Realizing the topological bands of helical states poses a challenge in studying ultracold atomic gases. Motivated by the recent experimental success in realizing chiral optical ladders, here we present a scheme for synthesizing topological quantum matter, especially the quantum spin Hall phase, in the chiral optical ladders. More precisely, we first establish the synthetic pseudo-spin-orbit coupling and Zeeman splitting in the chiral ladders. After analyzing the band structure of the ladders exposed to the bichromatic optical potentials, we report the existence of quantum spin Hall phase. We further identify a rich phase diagram of the bichromatic chiral ladders, illustrating that our proposal features a large space of system parameters exhibiting quantum phase transitions. Our scheme is within reach of the existing ladder optical lattices and hence provides a new method to engineer the elaborate topological bands for cold atomic gases.

中文翻译：

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在双色手性光学阶梯中为超冷原子合成量子自旋霍尔相。

实现螺旋态的拓扑带对研究超冷原子气体提出了挑战。受最近在实现手性光梯上实验成功的推动，这里我们提出一种在手性光梯中合成拓扑量子物质，特别是量子自旋霍尔相的方案。更准确地说，我们首先在手性阶梯中建立了合成的伪自旋轨道耦合和塞曼分裂。在分析了暴露于双色光学势的梯子的能带结构之后，我们报告了量子自旋霍尔相位的存在。我们进一步确定了双色手性梯子的丰富相图，说明了我们的建议具有显示量子相变的大系统参数空间。