Measurement of Spin Chern Numbers in Quantum Simulated Topological Insulators

Abstract

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