Interacting Hall Response in Quantum Gas Experiments

Recent experiments with ultracold quantum gases in artificial magnetic fields have shown the possibility to study the Hall effect in quasi one-dimensional highly tunable ladder systems. In this context we theoretically analyze the properties of the reactive Hall response on ladder models with strongly interacting bosons and fermions. We compare different methods for the computation of the static Hall coefficient and discuss its dependence on the various methods or limits considered. In the cases relevant for recent experiments in synthetic dimensions, we find a surprising universal behavior of the weak field Hall coefficient of single component phases in the case of an SU(M) symmetric interaction. For strong magnetic fields we study the interesting properties of the quantum-Hall effect in various quantum phases on ladder geometries including vortex-lattice, biased ladder or Laughlin like states.