Many-Body Cavity QED: Nonequilibrium and Emergent Phenomena

The aim of this project is to study theoretically nonequilibrium dynamics and emergent phenomena in the framework of "many-body cavity quantum electrodynamics" (QED). In particular, systems of interest include ultracold single- and multi-component Bose and Fermi quantum gases with their motional and internal dynamics strongly coupled to multi-mode cavities. These systems constitute a novel class at the interface between single- or few-body open quantum-optic systems and thermally-equilibrium many- body quantum-gas systems, and exhibit characteristic behaviors of both classes, namely, nonequilibrium dynamics and many-body collective effects. As a consequence of the interplay between these two aspects, nonequilibrium (self-)orders emerge in these systems. This project will initially develop a general theoretical framework based on the nonequilibrium Keldysh formalism to study such nonequilibrium many- body multi-mode cavity-QED setups. In particular, using the developed Keldysh formalism and other advance theoretical techniques, this project will thoroughly investigate intriguing quantum phenomena in these systems, namely, quantum spin models with tunable-range cavity-mediated interactions, cavity-induced emergent dynamical gauge potentials and dynamical phases, and cavity-based quantum-enhanced metrology and non-destructive measurements. This project will significantly deepen our understanding of many-body multi-mode cavity-QED systems. It should stimulate and guide near future experimental investigations as well as further theoretical studies. Implementing and exploring the systems considered in this project in state-of-the-art experiments in a controlled way could address important questions in open many-body quantum physics. Studies carried out in this project will be of interest to a broad scientific community, including both ultracold-atomic and cavity-quantum- electrodynamics communities, and may find applications in emergent technologies such as spintronics and quantum metrology. Furthermore, this project will provide crucial information regarding self-ordering and emergence -- phenomena relevant and vital to many scientific fields, from physics and chemistry to biology and social science. Therefore, this project will be a thrust to the thriving field of many-body cavity QED.