Ultrafast spectroscopy techniques are powerful tools for investigating quantum mechanical processes in real time. In particular, electronic spectroscopy (2DES) has yielded key insights into energy transfer processes in light-harvesting molecules. These systems never exist in isolation, but are coupled to some larger vibrational environment that will affect the dynamics of the system. Realistic environments are therefore generally non-Markovian, meaning that they retain a memory of their interactions with the system. Here we present an efficient method for simulating 2DES measurements of non-Markovian open quantum systems. With this, we introduce a general algorithm for computing multi-time correlation functions in a numerically exact way, using an object known as a process tensor. This is essentially the most general representation of an open system environment, and is particularly well-suited for the calculation of observables that span multiple time points. Using these techniques, we secondly propose a protocol for extracting the spectral density of a vibrational environment with 2DES. Although such experimental methods already exist, these generally only access modes that couples diagonally to the electronic system. In contrast, we focus on the spectral density of modes that couple to the transitions between electronic states, We lastly discuss a minimal model for vibrational control in a donor-bridge-acceptor molecule. Based on experimental work, charge transfer rates in such a molecule can be manipulated by perturbing certain intramolecular vibrational modes with an infrared laser pulse. We show how a model explaining the observed control mechanism could be formulated in an open quantum systems framework.
Roosmarijn Markje Arie de Wit (Wed,) studied this question.