Calculation of third-order signals via driven Schrödinger equations: General results and application to electronic 2D photon echo spectroscopy

We present the wavefunction (WF) version of the equation-of-motion phase-matching approach (EOM- PMA) for the calculation of four-wave-mixing (4WM) optical signals. For the material system, we consider a general electronic-vibrational Hamiltonian, comprising the electronic ground state, a manifold of singly-excited electronic states, and a manifold of doubly-excited electronic states. We show that the calculation of the third-order polarization for particular values of the pulse delay times and in a specific phase-matching direction requires 6 independent WF propagations within the rotating wave approximation. For material systems without optical transitions to doubly-excited electronic states, the number of WF propagations is reduced to 5. The WF EOM-PMA automatically accounts for pulse- overlap effects and allows the efficient numerical calculation of 4WM signals for vibronically coupled multimode material systems. The application of the method is illustrated for model systems with strong electron-vibrational and electronic inter-state couplings.