Uncover Topology by Quantum Quench Dynamics

TL;DR

This paper introduces a new high-precision dynamical method to detect topological invariants in quantum states by analyzing the unitary evolution after a quench, demonstrated with ultracold atom experiments.

Contribution

It presents a novel dynamical approach to uncover topological properties through quench dynamics, enabling precise measurement of Chern numbers and phase diagrams.

Findings

Ring structure in spin dynamics determines Chern number

Probes full phase diagram of band topology

Dynamically measures topological band gap and domain walls

Abstract

Topological quantum states are characterized by nonlocal invariants, and their detection is intrinsically challenging. Various strategies have been developed to study topological Hamiltonians through their equilibrium states. We present a fundamentally new, high-precision dynamical approach, revealing topology through the unitary evolution after a quench from a topological trivial initial state with a two-dimensional Chern band realized in an ultracold $^{87}$Rb atom gas. The emerging ring structure in the spin dynamics uniquely determines the Chern number for the post-quench band and enables probing the full phase diagram of the band topology with high precision. Besides, we also measure the topological band gap and the domain wall structure dynamically formed in the momentum space during the long-term evolution. Our dynamical approach provides a way towards observing a universal bulk-ring correspondence, and has broad applications in exploring topological quantum matter.