A new method for the calculation of two-pulse time- and frequency-resolved spectra

A method has been developed for the computation of two-pulse time- and frequency-resolved spectra (fluorescence up-conversion, pump-probe, and photon-echo spectra) for dissipative multilevel systems with electronic couplings, which is valid for overlapping pump and probe/gate pulses of arbitrary duration. The pump pulse may be of arbitrary strength, while the probe pulse is assumed to be weak. The calculation is carried out in two steps. An ideal time- and frequency-resolved spectrum is computed first by substituting an auxiliary CW pulse for the actual probe/gate pulse. The (actual and auxiliary) field-matter interactions are incorporated into the system Hamiltonian and treated numerically exactly. The simultaneous propagation of several (from two to three) auxiliary density matrices yields a time-dependent cut of the ideal spectrum at a particular frequency. The spectrum for the actual probe/gate pulse is calculated afterwards by convoluting the ideal spectrum with the appropriate joint time and frequency gate function. The method has a ∼Nω scaling of the computational cost for a time- and frequency-resolved spectrum, in contrast to the ∼Nt × Nω scaling of the previous nonperturbative methods, Nt (Nω) being the number of grid points in the time (frequency) domain.