Interacting open synthetic dimensions systems

Recent technological advances are propelling the field of quantum simulation, with pioneering light-matter experiments in electronic, cold-atomic, and photonic systems. These developments enable the creation of systems with “synthetic dimensions”, where observable effects emerge from dimensions higher than that of the physical experimental setup. Such systems are inherently out of equilibrium, as synthetic dimensions arise from parametric drives that couple internal degrees of freedom or adiabatic drives that sweep across periodic parameter spaces.Synthetic dimensions provide a powerful platform for realizing models previously considered purely theoretical. For instance, they allow for the experimental realization of 2D topological pumps that map to the 4D quantum Hall effects, with boundary phenomena that reveal the origin of high-order topological insulators and applications such as on-chip quantum light routing. These advancements open new avenues for fundamental discoveries and technological applications. However, the current focus remains largely on noninteracting systems, where research predominantly addresses the interplay between time-dependent drives, noise, disorder, and dissipative bath couplings in an out-of-equilibrium setting.This project aims to transcend the noninteracting paradigm, pioneering a theoretical exploration of many-body interaction effects in synthetic dimensions. We will develop advanced field-theoretical and numerical tools to analyze high-dimensional models and uncover their unique many-body phenomena. In collaboration with experimentalists, we will propose and design realizations that reveal exotic many-body physics in synthetic dimensions using cold-atomic and photonic systems, thus, elucidating effects in more traditional condensed matter systems. Our interdisciplinary approach bridges condensed matter physics and quantum engineering, facilitating the exploration of models typically associated with high-energy physics.