  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.
