Study on Time-Dependent Absorption Theory of Three Light Pulses in a Ladder-Type Four-Level System

The time-dependent theory of the absorption of three light pulses with an arbitrary duration in ladder-type four-level systems is proposed. The pulses are in resonance with the corresponding transitions. By using the time-dependent perturbation theory the spectral and temporal behaviour of the probability that the fourth level is excited at the moment t is found. We calculate and analyse the cases where the frequencies of the maxima of the two of three light pulses are fixed and the maximum of the remaining pules varies. Widths of possible absorption lines depend on different parameters. On the whole, three or four lines may exist, one of them corresponds to coherent contribution and the others do not.