ﬁelds are being investigated [2, 3]. One of the ﬁrst suggested applications for frequency combs was precision spectroscopy of two-photon transitions . While being essentially equivalent in terms of excitation probability and AC Stark shift as a CW laser with the same average power, frequency combs oﬀer access to UV and DUV wavelengths via second harmonic generation in crystals and high harmonic generation in gas targets. Additionally a small interaction region is well suited for trapped atoms and ions experiments and allows for simple characterization of electric and magnetic ﬁelds as well as pressure shifts. However, an additional systematic frequency shift arises from chirping of the pulses. I will report on the ﬁrst demonstration of the two-photon direct frequency comb spectroscopy in UV with sub kilohertz uncertainty, discussing advantages and drawbacks of this technique. Our measurement of the 1S3S transition in hydrogen is second most precise after the 1S2S transition , improving the Rydberg constant and shading light onto the Proton Radius Puzzle .
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