Measuring topology from dynamics by obtaining the Chern number from a linking number

Area of Science:

• Quantum physics
• Condensed matter physics
• Topological phases of matter

Background:

• Integer-valued topological indices characterize nonlocal properties of quantum states.
• The Chern number predicts equilibrium properties like quantized Hall conductivity.

Purpose of the Study:

• To experimentally demonstrate that the Chern number governs far-from-equilibrium quantum dynamics.
• To explore the relationship between static and dynamical topological indices in Floquet systems.

Main Methods:

• Utilizing non-interacting fermionic atoms in a periodically driven optical lattice.
• Implementing a strong quench and measuring momentum-space vortex trajectories.
• Calculating the linking number of vortex trajectories and the instantaneous Chern number.

Main Results:

• The measured linking number directly corresponds to the ground-state Chern number.
• A one-to-one relation was established between a dynamical and a static topological index.
• The instantaneous Chern number was observed to remain zero during unitary dynamics.

Conclusions:

• The Chern number dictates far-from-equilibrium dynamics in quantum systems.
• This finding enables experimental mapping of quantum phase diagrams using dynamical topological indices.
• The study highlights the predictive power of topological indices beyond equilibrium properties.