  Topological quantum states are characterized by nonlocal invariants, and
their detection is intrinsically challenging. Various strategies have been
developed to study topological Hamiltonians through their equilibrium states.
We present a fundamentally new, high-precision dynamical approach, revealing
topology through the unitary evolution after a quench from a topological
trivial initial state with a two-dimensional Chern band realized in an
ultracold $^{87}$Rb atom gas. The emerging ring structure in the spin dynamics
uniquely determines the Chern number for the post-quench band and enables
probing the full phase diagram of the band topology with high precision.
Besides, we also measure the topological band gap and the domain wall structure
dynamically formed in the momentum space during the long-term evolution. Our
dynamical approach provides a way towards observing a universal bulk-ring
correspondence, and has broad applications in exploring topological quantum
matter.
