Cross Peaks on Two-Dimensional Optical Spectra Arising from Quantum Cross-Correlation Functions

Cross peaks on 2D optical spectra are indicative of interactions between molecular excitonic states. Currently, the two conventional assignments of cross peaks are direct coupling and population transfer between excitonic states. Here, we show that there is another possible source of cross peaks. We theoretically demonstrate that for a model comprising two nondirectly interacting excitons or two-level systems (TLSs), cross peaks can arise if there is a complex-valued or quantum frequency-gap cross-correlation function between the two TLSs. Considering only real-valued or classical cross-correlation functions will result in no cross peaks. We derive and validate the mathematical expressions describing such cross peaks. We then simulate the 2D electronic spectra of an example model system comprising nondirectly interacting TLSs whose quantum cross-correlation functions arise from coupling to a common overdamped Brownian oscillator mode. We show that there are clear observational differences between such quantum correlation cross peaks with conventional direct coupling and population transfer cross peaks.