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

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

• Final Report Year: 2024

Final Report Abstract

Classical nonlinear phenomena like chaos and synchronization are pervasive in nature and underpin key applications like secure communication and power grids. A natural question arises: how are these classical phenomena modified in the quantum regime? While chaos is well understood via random matrix theory, quantum synchronization remains an emerging field, mostly explored in fewsite systems. In this project, we aimed to expand our understanding of quantum synchronization by studying large lattices, investigating the conditions under which synchronized dynamics emerges, its robustness, and whether genuine quantum synchronization phenomena exist. A key focus was integrating topological concepts, as they are known for their resilience to local perturbations and thus could enhance synchronization. We showed that in bosonic modes forming a topological insulator model, boundary oscillators can synchronize under local driving and dissipation. This holds in both the classical nonlinear model and when quantum fluctuations are accounted for. The synchronized dynamics remained robust against local perturbations and initial conditions, thanks to the underlying topology. Additionally, we demonstrated a truly quantum synchronization effect. By carefully engineering dissipation in a chain of interacting spins, we showed that not only microscopic but also emergent or fractionalized degrees of freedom can synchronize. This behavior, protected by symmetry-protected topological order, is more robust compared to previously studied spin chain models. While synchronization is typically linked to nonlinear dynamics, we showed that it can also occur in linearly coupled oscillators. Without dissipation, these oscillators form collective eigenmodes with fixed phase relations. With the right balance of driving and dissipative coupling, synchronized dynamics can be achieved even in the presence of small frequency perturbations. We also explored superradiance, a form of synchronization where densely spaced quantum emitters lock their dipole phases to emit light bursts. We demonstrated that superradiance could generate entanglement between nodes in a quantum network that had no prior interaction, even dissipatively. This entanglement occurs on timescales faster than single-atom interactions and is driven by collective dissipative dynamics and system symmetries. Lastly, we investigated the realization of topological insulator models in so-called Rydberg composites, where a Rydberg atom interacts with ground-state atoms confined within its electron’s orbit. This system allows precise tuning of topological models by adjusting the distances between scatterer atoms, enabling high control over topological properties.

Publications

• Entanglement generation between distant spins via quasilocal reservoir engineering. Physical Review Research, 5(4).
  Dias, Josephine; Wächtler, Christopher W.; Nemoto, Kae & Munro, William J.
  
• Topological synchronization of quantum van der Pol oscillators. Physical Review Research, 5(2).
  Wächtler, Christopher W. & Platero, Gloria
  
• Synchronized states in a ring of dissipatively coupled harmonic oscillators. Physical Review E, 109(1).
  Moreno, Juan N.; Wächtler, Christopher W. & Eisfeld, Alexander
  
• Topological edge states in a Rydberg composite. Physical Review B, 109(7).
  Eiles, Matthew T.; Wächtler, Christopher W.; Eisfeld, Alexander & Rost, Jan M.
  
• Topological Quantum Synchronization of Fractionalized Spins. Physical Review Letters, 132(19).
  Wächtler, Christopher W. & Moore, Joel E.