Strongly interacting fermionic atoms in a synthetic flux ladder*

Understanding the  behavior of  strongly interacting  electrons in  solids   under strong magnetic fields has been a paradigmatic goal of physics research. Ultracold alkaline-earth atoms (AEAs)  loaded  in  optical lattices featuring  a clean,  isolated and controllable  environment are emerging as powerful quantum simulators  which can shed light into this challenging problem. A unique appeal of  AEAs  fermionic atoms  featuring  n internal levels is their unique Su(n) symmetric collisions. Here I will discuss our studies on dynamical behaviors of SU(n) interacting fermionic AEAs subject to an effective magnetic field.  This system can be  engineered by coupling the  n  internal levels of the atoms, which can be visualized as a synthetic spatial dimension,  by   appropriate  laser drives. I will focus on the dense and strongly interacting regime where our  studies reveal rich and interesting  behaviors generated by the interplay between strong SU(n) interactions, the external magnetic flux and particle motion all  observable at conditions currently accessible  in  state-of-the art  experiments.