Elucidation of population and coherence dynamics using cross-peaks in two-dimensional electronic spectroscopy

In this work, we perform a theoretical study on the dynamics and two-dimensional electronic spectroscopy of a model trimer system and compare the results to experimental data on the Fenna-Matthews-Olson protein. We combine a time-nonlocal quantum master equation formalism and the recently developed method for the efficient calculation of third-order photon echo polarization [M.F. Gelin, D. Egorova, W.J. Domcke, J. Chem. Phys. 123 (2005) 164112] to simulate the 2D electronic spectra of the model system, and compare the time-evolution of the amplitude of cross-peaks to the coherent relaxation dynamics of the system following the excitation by a laser pulse. We show that beats of the upper diagonal peaks in the absolute value 2D spectra provide a direct probe for the coherence dynamics in the system, and the time-evolution of the amplitude of the lower diagonal cross-peaks in the real value 2D spectra can be used to reveal the population transfer among exciton states. Our results verify the intuitive description provided by response functions and demonstrate that the full coherent dynamics in a multichromophoric system can be elucidated using two-dimensional electronic spectroscopy.