Geometric phase of Wannier-Stark ladders in alkaline-earth(-like) atoms

TL;DR

This paper investigates the geometric phase in Wannier-Stark ladders created by periodically driven clock states in alkaline-earth-like atoms, revealing topological band changes and proposing experimental detection methods.

Contribution

It demonstrates how to map driven clock states to topological Wannier-Stark ladders and analyzes the quantized geometric phase related to band topology changes.

Findings

Geometric phase is quantized under adiabatic conditions.

Band topology changes can be detected via interference experiments.

The study provides a method to engineer exotic band structures in Floquet systems.

Abstract

We discuss the geometric phase of Wanner-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 driven by two detuned clock lasers can be mapped to two-band Wannier-Stark ladders, where dynamics of the system along the 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 geometric phase can be experimentally detected through interference between different nuclear spin states. Our study sheds light on the engineering of exotic band structures in Floquet dynamics.