Floquet engineering tunable periodic gauge fields and simulating real topological phases in cold alkaline-earth atom optical lattice

We propose to synthesize tunable periodic gauge fields via Floquet engineering cold alkaline-earth atoms in one-dimensional optical lattice. The artificial magnetic flux is designed to emerge during the combined process of Floquet photon assisted tunneling and internal state transitions. By varying initial phases of driving protocol, our proposal presents the ability to smoothly tune the periodic flux. Moreover, we demonstrate that the effective two-leg flux ladder model can simulate one typical real topological insulator, which is described by the first Stiefel Whitney class and protected by the $PT$ symmetry. Benefiting from the long lifetime of excited states of alkaline-earth atoms, our work opens new possibilities for exploiting the physics related to gauge fields, such as topological phases, in the current cold atom platform.