Symmetry-protected topological phases in a dipolar Bose Hubbard quantum simulator

Topological phases of matter are governed by mechanisms extending beyond Landau's symmetry-breaking paradigm. Notably, a class of topological phases in quantum matter known as symmetry-protected topological states (SPTs) can be defined by their protecting symmetries. Non-local order parameters characterize such phases. In the context of Hubbard simulators, long-range interactions enabled by magnetic atoms can compete with on-site interactions, giving rise to novel SPT phases. Here, we experimentally investigate (i) an SPT phase in the dipolar Bose-Hubbard model that maps to spin-1 Haldane SPT and (ii) a crystalline SPT phase that emerges with the introduction of a staggering chemical potential. Our findings demonstrate that magnetic atoms in optical lattices can probe soft-core Hubbard physics through fully tunable on-site interactions enabled by magnetic Fano-Feshbach resonances. This approach allows for the investigation of topological phases via quantum simulation.