Interplay of exciton annihilation and transport in fifth order electronic spectroscopy

Multidimensional fifth order spectroscopy is a sophisticated and specialized tool for probing bi-exciton dynamics. The complexity of the signals emitted into ±2K→₁∓2K→₂+K→₃ directions calls for a detailed theoretical treatment of 2D line shapes, including both exciton-exciton annihilation and intraband relaxation dynamics. Based on a master equation formalism, we discuss the signal's temporal evolution and clearly distinguish between intraband transport within first and second exciton manifolds. We prove analytically that signatures of single exciton transport vanish from spectrally integrated signals of parallel homo-aggregates of arbitrary length, while transport within the second manifold accounts for the diffusion limitations of annihilation. In an effort to model fifth order electronic spectra of tractably small systems, we develop a dynamical model for molecular dimers and trimers. We show that fifth order two-dimensional spectroscopy allows to track and pinpoint population transfer- and annihilation dynamics of bi-excitons, without the need to perform and analyse intensity dependent experiments.