Band and correlated insulators of cold fermions in a mesoscopic lattice

Conductance is one of the simplest measurable quantities revealing the conducting or insulating nature of a physical system, and yet an intricate non-local property sensitive to quantum interferences and interactions at a microscopic level. In our cold-atom setup, such a conductance measurement can be performed by connecting two macroscopic reservoirs of ultracold fermions to a smaller structure engineered by light potentials, and probing the current created by a atom number difference between the reservoirs. We report on the transport of degenerate Lithium-6 atoms through a structure tailored in a bottom-up approach: Using a Digital Micromirror Device to project up to nine consecutive scatterers inside a one-dimensional constriction, a lattice can be formed one site at a time. We observe the emergence of a band gap, originating from interferences among the scatterers. The coherent character of transport can be investigated by independently changing the lattice length and the temperature. The presence of a gap is robust against strongly attractive interparticle interactions and hints at the existence of a Luther-Emery liquid, a novel phase distinctive of the one-dimensional character of the underlying wire.