Mapping the spatial overlap of excitons in a photosynthetic complex via coherent nonlinear frequency generation.

We experimentally demonstrate a nonlinear spectroscopic method that is sensitive to exciton-exciton interactions in a Frenkel exciton system. Spatial overlap of one-exciton wavefunctions leads to coupling between them, resulting in two-exciton eigenstates that have the character of many single-exciton pairs. The mixed character of the two-exciton wavefunctions gives rise to a four-wave-mixing nonlinear frequency generation signal. When only part of the linear excitation spectrum of the complex is excited with three spectrally tailored pulses with separate spatial directions, a frequency-shifted third-order nonlinear signal emerges in the phase-matched direction. We employ the nonlinear response function formalism to show that the emergence of the signal is mediated by and carries information about the two-exciton eigenstates of the system. We report experimental results for nonlinear frequency generation in the Fenna-Matthews-Olson (FMO) photosynthetic pigment-protein complex. Our theoretical analysis of the signal from FMO confirms that the emergence of the frequency-shifted signal is due to the interaction of spatially overlapped excitons. In this method, the signal intensity is directly measured in the frequency domain and does not require scanning of pulse delays or signal phase retrieval. The wavefunctions of the two-exciton states contain information about the spatial overlap of excitons and can be helpful in identifying coupling strengths and relaxation pathways. We propose this method as a facile experimental means of studying exciton correlations in systems with complicated electronic structures.