Two-photon optical Ramsey–Doppler spectroscopy of positronium and muonium

Positronium and muonium, as purely leptonic atoms without internal structure, provide ideal systems for high-precision tests of quantum electrodynamics (QED) and measurements of fundamental constants. However, the high velocities of these lightweight atoms complicate precision spectroscopy, particularly in the 1 S-2 S transition, due to transit time broadening and second-order Doppler shifts. To overcome these challenges, we propose a novel method combining two-photon Ramsey spectroscopy with a technique to correct the second-order Doppler shifts on an atom-by-atom basis. Additionally, this approach suppresses systematic effects of the AC Stark shift to a negligible level compared to the target precision. Simulations predict that for both positronium and muonium, this method could improve the measurement precision of the 1 S-2 S transition by more than two orders of magnitude compared to the current state of the art. This approach opens up new avenues for rigorous bound state QED tests and searches for physics beyond the standard model.