Topological Quantum Synchronization

Synchronization is a particular example of driven-dissipative dynamics, where individual systems adjust their dynamics upon interactions to achieve a unified rhythm. With the recent developments in quantum technology which allow one to exquisitely tailor both the system and environmental properties, synchronization has emerged in the quantum domain with considerable current interest from both basic and applied perspectives. Since the underlying description of the world is quantum, it is natural to ask how synchronization phenomena are modified when the degrees of freedom are quantum, and how the principles of synchronization can be stated in a way compatible with quantum mechanics. In this talk, I will give an overview of different attempts to define and explore quantum aspects of synchronization; in particular, synchronization of quantum limit-cycle oscillators and within the framework of strong dynamical symmetries. Additionally, I will discuss the new frontier of topological quantum synchronization — an interdisciplinary topic which combines topological concepts with synchronization — focusing on two particular examples: First, edge state synchronization in a topological lattice of quantum van der Pol oscillators and second, synchronization of emerging, fractionalized spins in the gapped symmetric phase of the spin-1 Haldane chain. Compared to previous examples of many-body synchronization, this synchronized dynamics does not require any fine tuning and is thus inherently more robust. These examples demonstrate that the strategic use of dissipation can be a powerful tool to generate nontrivial nonequilibrium many-body dynamics.