Quantum many-body dynamics of atomic platforms for quantum simulation and metrology

A key goal in modern quantum science is to harness the complex behavior of quantum systems to develop new technologies. While precisely engineered platforms featuring ultracold atoms and trapped ions have emerged as powerful tools for this task, the limited ability to theoretically probe these systems poses challenges for improved control and characterization. In this thesis, I focus on the development of new computational tools, utilizing tensor networks and phase space methods, for studying the far-from-equilibrium dynamics of quantum many-body systems. As a specific case study, I explore robust protocols to generate entangled states for enhanced precision sensing.