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We propose a two-step protocol for inverting ultrafast spectroscopyexperiments on a molecular aggregate to extract the time-evolution of theexcited state density matrix. The first step is a deconvolution of theexperimental signal to determine a pump-dependent response function. The secondstep inverts the quantum state of the system from this response function, givena model for how the system evolves following the probe interaction. Wedemonstrate this inversion analytically and numerically for a dimer modelsystem, and evaluate the feasibility of scaling it to larger molecularaggregates such as photosynthetic protein-pigment complexes. Our schemeprovides a direct alternative to the approach of determining all Hamiltonianparameters and then simulating excited state dynamics.

Inverting pump-probe spectroscopy for state tomography of excitonic systems