The metastable He atom in its singlet or triplet states is an ideal system to perform tests of ab-initio calculations of two-electron systems that include quantum-electrodynamics and nuclear finite-size effects. The recent determination of the ionization energy of the metastable 2^1S0 state of 4He [1] confirmed a discrepancy between the latest theoretical values of the Lamb shifts in low-lying electronic states of triplet helium [2] and the measured 3 3D ← 2 3S [3] and 3 3D ← 2 3P [4] transition frequencies. This discrepancy could not be resolved in the latest calculations [5,6]. Recently, we developed a new experimental method for the determination of the ionization energy of the 2 3S1 state of 4He via the measurement of transitions from the 2 3S1 state to np Rydberg states. In this talk, we present the the first results on the ionization energy of metastable helium obtained with improved experimental setup and methods, which include (i) the preparation of a cold, supersonic expansion of helium atoms in the 2 3S1 state, (ii) the development and characterization of a laser system for driving the transitions to np Rydberg states, (iii) the implementation of a new sub-Doppler, background-free detection method [7], and (iv) the integration of an interferometer-based retro-reflector canceling the 1st-order Doppler shift to enable Doppler-free spectroscopy. We illustrate its power with a new determination of the ionization energy of 2 3S1 metastable He with a fractional uncertainty in the 10^(−12) range using extrapolation of the np series. The method is extended to measurements on the 3He isotope, as part of an effort to determine the difference between the charge radii of the alpha particle and the helion nuclei.

[1] G. Clausen et al., Phys. Rev. Lett. 127, 093001 (2021).

[2] V. Patkos et al., Phys. Rev. A. 103, 042809 (2021).

[3] C. Dorrer et al., Phys. Rev. Lett. 78, 3658 (1997).

[4] P.-L. Luo et al., Phys. Rev. A. 94, 062507 (2016).

[5] V. A. Yerokhin et al., Eur. Phys. J. D. 76, 142 (2022).

[6] V. A. Yerokhin et al., Phys. Rev. A. 107, 012810 (2023).

[7] G. Clausen et al., Phys. Rev. Lett. 131, 103001 (2023).