Recent conceptional and technical progress makes it possible to prepare and explore strongly-correlated non-equilibrium quantum states of matter. The tremendous level of control and favorable time scales achieved in experiments with synthetic quantum matter, such as ultracold atoms, polar molecules, or trapped ions, renders these systems as ideal candidates to explore non-equilibrium quantum dynamics. Furthermore, very powerful experimental techniques have been developed to study dynamic processes in condensed matter systems as well. These techniques are based on pump-probe spectroscopy on time scales reaching down to sub-femtoseconds. Such technology therefore makes it possible to manipulate and control material properties.
We develop both analytical and numerical techniques to explore the far-from-equilibrium quantum dynamics of these systems. The techniques range from non-equilibrium field theories to exact numerical calculations based on matrix product states. We study fundamental questions including thermalization in closed quantum systems, emergent phenomena in periodically driven Floquet systems, dynamic phase transitions, intertwined order far-from-equilibrium, and the competition between coherence and dissipation.