Extracting the excitonic Hamiltonian of the Fenna-Matthews-Olson complex using three-dimensional third-order electronic spectroscopy.

We extend traditional two-dimensional (2D) electronic spectroscopy into a third Fourier dimension without the use of additional optical interactions. By acquiring a set of 2D spectra evenly spaced in waiting time and dividing the area of the spectra into voxels, we can eliminate population dynamics from the data and transform the waiting time dimension into frequency space. The resultant 3D spectrum resolves quantum beating signals arising from excitonic coherences along the waiting frequency dimension, thereby yielding up to 2n-fold redundancy in the set of frequencies necessary to construct a complete set of n excitonic transition energies. Using this technique, we have obtained, to our knowledge, the first fully experimental set of electronic eigenstates for the Fenna-Matthews-Olson (FMO) antenna complex, which can be used to improve theoretical simulations of energy transfer within this protein. Whereas the strong diagonal peaks in the 2D rephasing spectrum of the FMO complex obscure all but one of the crosspeaks at 77 K, extending into the third dimension resolves 19 individual peaks. Analysis of the independently collected nonrephasing data provides the same information, thereby verifying the calculated excitonic transition energies. These results enable one to calculate the Hamiltonian of the FMO complex in the site basis by fitting to the experimental linear absorption spectrum.