Precision Measurements in Rydberg States of Few-Electron Atoms and Molecules
Prof. Dr. Frédéric Merkt (ETH Zürich)

High-resolution spectroscopic measurements in few-electron atoms and molecules are increasingly used as a means to test the foundations of the theory of atomic and molecular structure. Modern first-principles calculations of the energy-level structure of few-electron atomic and molecular systems consider all known interactions [1-4]. Systematic comparisons of the results of such calculations with precise spectroscopic measurements in simple atoms and molecules such as H, He, H2+, H2 and He2+ aim at searching for effects not yet included in the theory (see, e.g., Refs. [5,6]) and at reducing the uncertainties of physical constants, (see e.g., Refs. [7,8]).

This talk will present precision spectroscopic measurements of transitions to high Rydberg states of H, He, and H2, which we use to determine accurate values of their ionization energies and, in the case of H2, also of the spin-rovibrational energy-level structure of H2+. The talk will describe our experimental strategy to overcome limitations in the precision and accuracy of the measurements originating from the Doppler effect, the Stark effect, and the laser-frequency calibration. The experimental results will then be compared with the results of first-principles calculations that include the treatment of finite-nuclear-size effects and relativistic and quantum-electrodynamics corrections up to high order in the fine-structure constant. Recent aspects of these investigations include a new determination of the Rydberg constant [9] as a contribution to the resolution of the proton-size puzzle [10], a new method to record Doppler-free single-photon excitation spectra in the visible and the UV spectral ranges [11], a “zero-quantum-defect” method to determine the energy-level structure of homonuclear diatomic molecular ions such as H2+ [12], and a 9 discrepancy between theory and experiment in the ionization energies of metastable (1s2s 3S1) 4He [13] and 3He [14].

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[8] S. Schiller, J.-Ph. Karr, Phys. Rev. A 109, 042825 (2024)
[9] S. Scheidegger, and F. Merkt, Phys. Rev. Lett. 132, 113001 (2024)
[10] R. Pohl et al., Nature (London) 466, 213 (2010); A. Antognini et al., Science 339(6118), 417 (2013)
[11] G. Clausen, S. Scheidegger, J. A. Agner, H. Schmutz, and F. Merkt, Phys. Rev. Lett. 131, 103001 (2023)
[12] I. Doran, N. Hölsch, M. Beyer, and F. Merkt, Phys. Rev. Lett. 132, 073001 (2024)
[13] G. Clausen, K. Gamlin, J. A. Agner, H. Schmutz, and F. Merkt, Phys. Rev. A 111, 012817 (2025)
[14] G. Clausen and F. Merkt, Phys. Rev. Lett. 134, 223001 (2025)