Quasi-analytical lineshape for the 1S-2S laser spectroscopy of antihydrogen and hydrogen
The accuracy of high precision and fundamental measurements of atomic transition frequencies via laser spectroscopy depends upon fitting the spectral data with a lineshape. With atomic hydrogen and antihydrogen 1S-2S two-photon spectroscopy, computer intensive Monte-Carlo simulations have been used to compute the optical Bloch equations in order to match and interpret the experimental spectra. For the highest resolutions, one tries to minimize saturation effects going to regimes of low excitation probability, where perturbation theory can provide reliable results. Here we describe an analytical approach to the lineshape based on perturbation theory accounting for the AC-Stark shift and ionization. The expressions can be used for beam experiments or integrated over the magnetic field profile for a trapped sample. Theses lineshapes, providing fast results, allow for studies of many systematic effects that influence the accuracy of the determination of the central frequency. This development has relevance to hydrogen beam experiments and to trapped hydrogen and antihydrogen, as developed by the ALPHA collaboration at CERN, for tests of the CPT-symmetry and the highest accuracy measurement on antimatter.