Band Gap Closing in a Synthetic Hall Tube of Neutral Fermions

We report the experimental realization of a synthetic three-leg Hall tube with ultracold fermionic atoms in a one-dimensional optical lattice. The legs of the synthetic tube are composed of three hyperfine spin states of the atoms, and the cyclic interleg links are generated by two-photon Raman transitions between the spin states, resulting in a uniform gauge flux phi penetrating each side plaquette of the tube. Using quench dynamics, we investigate the band structure of the Hall tube system for a commensurate flux. phi = 2 pi/3. Momentum-resolved analysis of the quench dynamics reveals a critical point of band gap closing as one of the interleg coupling strengths is varied, which is consistent with a topological phase transition predicted for the Hall tube system.