High-precision spectroscopy on molecular hydrogen and molecular deuterium

Over the past century, our understanding of the atomic-scale physical world has been shaped by quantum theory and relativity. Laser spectroscopy of atoms and molecules enables to test this theoretical understanding with high precision. By comparing theory with experiment in simple, well-understood systems, such as molecular hydrogen or singly ionized helium, one can e.g. test bound-state quantum electrodynamics (QED), one of the best tested parts of the Standard Model. Any discrepancies found between theory and experiment may point to new physics, or indicate that fundamental constants or properties like nuclear charge radii are different than assumed until now. It can also point to previously unrecognized systematic effects. In 2010, a discrepancy emerged for the proton charge radius measured via spectroscopy of muonic hydrogen, where the electron is replaced by the 200 times heavier muon, compared to regular atomic hydrogen. The muonic measurement yielded a proton radius approximately 4% smaller. This ‘proton radius puzzle’ suggested possible new physics. However, most subsequent spectroscopic measurements on regular hydrogen confirmed the smaller proton radius. This shows the importance of measuring parameters across different systems. This thesis presents high-precision experiments on H₂ and D₂, to test molecular physics and QED. Molecular hydrogen is the simplest neutral molecule and a calculable system, enabling sub-MHz theoretical accuracy. For over a century the dissociation energy D₀ has served as a benchmark for theory and spectroscopy. The most accurate experimental D₀ combines the ionization energies of the hydrogen atom, the neutral molecule, and its ion. Currently, the neutral molecule's ionization energy carries the largest uncertainty. The research presented in this thesis improves this quantity through a high-precision frequency measurement of the EF¹Σg⁺(v′=0, N′=0) ← X¹Σg⁺(v″=0, N″=0) Q₀ two-photon transition at 201 nm, in H₂ as well as in D₂. Combining this with excited-state ionization energy measurements from our collaborators at ETH Zürich will yield an improved ionization energy of the neutral molecule. The molecular hydrogen transitions require high-energy photons that are produced through nonlinear optics. In order to combine this with high precision, Ramsey-comb spectroscopy is employed. This time-domain Ramsey-type excitation method is based on two phase-coherent amplified and upconverted frequency comb pulses, referenced to an atomic clock. Measurements of the Q₀ transition in H₂ and D₂ are demonstrated with an accuracy of 31 kHz and 19 kHz, respectively. The laser system and molecular excitation setup are described, including the excitation method of counterpropagating pulses to reduce Doppler effects. Other systematic effects such as the ac-Stark shift and residual phase shifts from pulse amplification are analyzed as well. Work towards precision spectroscopy of singly-ionized helium (He⁺) is also discussed; with a nuclear charge Z=2, He⁺ exhibits enhanced sensitivity to higher-order QED terms compared to atomic (or molecular) hydrogen. The He⁺ 1S–2S transition has never been measured with high precision and offers therefore opportunities for independent QED tests or a determination of the nuclear charge radius. An outlook discusses contributions to future molecular hydrogen dissociation energy determinations and progress toward 1S–2S spectroscopy of He⁺.