Synthesizing quantum spin Hall phase for ultracold atoms in bichromatic chiral optical ladders

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.