Direct measurement of topological numbers with spins in diamond

TL;DR

This paper demonstrates a method to directly measure topological numbers using a nitrogen-vacancy center in diamond, enabling quantum simulation of topological phase transitions and eigenvalue extraction.

Contribution

It introduces a quantum simulation approach with NV centers to directly measure topological invariants, advancing experimental capabilities in topological phase characterization.

Findings

Successfully simulated topological phase transition in a quantum wire

Able to reliably extract dispersion relations and topological numbers

Provides a new experimental method for topological phase measurement

Abstract

Topological numbers can characterize the transition between different topological phases, which are not described by Landau's paradigm of symmetry breaking. Since the discovery of quantum Hall effect, more topological phases have been theoretically predicted and experimentally verified. However, it is still an experimental challenge to directly measure the topological number of various predicted topological phases. In this paper, we demonstrate quantum simulation of topological phase transition of a quantum wire (QW) using a single nitrogen-vacancy (NV) center in diamond. Deploying quantum algorithm of finding eigenvalues, we can reliably extract both the dispersion relations and topological numbers.