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A theory for four-wave-mixing signals from molecular aggregates, which includes effects of two-exciton states, static disorder, and coupling to a phonon bath with an arbitrary spectral density, is developed. The third-order polarization is rigorously partitioned into a coherent and a sequential contribution. The latter is given by a sum of an exciton-hopping and a ground state ͑bleaching͒ terms, both expressed using the doorway-window representation. Applications are made to photon-echo and pump-probe spectroscopies of the B850 system of the LH2 antenna in purple bacteria. ͑1͒where B n † (B n ) are exciton creation ͑annihilation͒ operators for the n'th molecule, which satisfy the commutation relationsThe polarization operator P representing coupling of the aggregate to the optical field ϪE(t)• P has a form

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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 (L f ) and localization size (L F ) 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 F ) 15 and that the shift ∆Ω 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 F .

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