Efficient calculation of the polarization induced by N coherent laser pulses

We have developed a novel method, the equation-of-motion phase-matching approach (EOM-PMA), for the calculation of the response of a quantum system to N coherent laser fields. The N-pulse EOM-PMA is limited to weak fields (its domain of validity is equivalent to the traditional nonlinear response functions approach), but allows for arbitrary pulse durations and automatically accounts for pulse-overlap effects. The N-pulse EOM-PMA allows the evaluation of the time evolution of the N-pulse-induced polarization in any phase-matching direction by performing 2(N)-1 independent propagations of certain auxiliary density matrices. The N-pulse EOM-PMA can straightforwardly be incorporated into codes which provide the time evolution of the density matrix of material systems of interest and can efficiently be implemented on parallel computers.