一维动力学拓扑的观测
Observation of dynamical topology in 1D
摘要：
晶格中的非平凡拓扑由不变量表征--例如一维（1D）晶格的Zak相位--源自覆盖布里渊区的波函数。我们利用超冷$^{87}$ Rb实现了一维二分Rice-Mele（RM）晶格，重点研究了具有手征对称性、时间反演对称性和粒子-空穴对称性的各种组合的晶格构型。我们淬火配置之间，并使用一种形式的量子态层析成像，使非绝热调谐晶格参数，直接遵循的Zak相位的时间演化以及手性绕组数。Zak相是连续演化的，然而，当手征对称性在非平衡系统中瞬时出现时，手征缠绕数是明确定义的，并且可以取不同的整数值。当两个配置之间的淬火遵守所有三个对称性的Zak阶段是时间无关的，我们证实了对比预测[M。McGinley和N. R.Cooper，PRL 121 090401（2018）]手征对称性周期性恢复，此时缠绕数改变$\pm 2$，产生原生RM哈密顿量中不存在的值。
英文摘要：
Nontrivial topology in lattices is characterized by invariants--such as the Zak phase for one dimensional (1D) lattices--derived from wave functions covering the Brillouin zone. We realized the 1D bipartite Rice-Mele (RM) lattice using ultracold $^{87}$Rb and focus on lattice configurations possessing various combinations of chiral, time-reversal and particle-hole symmetries. We quenched between configurations and used a form of quantum state tomography, enabled by diabatically tuning lattice parameters, to directly follow the time evolution of the Zak phase as well as a chiral winding number. The Zak phase evolves continuously; however, when chiral symmetry transiently appears in the out-of-equilibrium system, the chiral winding number is well defined and can take on different integer values. When quenching between two configurations obeying all three symmetries the Zak phase is time independent; we confirm the contrasting prediction of [M. McGinley and N. R.Cooper, PRL 121 090401 (2018)] that chiral symmetry is periodically restored, at which times the winding number changes by $\pm 2$, yielding values that are not present in the native RM Hamiltonian.
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