We develop the group-theoretical approach for analytically solving the time-dependent Schrodinger equations for multilevel atoms driven by amplitude- and/or frequency-modulated concurrent laser fields. The time evolution of externally driven N-level atoms is calculated in an explicit matrix form. The exact analytical conditions for complete population transfer and its return are simply connected with the parameters of the symmetry. We consider in detail the case of a four-level system driven by concurrent laser pulses of different forms.
Sergey V. Prants,
"Multilevel atomic dynamics in modulated laser field", Proc. SPIE 2098, Computer Simulation in Nonlinear Optics, (3 May 1994); doi: 10.1117/12.175134; https://doi.org/10.1117/12.175134