Measurement of spin Chern numbers in quantum simulated topological insulators

TL;DR

This paper demonstrates the experimental measurement of the spin Chern number in a quantum simulated topological insulator using cold atoms, providing a new way to detect topological invariants.

Contribution

It introduces an experimental approach to measure the spin Chern number in a quantum simulation, overcoming previous challenges related to wavefunction construction.

Findings

Successfully measured the spin Chern number using linear response theory.

Showed the spin Chern number is well-defined when energy and spin gaps are non-zero.

Validated the measurement method with cold atom simulations of the BHZ model.

Abstract

The topology of quantum systems has become a topic of great interest since the discovery of topological insulators. However, as a hallmark of the topological insulators, the spin Chern number has not yet been experimentally detected. The challenge to directly measure this topological invariant lies in the fact that this spin Chern number is defined based on artificially constructed wavefunctions. Here we experimentally mimic the celebrated Bernevig-Hughes-Zhang model with cold atoms, and then measure the spin Chern number with the linear response theory. We observe that, although the Chern number for each spin component is ill defined, the spin Chern number measured by their difference is still well defined when both energy and spin gaps are non-vanished.