Non equilibrium dynamics and relaxation in many-body quantum systems

Non-equilibrium systems are found everywhere in nature. Even though much is know 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 diverse 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 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 many body quantum 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 and the related quantum field theories Through building specific model systems we will to 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 instabilities and exponential growth. 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 dynamics, which is quantum. This will, in addition to the more general questions above, allow probing 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.

Even though much is known about equilibrium states of quantum many body systems, very little do we know about non-equilibrium dynamics and relaxation in these systems. Especially if and how an isolated quantum system relaxes towards a (thermal) equilibrium remains elusive. In this project we employ ultra-cold quantum gases to study many body quantum systems out of equilibrium in a large variety of settings from weakly to strongly interacting. In particular we will focus on non-equilibrium states in continuous 1D systems created (1) by fast quenches and (2) by special designed protocols that allow to reach a non-perturbative regime by keeping the product of coupling strength and number of excitations g Nexc >> 1. A central objective is to uncover universal properties and the related scaling laws governing non-equilibrium relaxation and its quasi steady states across different systems and settings. During the last 4 years we developed novel methods to probe quantum many body physics by high order correlations and employed those to extract the fundamental parameters of the effective field theory description: the propagators and the vertices and their dependence on momentum (running coupling constants) describing the system. We furthermore elucidated the role of information about a system under investigation and its relaxation behavior. We demonstrated quantum recurrences for many body systems with thousands of particles, directly demonstrating the quantum physics is still full alive underneath an apparent classical density matrix. Finally, together with a parallel experiment in the Oberthaler lab in Heidelberg we demonstrated universal scaling and non-equilibrium universality in relaxation. This points to a generalization of the renormalization group to non-equilibrium physics and to the existence of non-thermal fixed points. This suggest that non-equilibrium evolution can be classified in universality classes. If this solidifies, then, in analogy to equilibrium phase transitions, building one system can quantum simulate the non-equilibrium evolution in any system of the same universality class.