Probing Half-odd Topological Number with Cold Atoms in a Non-Abelian Optical Lattice

TL;DR

This paper proposes an experimental method using cold atoms in a non-Abelian optical lattice to measure the contribution of individual Dirac cones to the Hall conductivity, revealing half-odd topological numbers.

Contribution

It introduces a novel scheme to probe half-odd topological numbers via laser-tuned gauge flux in cold atom systems, linking Dirac cone contributions to measurable atomic density profiles.

Findings

Demonstrates how to shift Dirac point energies with laser intensity.

Shows the atomic Hall conductivity contribution from single Dirac cones.

Proposes experimental detection through atomic density measurements.

Abstract

We propose an experimental scheme to probe the contribution of a single Dirac cone to the Hall conductivity as half-odd topological number sequence. In our scheme, the quantum anomalous Hall effect as in graphene is simulated with cold atoms trapped in an optical lattice and subjected to a laser-induced non-Abelian gauge field. By tuning the laser intensity to change the gauge flux, the energies of the four Dirac points in the first Brillouin zone are shifted with each other and the contribution of the single Dirac cone to the total atomic Hall conductivity is manifested. We also show such manifestation can be experimentally probed with atomic density profile measurements.