Topology in Nonequilibrium Quantum Many-Body Dynamics

• Applicant: Professor Dr. Jan Budich
• Subject Area: Theoretical Condensed Matter Physics ; Optics, Quantum Optics and Physics of Atoms, Molecules and Plasmas
• Term: from 2019 to 2023
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 419241108

The discovery of topological phases has led to a paradigm shift in the way scientists think about the classification of matter. Going conceptually beyond the conventional Landau paradigm, topological phases characterized by global topological properties rather than local order parameters have become a broad frontier of research, with promising applications regarding new forms of information processing and high precision metrology. In parallel, exploring dynamical properties beyond the realm of thermal equilibrium has proven to be key to the understanding of crucial many-body phenomena. Prominent examples in this non-equilibrium context that are of relevance for the present project include the study of thermalization and state preparation as dynamical processes, as well as revealing dynamical signatures of phases of matter. Our proposed research bridging the fields of non-equilibrium quantum dynamics and topological quantum matter is aimed at revealing the role of topology in the real-time dynamics of quantum many-body systems. This research is not only of deep theoretical interest, but is also strongly motivated by its immediate relevance for ongoing experimental activity on inherently non-equilibrium quantum many-body systems, such as ultracold atomic gases and light-driven solid state systems. Starting from a controlled (topologically trivial) initial state, the generic experimental protocol in such systems is to perform a parameter quench by switching on some external driving to realize some Hamiltonian of interest. This may lead to situations which are qualitatively different from any equilibrium scenario, e.g. when the topological properties of the instantaneous Hamiltonian and the wave-function differ after the quench. Despite their natural occurrence in ongoing experiments, the physical consequences of such situations are far from being conclusively understood, in particular for correlated systems – the main focus of the present project. Concretely, in this project we will (A) identify new ways to dynamically probe topological properties far from equilibrium in correlated systems, and (B) propose and study scenarios to dynamically prepare low-temperature states of topological phases in a non-equilibrium fashion. Relating to (A), we will analyze as to what extent topological properties can dynamically equilibrate in interacting many-body systems, and search for dynamically defined topological invariants without a direct equilibrium analog. Regarding (B), we aim at proposing experimentally feasible scenarios to dissipatively prepare strongly correlated topological phases as steady states of a quantum master equation. In this open quantum system context, we also intend to address natural questions regarding the topological classification and its observable consequences beyond the realm of Hamiltonian dynamics and pure quantum states.

• DFG Programme: Research Grants