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.The discovery of the quantum Hall effect introduced a new fundamental concept, topological quantum phase, to condensed-matter physics [1,2]. In contrast to symmetry-breaking quantum phases that are characterized by local order parameters in the Landau paradigm, topological quantum matter is classified by nonlocal topological invariants [3], which usually do not directly correspond to the local physical observables. In consequence the detection of topological states is intrinsically challenging. In solid-state experiments, various strategies have been developed and great success has been achieved in the discovery of topological quantum matter like topological insulators [4][5][6][7] and semimetals [8,9]. For instance, transport measurements and angle-resolved photoemission spectroscopy are used to detect gapless boundary modes that reflect the bulk topology [10,11]. In some circumstances, these strategies do not provide fully unambiguous evidences for topological quantum phases, as they do not directly measure topological numbers. An important example is topological superconductivity, which supports a kind of exotic non-Abelian quasiparticle called Majorana modes [12][13][14][15] and remains to be rigorously confirmed by experiment.To precisely detect the topology for an ultracold-atom system can be more challenging, whereas the extensive tool box of manipulating and probing ultracold atoms may offer distinct new strategies for measurement. For a one-dimensional (1D) Su-Schrieffer-Heeger model simulated with a 1D double well lattice, the band topology can be determined by measuring the Zak phase [16]. Furthermore, the bulk topology of a 2D Chern insulator, characterized by Chern invariants, can be observed by Hall transport studies [17,18], by Berry curvature mapping [19], and by a minimal measurement strategy [20] of imaging the spin texture at symmetric Bloch momenta [21]. The Chern invariants are precisely detectable only in a few special cases, e.g. when the bulk band is flat [17] or the system is of inversion symmetry [20,21]. Nevertheless, the ...
