Cold

. We discuss the geometric phase of Wannier–Stark ladders generated by periodically driven clock states in alkaline-earth(-like) atoms. Using 171 Yb atoms as a concrete example, we show that clock states coupled by a set of detuned clock lasers can be mapped to a pair of two-band Wannier–Stark ladders, where dynamics of the system along each ladder is mapped to Bloch oscillations in a one-dimensional topological lattice. When the adiabatic condition is satisfied, the geometric phase accumulated in one period of the oscillation is quantized, and reveals the change of band topology as the laser parameters are tuned. We show how the difference in geometric phase between different ladders can be experimentally detected through interference between different nuclear spin states, revealing the inherent topological phase transition. Our study sheds light on the engineering of exotic band structures in Floquet dynamics