Extracting dynamics of excitonic coherences in congested spectra of photosynthetic light harvesting antenna complexes.

We present an analysis of dephasing rates for multiple zero-quantum electronic coherences in the Fenna-Matthew-Olson (FMO) pigment-protein complex using two-dimensional electronic spectroscopy. We employ the linear prediction Z-transform to determine both the frequency and decay rates of 8 individually assigned exciton-exciton coherences. Despite congestion in the spectra, we can isolate multiple crosspeaks signals and analyze their dephasing rates. A nontrivial relationship exists between the excitons and the bath determining the lifetimes of different exciton-exciton coherences. We propose that the correlations that protect long-lived electronic coherence may yield microscopic knowledge regarding the structure of the protein bath surrounding the chromophores.