On the divergence of time-dependent perturbation theory applied to laser-induced molecular transitions

Population transfer between electronic molecular states can be effectively induced via the interaction with shaped laser pulses. Regarding a numerical example, it is demonstrated that perturbation theory, as is often applied in numerical simulations of field-matter interactions, might lead to divergences. The occurring error accumulating in the norm of the wavefunction can be decomposed into two contributions. The first one is a small numerical error, which is controllable by minimization of the time-propagation step, whereas the second one is related to the order of the perturbative expansion. These two contributions behave differently upon variations of the potential energy surface of the system and also the laser pulse parameters. An improved scheme is proposed in which the first part carrying the numerical error disappears.