Realizing a symmetry-protected topological phase in the antiferromagnetic spin-1/2 Hubbard ladder

The spin-1 Haldane chain is the paradigmatic example of symmetry protected topological (SPT) phases, which are characterized by non-local quantities and edge states. Here we report on the experimental realization of such a phase using ultracold fermions in optical lattices. Site-resolved potential shaping allows us to create a tailored spin-1/2 ladder geometry needed to explore the topologically nontrivial spin-1 phase. Harnessing the full spin and density resolution of our Fermi-gas microscope, we detect a finite non-local string correlator in the bulk and localized spin-1/2 states at the edges. We confirm the robustness of the state by tuning the ratio of the leg to rung coupling of the ladder. We finally go beyond the spin model and explore the effect of charge fluctuations on the SPT phase in the general Hubbard regime.