Quantum interferometry and pathway selectivity in the nonlinear response of photosynthetic excitons

We propose a time-frequency resolved spectroscopic technique which employs nonlinear interferometers to study exciton-exciton scattering in molecular aggregates. A higher degree of control over the contributing Liouville pathways is obtained as compared to classical light. We show how the nonlinear response can be isolated from the orders-of-magnitude stronger linear background by either phase matching or polarization filtering. Both arise due to averaging the signal over a large number of noninteracting, randomly oriented molecules. We apply our technique to the Frenkel exciton model which excludes charge separation for the photosystem II reaction center. We show how the sum of the entangled photon frequencies can be used to select two-exciton resonances, while their delay times reveal the single-exciton levels involved in the optical process.