Interference effects on relaxation in three-level systems: breakdown of the rate equation description

The stochastic Liouville equation and exact quantum mechanical simulations have been used to test the validity of rate law predictions for the vibrational energy relaxation in a three-level system. The model system consists of a low lying ground state which is radiatively coupled to only one of three closely spaced excited states. All three excited states are strongly coupled to baths of known statistical properties (either Gaussian or Poisson). We follow the energy exchange between the excited states after the light is turned off. Two different types of bath correlation have been considered: (A) The couplings between the different levels are the same and (B) the couplings are uncorrelated with each other. We find that relaxation differs for these two cases, in contradication to the prediction of the simple rate law description. We also present the first quantitative study of the interference between different pathways that can occur in such a three-level system. We find that the interference has a considerable effect on the decay of the middle level for the same bath (case A), even in the Markovian limit, while for independent baths (case B) interference becomes important only in the non-Markovian limit. These results are entirely different from the prediction of the conventional rate laws. We also discuss the effect of the excitation on the subsequent relaxation and the coherence transfer processes that lead to an oscillatory decay in the non-Markovian limit