Resonant dynamics of fermions in synthetic flux ladders with strong SU(n) interactions

We theoretically study the dynamics of strongly interacting fermionic alkaline earth atoms with n internal levels in an optical lattice. When treating the internal flavors as a synthetic dimension, the system realizes a synthetic ladder structure. We use laser driving to couple the internal levels and induce an effective magnetic flux piercing the ladder. The system dynamically generates chiral spin currents in response to the flux. While strong interactions with one atom per site tend to inhibit motion, we show that transport is enhanced at special integer and fractional ratios of the driving and interaction strength, reminiscent of the enhancement of longitudinal conductivity in the fractional quantum Hall effect. At these resonant points, tunneling is induced by multi-body resonances that are enabled by the flux. For some resonances the particle transport approaches that of an effectively non-interacting system, while other resonances yield non-thermal behavior due to non-trivial kinetic constraints upon the motion. Our results showcase the plethora of complex dynamical phenomena that strongly interacting SU(n) fermions exhibit in the presence of an effective magnetic flux, many of which can manifest on timescales well within reach of current-generation experiments.