Strongly interacting lattice fermions with coherent state manipulation: from universal Hall response to Hall voltage measurement

We report on the first quantum simulation of the Hall effect for strongly interacting fermions. By performing direct measurements of current and charge polarization in an ultracold-atom simulator, we trace the buildup of the Hall response in a synthetic ladder pierced by a magnetic flux, going beyond stationary Hall voltage measurements in solid-state systems. We witness the onset of a clear interaction-dependent behavior, where the Hall response deviates significantly from that expected for a non-interacting electron gas, approaching a universal value. Our system, able to reach hard to compute regimes also demonstrates the power of quantum simulation for strongly correlated topological states of matter. As a further step, by implementing an additional potential gradient along the synthetic dimension, we have extended measurements of the Hall response to a study of the Hall voltage in coldatom systems. The observed dependence of the Hall voltage on the particle density will enable new benchmarks of recent theoretical predictions for the Hall effect in the strongly correlated regime.