Topological quantum synchronization: Integrating nonnlinear dynamics and topological phases under nonequilibrium conditions

• Applicant: Dr. Christopher Wächtler
• Subject Area: Theoretical Condensed Matter Physics
• Term: from 2022 to 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 496502542

When systems are coupled to external reservoirs a variety of phenomena with no counterpart in closed systems may be observed. One of these is synchronization, which is a hallmark of collective behavior in nonequilibrium systems and which describes the adjustment of rhythms due to (even inhomogeneous) interactions. Recently, this ubiquitous phenomenon found throughout nature has emerged as a field in the quantum domain for understanding correlations and with applications in quantum networks, where controlling synchronization is essential to fulfill their functions. Yet, unavoidable defects, local deformations caused by temperature or other ambient conditions difficult to control as well as long-term degradation can have a large impact on the collective behavior or even destroy the synchronicity altogether. It is therefore desirable to investigate universal principles to enhance the robustness of synchronization. On the other hand, the application of topology has become an integral part in condensed matter physics leading to the discovery of phases characterized by global invariants rather than by local order parameters. These new phases of matter exhibit an unusual robustness to the adverse effects of impurities and defects. However, it is far from being completely understood what impact interactions with the environment have on topological systems and whether topological features are still available under such open system conditions. In this research proposal we aim to integrate topology 
known from condensed matter physics with nonlinear dynamics and open quantum systems. This will shine light on fundamental theoretical questions like how many-body classical
nonlinear dynamical effects like synchronization get translated to the quantum domain and how they can be combined with topological concepts. Moreover, quantum synchronization stabilized by topology may improve the performance of devices like for example frequency-locking lasers or high-precision clocks.

• DFG Programme: WBP Fellowship
• International Connection: USA
• Hosts: Professor Joel Moore, Ph.D.; Professor Norman Yao, Ph.D.