Signatures of exciton–exciton annihilation in 2DES spectra including up to six-wave mixing processes

Two-dimensional electronic spectroscopy (2DES) is a powerful spectroscopic tool that allows us to study the dynamics of excited states. Exciton-exciton annihilation is at least a fifth order process, which corresponds to intrachromophoric internal conversion from the double-excited high-energy chromophoric state into the single-excited state of the same chromophore. At high excitation intensities, this effect becomes apparent in standard 2DES and can be inspected via high order nK1⃗-nK2⃗+K3⃗ nonlinear processes. We calculate 2DES based on K1⃗-K2⃗+K3⃗ and 2K1⃗-2K2⃗+K3⃗ wave mixing processes to reveal exciton-exciton annihilation (EEA) induced exciton symmetry breaking, which occurs at high excitation intensities. We present the general theory that captures all these processes for bosonic and paulionic quasiparticles in a unified way and demonstrate that the NEEs can be easily utilized for highly nonlinear two-dimensional spectra calculations by employing phase cycling for separating various phase matching conditions. The approach predicts various excitonic third- to fifth-order features; however, due to high excitation intensities, contributions of different order processes become comparable and overlap, i.e., the signals no longer can be associated with well-defined order-to-the-field contributions. In addition, EEA leads to breaking of the exciton symmetries, thus enabling population of dark excitons. Such effects are due to the local nature of the EEA process.