Phase space and tensor network methods for two-dimensional quantum dynamics with power-law interactions

A key goal in modern quantum science is to harness the complex behavior of quantum systems to develop new technologies. While precisely engineered platforms with ultracold atoms and trapped ions have emerged as powerful tools for this task, our limited ability to theoretically and numerically model these systems poses immense challenges for their improved control and characterization. Here, I discuss the application of modern computational techniques, including tensor networks and efficient phase space methods, to study the quantum dynamics of many-body systems, with features relevant for an array of current experiments. As a specific case study, I will present strategies for the robust generation of spin squeezed states – a special type of entangled resource that can be used for enhanced precision sensing – in current quantum sensors. Beyond applications for current experiments, including arrays of Rydberg atoms, polar molecules, and trapped ions, these studies shed light on the fundamental behavior of canonical models for quantum chaos and quantum magnetism.