Nonequilibrium dynamics and relaxation in many-body quantum systems

Non-equilibrium systems are found everywhere in nature. Even though much is known about equilibrium properties, the pathways of relaxation and their relevant time scales are much less understood. Many-body quantum systems out of equilibrium and their dynamics and relaxation are central to many different areas of physics. Open problems appear at vastly different energy and length scales, ranging from high-energy physics and cosmology to electron dynamics in condensed matter and the emerging field of quantum biology. Moreover de -coherence and the emergence of the classical world from the microscopic quantum description is an inherent non-equilibrium process. In this project we propose to probe the fundamental physics governing the non -equilibrium evolution and relaxation in quantum many-body systems through laboratory experiments. Systems of ultra-cold atoms provide unique opportunities for studying non-equilibrium problems and their related quantum dynamics. A large variety of tools allow precise preparation of far-from-equilibrium initial states and coherent quantum evolution can be observed on experimentally accessible timescales. In addition, the tunability in interaction, temperature and dimensionality allows the realization of a multitude of different physical situations, giving insight into the corresponding quantum field theories. Through building specific model systems we will study a wide variety of non-equilibrium quantum dynamics under conditions ranging from weakly interacting to strongly correlated, from weakly disturbed to quantum turbulent, from slowly progressing to unstable and exponentially growing. We expect to get deep insight into such intriguing phenomena as pre- thermlization, (quasi)particle creation, amplification of excitations and entanglement spreading. A central part in our investigations is played by isolated systems, where the relaxation is entirely due to internal quantum dynamics. This will, in addition to the more general questions above, allow to probe directly if, and under which circumstances, classical physics can emerge from microscopic quantum evolution through the dynamics of complex many- body systems. Our ultimate goal is insight into: What does it take for a many-body quantum system to relax to an (apparent) equilibrium state? Which universal properties and scaling laws govern its evolution? We hope to pave the way for a general, even universal, understanding of non- equilibrium many-body quantum systems across the plethora of research fields for which they are important.

This research project builds on the successful results of the previous funding phase and continues exploring the behavior of quantum systems far from equilibrium, with a focus on one-dimensional (1D) quantum gases. One central theme is understanding universal scaling-patterns that remain consistent across different systems-and connecting these observations to theoretical models such as the Kibble-Zurek mechanism, which describes how systems transition across critical points. A key achievement was the study of gaussification-how a system's distribution evolves towards a Gaussian shape during relaxation. This work was published in Nature Physics and further elaborated in SciPost Physics. Parallel efforts targeted improved experimental control using advanced optical techniques and machine learning for precise shaping of trapping potentials. Another major research direction addressed a long-standing puzzle from earlier work on a 1D bosonic Josephson junction. The team, in collaboration with international theory groups, identified that unexpected relaxation behavior stems from complex nonlinear dynamics caused by harmonic potentials. Ongoing work explores how alternative geometries, such as flat-bottom traps and ring potentials, might suppress these effects. The group also investigated Floquet engineering, where a periodically modulated double-well potential enables precise control of tunneling between two quantum gases. This method allowed them to initiate coherence between initially uncorrelated systems and explore the emerging dynamics under the sine-Gordon model, a fundamental theory in quantum field physics. In a pioneering study, the researchers examined universal scaling in strongly interacting Bose-Einstein condensates (BECs) of Li molecules-a regime where standard models and even simulations fail. Despite the complexity, they observed clear scaling behavior and connections to previous results in weakly interacting rubidium systems. To refine the measurements, they developed techniques to reduce final-state interaction effects, including studies on diffraction of molecular BECs. The project also pushed the frontier of quantum information in field theory. Using quantum field tomography, the team reconstructed the full fluctuation structure of a 1D quantum field and demonstrated the area law of mutual information. In another experiment, they observed how information spreads in a quantum field in an effectively curved space-time-a novel link between quantum dynamics and general relativity. Further theoretical work advanced Generalized Hydrodynamics (GHD) for describing non-equilibrium dynamics in near-1D systems. They successfully extended GHD into the dimensional crossover regime and benchmarked it against their own experiments. Lastly, a new collaboration explored Hamiltonian Learning-a powerful method for inferring the structure of quantum field theories from experimental data, offering insight into energy-scale-dependent behavior and the flow of effective theories. Together, these advances bring us closer to understanding and controlling complex quantum systems with implications for both fundamental science and future quantum technologies.