# Observing topological charges and dynamical bulk-surface correspondence with ultracold atoms

## TL;DR

This paper experimentally demonstrates the dynamical bulk-surface correspondence in a 2D quantum anomalous Hall system using ultracold atoms, linking topological charges and invariants to quench dynamics.

## Contribution

First experimental observation of dynamical bulk-surface correspondence in a 2D topological system via ultracold atoms, measuring topological charges and invariants dynamically.

## Key findings

- Topological charges measured dynamically match the Chern index.
- Dynamical topological invariant equals the post-quench band Chern number.
- Observation of nontrivial topology in the emergent dynamical field.

## Abstract

In quenching a topological phase across phase transition, the dynamical bulk-surface correspondence emerges that the bulk topology of $d$-dimensional ($d$D) phase relates to the nontrivial pattern of quench dynamics emerging on $(d-1)$D subspace, called band inversion surfaces (BISs) in momentum space. Here we report the first experimental observation of the dynamical bulk-surface correspondence through measuring the topological charges in a 2D quantum anomalous Hall model realized in an optical Raman lattice. The system can be quenched with respect to every spin axis by suddenly varying the two-photon detuning or phases of the Raman couplings, in which the topological charges and BISs are measured dynamically by the time-averaged spin textures. We observe that the total charges in the region enclosed by BISs define a dynamical topological invariant, which equals the Chern index of the post-quench band. The topological charges relate to an emergent dynamical field which exhibits nontrivial topology on BIS, rendering the dynamical bulk-surface correspondence. This study opens a new avenue to explore topological phases dynamically.