Two-dimensional electronic spectra investigated using hierarchical equation of motion and cumulant expansion

Abstract

We investigate the two-dimensional third-order nonlinear electronic spectra using the cumulant expansion (CE) and hierarchical equation of motion (HEM) methods. The HEM method is non-Markovian and nonperturbative. In the CE method, the Markovian approximations are always applied in solving dynamical equations and calculating the line-broadening function. If the Markovian approximation is used in the dynamical solutions and theaffected by the line-broadenin calculations of the line-broadening function in the CE method, the nonlinear electronic spectra obtained are different from those obtained using the HEM method. However, using the non-Markovian line-broadening function, we obtain almost the same spectra from the two methods, even when keeping the Markovian approximation in the dynamical solutions. This may imply that in order to obtain the correct nonlinear electronic spectra, it is crucial to include the non-Markovian effect in the line-broadening function, but it may not matter if the Markovian approximation is used in solving the dynamical equations.