Accurate tests of a physical theory require a system whose properties can be both measured and calculated with very high precision. One famous example is the hydrogen atom which, due to its simplicity, can be precisely described by bound-state quantum electrodynamics (QED). On the experimental side, laser spectroscopy employing frequency combs enables accurate measurements of the atomic transition frequencies. By comparing the experimental data to theory, fundamental constants, in particular the Rydberg constant and the nuclear charge radius, can be determined and the consistency of QED itself  can be tested.

   In atomic hydrogen, the frequency of the extremely narrow 1S–2S two-photon transition was measured with a relative uncertainty below 10 −14 , while relative uncertainties on the 10 −12 level have been recently achieved for broader transitions. Since trapping and cooling of atomic hydrogen under conditions suitable for high precision spectroscopy has not yet been achieved, these experiments were performed on atomic beams where the thermal motion of the atoms ultimately limits the achievable accuracy.

   We are currently setting up an experiment with the aim to perform spectroscopy on the 1S–2S transition in the simplest hydrogen-like ion, He+ . Due to their charge, He+ ions can be held near-motionless in the field-free environment of a Paul trap, providing ideal conditions for a high precision measurement. Furthermore, interesting higher-order QED corrections scale with large exponents of the nuclear charge, which makes this measurement much more sensitive to these corrections compared to the hydrogen case. Finally, an accurate QED test in this yet unexplored system could give new insights into a so-far unresolved discrepancy between different determinations of the proton charge radius which is known as the proton radius puzzle.

   The main challenge of the experiment is that driving the 1S–2S transition in He + requires narrow-band radiation at 61 nm. This lies in the extreme ultraviolet (XUV) spectral range where no transparent solids and no cw laser sources exist. Our approach is to use direct frequency comb spectroscopy with an XUV frequency comb which is generated from an infrared high power frequency comb using intracavity high harmonic generation. The spectroscopy target will be a small number of He+ ions which are trapped in a linear Paul trap and sympathetically cooled by co-trapped Be + ions. My talk will give an overview of the plans for the experiment and will report on the progress achieved so far.