Detection of Topological Order in Ultracold Atoms

Abstract

Designing feasible and qualitative methods for estimation of topological invariants, such as the Chern number, is of great significance for experimental realization of topological quantum matter.We present two key results in this direction. We first show that for two-band systems supported on Bravais lattices with 2n-fold rotation symmetry, the Chern number (mod 2n) of one of the energy bands can be inferred from the spin polarization of the band wavefunction at the high-symmetry crystal momenta in the Brillouin zone. We leverage this result to design an experimental scheme for ultracold bosonic gases that uses Bloch oscillations and Zeeman spectroscopy for validation of the topological phases with Chern number ±2 on a triangular lattice. As part of the latter result, we present the first experimental scheme to our knowledge for simulating spin-orbit coupling on a triangular optical lattice. Our results highlight Bloch oscillations as a robust tool for detection of topological order, and also open doors to new experiments based on spin-orbit coupled systems beyond square lattices.