Time evolution of two-photon population transfer between the 1s and 2s statesof a hydrogen atom

We have solved the time-dependent Schr\"odinger equation to analyze the time evolution of a hydrogen atom, initially in its ground 1s state, interacting with a one- or two-color linearly polarized laser pulse which is tuned close to a two-photon resonance with the 2s metastable state. The two-photon transition therefore does not involve an intermediate resonance state. Using a suitable combination of two laser pulses of different frequencies, population can be transferred from the 1s state to the 2s state via the continuum. In both the single-color and the two-color cases, a maximum amount of 17% of population can be found in the 2s state at the end of the pulse. We compare and interpret our results in terms of the time-independent Floquet eigenvalues. The system can also be modeled by an ``essential states'' two-level atom with decay. Both the Floquet and the time-dependent solutions are compared with the model predictions. The model allows systematic optimization studies for population transfer under a wide range of laser pulse parameters.