# Experimental observation of dynamical bulk-surface correspondence for topological phases

## TL;DR

This paper demonstrates a method to classify topological quantum phases dynamically using NV centers in diamond, revealing a bulk-surface correspondence in momentum space through a quench process.

## Contribution

It introduces a robust dynamical classification approach for topological phases that is independent of quench methods and resilient to decoherence effects.

## Key findings

- Measured dynamical topological invariants via spin-texture imaging
- Observed high topological numbers in experiments
- Validated the robustness of the dynamical classification method

## Abstract

We experimentally demonstrate a dynamical classification approach for investigation of topological quantum phases using a solid-state spin system through nitrogen-vacancy (NV) center in diamond. Similar to the bulkboundary correspondence in real space at equilibrium, we observe a dynamical bulk-surface correspondence in the momentum space from a dynamical quench process. An emergent dynamical topological invariant is precisely measured in experiment by imaging the dynamical spin-textures on the recently defined band-inversion surfaces, with high topological numbers being implemented. Importantly, the dynamical classification approach is shown to be independent of quench ways and robust to the decoherence effects, offering a novel and practical strategy for dynamical topology characterization, especially for high dimensional gapped topological phases.