Proposal for Two-Photon Doppler-Free Extreme Ultraviolet Direct Frequency Comb Spectroscopy of the Helium Ground State

Tests of quantum electrodynamics (QED) are part of the search for physics beyond the standard model. QED calculations are most precise in simple systems, e.g., few-electron atoms. Hydrogen spectroscopy yielded the most stringent test so far, however QED effects are stronger in helium ground state transitions. Furthermore, experimental results disagree on the $^3He-^4He$ nuclear charge radius difference, measured using excited state transitions. This discrepancy might be related to the proton radius puzzle, and could potentially be resolved by measuring a helium ground state transition, where the effect of the nucleus is greatest. However, such transitions are in the extreme ultraviolet (XUV), where the only available stabilized laser is a frequency comb, which has so far lacked sufficient power for direct spectroscopy. We propose to perform direct two-photon frequency comb spectroscopy of the 20.6eV $1^1S-2^1S$ transition in helium, using a cell of cryogenic helium. This approach just became available, due to our success in scaling the power of our XUV frequency comb. The use of cold ($\sim$4K) helium gas significantly reduces transit-time broadening and also allows for high gas densities. We expect to achieve the first spectroscopic measurement in the XUV with sub-MHz precision.