Reverse-engineering control of the population and phase dynamics of strongly driven open systems

We apply reverse engineering to design laser pulse shapes for controlling the time evolution of strong-field transitions under environmental effects. Our effective two-state representation of the full quantum system involves dynamic Stark shifts and multiphoton Rabi frequency. Furthermore, the environment is modeled with dephasing and dissipative terms. Solving the master equation of the two-level density matrix inversely for the field, we obtain quasianalytic laser pulse shapes that simultaneously drive the populations and relative phase according to user-defined quantum pathways. The validity of the proposed scheme is demonstrated with the example of the $3s\ensuremath{\rightarrow}\ensuremath{\rightarrow}4s$ two-photon transition of atomic sodium by solving the master equation of the multilevel system that incorporates effects beyond the adiabatic elimination and the rotating wave approximation. Due to the open character of the system, the proposed control is not always possible. We explore these situations and point out the conditions for creating steady states with large coherence.