Unsupervised learning approach to quantum wave-packet dynamics from coupled temporal-spatial correlations

Understanding complex quantum dynamics in realistic materials requires insight into the underlying correlations that dominate the interactions between the participating particles. Due to the wealth of information involved in these processes, the application of artificial intelligence (AI) methods is compelling. However, unsupervised data-driven approaches typically focus on identifying maximum variations in data, rather than considering the correlations between them. Here, we present an approach that recognizes correlation patterns to explore convoluted dynamical processes. Our scheme uses singular value decomposition to extract dynamical features, unveiling the internal temporal-spatial interrelations that generate the dynamical mechanisms. We apply our approach to study light-induced wave-packet propagation in organic crystals, of interest for applications in material-based quantum computing and quantum information science. We show how transformation from the input momentum and time coordinates onto a new correlation-induced coordinate space allows direct recognition of the relaxation and dephasing components dominating the dynamics and we demonstrate their dependence on the initial pulse shape. A tensor product state composed of a linear combination of singular vectors is suggested as a pathway to reproduce the information required for further explainability of these mechanisms. Our method offers a route for elucidating complex dynamical processes using unsupervised AI-based analysis in multicomponent systems.