A study on cross peaks in two-dimensional optical spectroscopy: Quantum cross-correlation functions and interplay with excitonic coupling

We present a comprehensive theoretical framework for simulating the two-dimensional (2D) optical spectra of molecular systems with complex-valued quantum frequency fluctuation cross-correlation functions (FXCFs). The FXCF contains information on the indirect interactions between two separate molecular excitations via coupling to common harmonic bath modes. We derive the complete set of third-order nonlinear optical response functions and systematically analyze their dynamic spectral features in the resulting 2D spectra. These include cross peaks and oscillating features, which appear only when the full complex-valued FXCF is used. If only the real-valued or "classical" FXCF is considered, the spectral signatures of the indirect interactions via coupling to the common modes do not manifest in the 2D spectra. In addition, we investigate how these spectral signatures of indirect interaction are modulated in the presence of excitonic coupling.