Quantum Many-Body Dynamics of Matter and Light in Cavity-QED

Ultracold atoms strongly coupled to optical cavities formed by two high-quality tiny mirrors constitute a novel class of quantum light and matter systems, commonly referred to as "cavity quantum electrodynamics" (CQED). These hybrid systems of photons and mater waves offer a versatile platform for fundamental studies as well as quantum control and quantum simulation due to unprecedented controllability of these systems. On the University of Innsbruck side the focus of this international project is the theoretical study of atomic quantum gas cavity QED, as well as providing simulation support and predictions for our experimental partners in the ETH Zurich and EPFL Lausanne. In particular, we will study theoretically two topics: Adaptive self-organization: Atoms located inside optical cavities organize themselves dynamically to scatter light efficiently under changing illumination. This process, called "adaptive self-organization", involves atoms forming patterns that maximize light scattering into the cavity. Remarkably, the system "remembers" some optimum patterns and can quickly reorder to recover those patterns. This memory is linked to metastability -- states where atoms temporarily settle before reaching optimal arrangements. We believe the role of cavity dissipation (energy loss from mirrors) is central to this behavior and we will investigate this in detail. In particular, dissipation modifies the stability of metastable configurations, reducing the time needed to switch between patterns and reach the desired optimal state. At extremely low temperatures, quantum motion of the atoms may further enhance this process. Simulation of gauge potentials: The simplest gauge field is electromagnetism. When charge particles, like electrons, are located in space which is filled by electromagnetic potentials, their behavior changes fundamentally. However, charge neutral particles, such as atoms, do not experience these gauge potentials in the same way. It is, nonetheless, fundamentally important to understand what happens if charge neutral particles can also "somehow" experience gauge potentials. This idea is the corner stone of this part of our research. In particular, we will explore how to create and manipulate artificial gauge fields in ultracold atomic systems using cavities. These gauge fields, which act as dynamic variables, can mimic phenomena such as those encountered in condensed matter physics as well as the standard model of elementary particles, therefore offering a practical window to physics of highly correlated systems and sub-atomic particles.