Towards a coherent picture of excitonic coherence in the Fenna-Matthews-Olson complex

Observations of long-lived coherence between excited states in several photosynthetic antenna complexes has motivated interest in developing a more detailed understanding of the role of the protein matrix in guiding the underlying dynamics of the system. These experiments suggest that classical rate laws may not provide an adequate description of the energy transfer process and that quantum effects must be taken into account to describe the near unity transfer efficiency in these systems. Recently, it has been shown that coherences between different pairs of excitons dephase at different rates. These details should provide some insight about the underlying electronic structure of the complex and its coupling to the protein bath. Here we show that a simple model can account for the different dephasing rates as well as the most current available experimental evidence of excitonic coherences in the Fenna-Matthews-Olson complex. The differences in dephasing rates can be understood as arising largely from differences in the delocalization and shared character between the underlying electronic states. We also suggest that the anomalously low dephasing rate of the exciton 1-2 coherence is enhanced by non-secular effects.