Spin-orbit coupling in interacting bosonic systems: density-dependent gauge fields and flux ladders

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Topology is a key concept in physics, with implications in areas as diverse as high-energy and condensed-matter physics. There, topological order gives rise to highly counterintuitive phenomena such as the existence of anyonic excitations in quantum Hall systems or the emergence of gauge theories in strongly-correlated materials. Ultracold atomic gases subjected to artificial gauge fields constitute an ideal platform for the controlled simulation of topological systems. During the last years, experiments have demonstrated an impressive level of control over single-particle topological properties,allowing to engineer paradigmatic topological Hamiltonians and to reach extreme parameter regimes and observables not accessible in solid-state samples. However, extending these experimental studies to the many-body regime is a highly challenging task. As a consequence, many-body topological phases remain largely unexplored in the ultracold atom context. In this project, we will study the interplay of topology and interactions using spin-orbit coupled ultracold bosonic gases, building on the experience accumulated during the first funding period. Our research will be structured along two lines. In the continuum we will implement and study density-dependent artificial gaugefields where the interatomic interactions produce a back-action of matter on the gauge field and realize an interacting gauge theory. In optical lattices we will realize flux ladders – ribbon versions of the celebrated Hofstadter model – in the many-body regime, characterize their phase diagram and study the effect of interactions on their quench dynamics. This work will be carried out in close collaboration with theory teams of this Research Unit, allowing for a direct comparison between experiments and theoretical calculations.