Precision Rydberg spectroscopy in the H atom, the He atom and the H 2 molecule

Precision measurements of the Rydberg spectra of H, He and H2 will be presented which aim at determining their ionization energies and, in the case of H2, also the spin-rovibrational energy-level structure of H2 +. These measurements are carried out for comparison 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. 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. Results will be presented on all three systems, including a new determination of the Rydberg constant and a new method to record Doppler-free single-photon excitation spectra of Rydberg states.