Time-dependent pulse and frequency effects in population trapping via the continuum

We investigate the effects of smooth laser pulses in both an autoionization system and in the laser-induced continuum structure scheme. We are particularly interested in the phenomenon of population trapping in these systems and discuss the effects of time-dependent pulses on this trapping. We present analytical solutions to both systems which hold for any pulse shape, provided the adiabatic approximation holds. We also pay special attention to the effects of large pulse energies on the trapped population, which we find to be detrimental and propose a possible solution to this problem by using chirped (time-dependent) frequencies.