Theoretical and Computational Insights into Non-Linear Response in Action-2D Electronic Spectroscopy

Two-Dimensional Electronic Spectroscopy (2DES) is a powerful tool for investigating the properties of complex molecular aggregates and nanostructures. By probing the system with a sequence of ultrafast laser pulses, spectral and temporal information are dissected along multiple dimensions, allowing to track energy and charge transfer pathways within multichromophoric systems. Because of the wealth of information contained in the spectra, the origin of certain spectral features can be ambiguous. Therefore, the development of theoretical models and numerical simulations is essential to support their correct interpretation. Recently, a novel implementation of the technique has been realized, known as Action-2DES (A-2DES), calling for theoretical and numerical efforts to establish the correlation between spectral features and the dynamical processes occurring at the molecular scale. While probing the coherent dynamics induced by the interaction with four collinear laser pulses, the technique relies on the measurement of an incoherent signal proportional to the excited-state population, e.g., fluorescence or photocurrent, allowing the investigation of functional dynamics of systems in operando conditions. In this Thesis, we delve into the theory of A-2DES and its numerical simulation to clarify essential aspects of the incoherent signal detected with this technique. To this end, we employed a combination of perturbative and non-perturbative approaches to describe the light-matter interaction. While the former provides the conceptual basis for the analysis of the response in terms of several dynamical pathways, the latter allows the complete simulation of the entire spectroscopic experiment. In A-2DES, the signal is detected over a timescale during which the excited-state population may undergo several processes. We investigated the effects of such population dynamics on the spectra by characterizing the spectroscopic response of a model of quantum dot featuring the interplay between exciton and biexciton contributions to the signal. The involvement of the double-excited manifold in the signal represents a crucial factor shaping the signal in A-2DES. Thus, we analyzed the case in which the double-excited manifold consists of excited states localized on different weakly interacting chromophores. This setting allows to discuss the origin of cross-peaks and incoherent mixing in the signal, first considering the case of a simple molecular dimer and then in a larger molecular assembly. The analysis shows that mixing effects are intrinsic in the A-2DES, and they must be carefully addressed in the design of the sample and the choice of the detection scheme. Our investigation further proceeded by focusing on the dependence of the spectral features on varying the excitonic coupling strength, showing how cross-peaks can either reflect the presence of exciton-exciton annihilation or excitonic delocalization between chromophores, depending on the coupling regime. Finally, we shifted the focus toward a related yet distinct subject, wondering whether emerging quantum computing technologies could contribute to the efficient simulation of 2DES spectra. Accordingly, we designed a quantum algorithm for simulating the non-linear response of multichromophoric systems and provided a proof-of-concept computation considering an excitonic dimer model.