We theoretically investigate the evolutions of two-dimensional, third-order, nonlinear photon echo rephasing spectra with population time by using an exact numerical path integral method. It is shown that for the same system, the coherence time and relaxation time of excitonic states are short, however, if the couplings of electronic and intra-pigment vibrational modes are considered, the coherence time and relaxation time of this vibronic states are greatly extended. It means that the couplings between electronic and vibrational modes play important roles in keeping long-lived coherence in light-harvesting complexes. Particularly, by using the method we can fix the transition path of the energy transfer in bio-molecular systems.
