Non-perturbative approach to three-pulse photon echo

We rewrite the nonlinear spectroscopy response with the formalism developed in quantum optics. Instead of commonly used perturbation approach, we adapt a quantum dynamical evolution into the calculation of signal. In this new approach, we show that high-order terms has essential contribution to the nonlinear signal of the three-pulse photon echo. A detailed study of the two-pulse and three-pulse echo is performed to show the advantage of using three pulses in the experiments to direct probe the coherence between two excited states. We demonstrate the principal with a three-level V-type system. And we show the correlation between the bath modes of the two excited states may induce a longer decoherence time than that with only independent baths.