  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.
