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 (Lf) and localization size (Lρ) 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 Lρ = 15 and that the shift ΔΩ between the positive and negative peaks in the differential absorption is determined by a different effective size Lf/2 = 5.6 associated with the exciton mean free path. Our model further predicts the recently observed superradiance coherence size determined by Lρ.