Observation of the Knot Topology of Non-Hermitian Systems in a Single Spin

TL;DR

This paper demonstrates the observation of non-Hermitian knot topology in a single spin system using a nitrogen-vacancy center, revealing braiding patterns, eigenstate topology, and the biorthogonal Berry phase, advancing understanding of non-Hermitian quantum systems.

Contribution

It introduces a universal dilation method to study non-Hermitian knot topology in a single spin system, revealing new topological invariants and braiding patterns.

Findings

Observation of non-Hermitian knot topology in a single spin system

Revealed braiding patterns of energy bands and eigenstate topology

Successfully measured the global biorthogonal Berry phase

Abstract

The non-Hermiticity of the system gives rise to distinct knot topology that has no Hermitian counterpart. Here, we report a comprehensive study of the knot topology in gapped non-Hermitian systems based on the universal dilation method with a long coherence time nitrogen-vacancy center in a $^{\text{12}}$C isotope purified diamond. Both the braiding patterns of energy bands and the eigenstate topology are revealed. Furthermore, the global biorthogonal Berry phase related to the eigenstate topology has been successfully observed, which identifies the topological invariance for the non-Hermitian system. Our method paves the way for further exploration of the interplay among band braiding, eigenstate topology and symmetries in non-Hermitian quantum systems.