  A vibronic exciton model is developed to investigate the origin of long lived
coherences in light-harvesting complexes. Using experimentally determined
parameters and uncorrelated site energy fluctuations, the model predicts
oscillations in the nonlinear spectra of the Fenna-Matthews-Olson (FMO) complex
with a dephasing time of 1.3 ps at 77 K. These oscillations correspond to the
coherent superposition of vibronic exciton states with dominant contributions
from vibrational excitations on the same pigment. Purely electronic coherences
are found to decay on a 200 fs timescale.
