Extracting coupling-mode spectral densities with two-dimensional electronic spectroscopy

Methods for reconstructing the spectral density of a vibrational environment from experimental data can yield key insights into the impact of the environment on molecular function. Although such experimental methods exist, they generally only access vibrational modes that couple diagonally to the electronic system. Here we present a method for extracting the spectral density of modes that couple to the transition between electronic states, using two-dimensional electronic spectroscopy. To demonstrate this, we use a process-tensor method that can simulate two-dimensional electronic spectroscopy measurements in a numerically exact way. To explain how the extraction works, we also derive an approximate analytical solution, which illustrates that the non-Markovianity of the environment plays an essential role in the existence of the simulated signal.