Observation of dynamical topology in 1D

TL;DR

This paper experimentally observes dynamical topological phenomena in a 1D ultracold atom lattice, demonstrating how symmetry conditions affect the evolution of topological invariants like the Zak phase and winding number.

Contribution

It introduces a method to directly measure the time evolution of topological invariants in a 1D lattice with ultracold atoms, revealing symmetry-dependent dynamical topological transitions.

Findings

Zak phase evolves continuously during quenches.

Chiral symmetry transiently defines a winding number with integer values.

Periodic restoration of chiral symmetry causes winding number changes of ±2.

Abstract

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.