Multiple exciton coherence sizes in photosynthetic antenna complexes viewed by pump-probe spectroscopy

The pump-probe signal from the light-harvesting antenna LH2 of purple bacteria is analyzed using a Green function expression derived by solving the nonlinear exciton-oscillator equations of motion (NEE). A microscopic definition of the exciton mean free path (L-f) and localization size (L-rho) is given in terms of the off-diagonal elements of the exciton Green function and density matrix, respectively. Using phonon-induced (homogeneous) and disorder-induced (inhomogeneous) line widths compatible with superradiane measurements, we find that at 4.2 K the localization size is L-rho = 15 and that the shift Delta Omega between the positive and negative peaks in the differential absorption is determined by a different effective size L-f/2 = 5.6 associated with the exciton mean free path. Our model further predicts the recently observed superradiance coherence size determined by L-rho.