Theory of photon echoes from a pair of coupled two level systems: Impurity dimers and energy transfer in molecular crystals

We present the theory of the photon echo and stimulated photon echo from a four level system that results from a pair of weakly coupled two level systems. This model describes an impurity dimer in a molecular crystal. We include the effect of relaxation processes, focusing on energy transfer between delocalized states. We find that both the photon and stimulated echoes contain information about static level splittings and dynamic energy transfer processes. Moreover, these observables show a dramatic dependence on the excitation power. We discuss implications of our results for recent experiments on concentration dependent dephasing of impurities in molecular crystals. Our analysis casts considerable doubt on the intermolecular interaction interpretation of these experiments.