Realizing a topological staggered Su-Schrieffer-Heeger ladder with atomic momentum lattice

Quasi-one-dimensional or ladder models serve as a bridge between one-dimensional and two-dimensional models, providing a simplified framework for incorporating intricate physics. In this study, we extend the concept of the momentum-state lattice by introducing couplings between next-nearest-neighbor sites throughout the entire momentum chain to simulate the staggered Su-Schrieffer-Heeger (SSH) ladder model. This ladder model is a direct extension of the well-known SSH model, recognized as a fundamental progression in modeling systems. Through this model, we explore compelling physical phenomena and successfully replicate the topological phase diagram of the Kitaev-Majorana chain. Utilizing time-averaged mean displacements of wave packets as a metric, we ascertain the topological invariants of the model. By varying staggered dimerization and interchain hopping parameters, we map out the topological phase diagram of the staggered SSH ladder, elucidating the presence of three distinct phases classified by their winding numbers: W = + 1 , 0, and − 1 , respectively.