Abstract

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.

Graphical abstract

中文翻译：

---

碱土原子中Wannier–Stark阶梯的几何相

摘要

我们讨论了在碱土（类）原子中周期性驱动的时钟状态所产生的Wannier–Stark阶梯的几何相位。使用\（^ {171} \）以Yb原子为例，我们展示了由一组失谐的时钟激光器耦合的时钟状态可以映射到一对两波段的Wannier–Stark梯子，其中沿着每个梯子的系统动力学被映射到a中的Bloch振荡。一维拓扑格。当满足绝热条件时，量化在一个振荡周期中积累的几何相位，并揭示出随着调谐激光参数而产生的能带拓扑变化。我们展示了如何通过不同核自旋态之间的干扰通过实验检测不同阶梯之间几何相位的差异，从而揭示固有的拓扑相变。我们的研究为Floquet动力学中的奇异带结构工程提供了启示。

图形概要