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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.

Multiple Exciton Coherence Sizes in Photosynthetic Antenna Complexes viewed by Pump−Probe Spectroscopy