Measuring Non-Hermitian Topological Invariants Directly from Quench Dynamics

TL;DR

This paper introduces a universal method to directly measure non-Hermitian topological invariants in quantum systems using quench dynamics, applicable to various dimensions and symmetries, and proposes a feasible cold-atom experimental setup.

Contribution

A unified framework for directly measuring non-Hermitian topological invariants via quench dynamics, including practical experimental proposals.

Findings

Extraction of line-gap winding number from post-quench spin textures.

Detection of point-gap braiding degree through winding patterns.

Feasibility of implementing the measurement scheme in cold-atom experiments.

Abstract

While non-Hermitian (NH) topological phases and phenomena have been observed across various quantum systems, directly measuring NH topological invariants remains a significant challenge. In this study, we present a generic and unified framework for the direct measurement of various NH topological invariants in odd-dimensional systems through quench dynamics. We demonstrate that in one-dimensional (1D) NH systems with sublattice symmetry, the line-gap winding number and point-gap braiding degree can be extracted from the winding patterns of a dynamically constructed field based on post-quench spin textures. Specifically, line-gap topology is characterized by integer-valued winding, whereas point-gap complex-band braiding is revealed by half-integer or integer winding with abrupt jumps. We also extend our approach to higher-dimensional winding numbers and non-Bloch topological invariants under open-boundary conditions. Additionally, we propose a practical cold-atom setup to realize and detect 1D NH topological phases, showing that our dynamical measurement scheme is feasible in current experimental settings. This work paves the way for the direct measurement of NH topological invariants in quantum systems.