Final Report Summary - QUANTUM VIBES (Structured Vibrational Environments and Quantum-Coherent Transport in Chiral Systems) The last few years have seen a renewed interest into the mechanism of electronic energy transfer (EET) during the first steps of photosynthesis stimulated by surprising experimental findings that indicate that EET in natural light-harvesting complexes may involve long-lived quantum-coherent dynamics. EET is a fundamental process relevant not only for biology but also for many applications based on synthetic molecular aggregates. Thus, establishing design principles that support quantum coherent dynamics of electronic excitation in the noisy vibrational environment typical of supramolecular structures may bring paradigmatic changes to the development of quantum-enhanced technologies.The grand challenge of this project was to provide new understandings on the relation between the structured environment of supramolecular aggregates, in particular molecular vibrations, and quantum coherent energy transfer, and how this reflects in measurable spectroscopic features.We first investigated exciton dynamics in a TPPS J-aggregate that has been experimentally studied in the group of Prof. E. Collini in Padova. TPPS J-aggregates are good model systems for biological light-harvesting antenna, and consist of a linear chain of several strongly electronically coupled molecules. The total number of molecules and the details of the electronic parameters is not well-known. By a mutual feedback between theory and experiments, we developed a microscopic model for the electronic excitations and vibrations in the aggregate, which we applied to simulate linear and non-linear optical responses. We applied this model and fine-tuned the parameters to achieve a very good agreement between the simulated and experimental linear (absorption) and non-linear (two dimensional electronic spectroscopy (2DES) rephasing, non-rephasing and 2Q2D) optical spectra. This allowed us to reach two important results: The determination of the energy structure of the one-exciton and two-exciton states in the aggregate, and most importantly, the evidence that exciton dephasing is highly correlated in these strongly coupled aggregates.We have also studied the effect of coupling of excitons with a resonant underdamped vibrational mode on energy transfer efficiency and time-scale of coherent dynamics, a mechanism that has been suggested as responsible for the observation of long-lived coherent dynamics in light-harvesting systems. Starting from an exactly solvable toy model, we have been able to provide new insight into the effect of vibrationally assisted electronic coherence. One of the main contributions of this work was to determine what is the correct basis (global or local basis) to describe the master equation’s dissipator in these kind of problems, which is usually overlooked in the literature, and how the choice affects dynamics and its consistency with quantum thermodynamics. Furthermore, we have investigated in detail the effect of finite bandwidth of the pump and probe pulses in 2DES spectra. This goes beyond most theoretical studies on 2DES that assume that the laser pulses are delta-pulses in time (infinitely broad in frequency), and is crucial for understanding the origin of coherent phenomena in non-linear optical responses.Finally, we have assessed the applicability of the non-Markovian quantum jump approach to excitonic energy transfer and found that it is only efficient under the action of an approximate dissipator for large systems.The results of this project provide new insight into the mechanisms that support quantum coherent dynamics in light-harvesting systems and the microscopic origin of optical spectra.