STIRAP for 1S-2S transition in Hydrogen atoms

We present simulations for the STIRAP (Stimulated Raman Adiabatic Passage) process for transferring population from the 1S level to the 2S level of hydrogen atoms. We utilized a circularly polarized Ly-$\alpha$ pulse to couple the 1S state to the 2P state and a microwave pulse to couple the 2P state and the 2S state. We study the efficiency of the STIRAP process for transferring the population between the stretched states $\{1S_d, 2S_d\}$ as a function of experimental parameters such as Rabi frequencies and the pulse durations. We find that a Ly-$\alpha$ pulse with an energy of a few nanojoules could produce nearly perfect transfer at zero detunings. We extended the analysis to a thermal ensemble of atoms where the Doppler detuning plays a crucial role in the velocity distribution of the produced hydrogen atoms in the 2S level. We found that the width of such velocity distribution is controlled by the Rabi frequency with the location of the peak velocity after recoil adjustable by the Ly-$\alpha$ pulse detuning. The STIRAP efficiency in transferring population increases at lower temperature, $T\sim 1mK$. Finally, we showed that a background magnetic field improves the transfer rates between the other trappable states $\{1S_c, 2S_c\}$. The idea behind this work came through discussions with the HAICU group for their future experiments.