Fig. 5: Measurements of dynamical topological structures from quench dynamics.
a The skyrmion-antiskyrmion structures for the vectors a(k) obtained by measuring the time-evolving state at t = π/2 under the nontrivial postquench Hamiltonian H(k) with m = 1. The skyrmion or antiskyrmion structures appear in each half of the 2D Brillouin zone, contributing a Chern number of ±1, respectively. b The skyrmion and antiskyrmion structure is directly associated with the nontrivial linking structure with a link and an antilink composed of the inverse images \({f}^{-1}({\hat{{{{{{{{\boldsymbol{p}}}}}}}}}}_{1})\) and \({f}^{-1}({\hat{{{{{{{{\boldsymbol{p}}}}}}}}}}_{2})\) in (kx, ky, t) space for any two distinct points \({\hat{{{{{{{{\boldsymbol{p}}}}}}}}}}_{1}\) and \({\hat{{{{{{{{\boldsymbol{p}}}}}}}}}}_{2}\) on S2. Here we take \({\hat{{{{{{{{\boldsymbol{p}}}}}}}}}}_{1}=(1,0,0)\) and \({\hat{{{{{{{{\boldsymbol{p}}}}}}}}}}_{2}=(-1,0,0)\). The red and blue arrows show the images of the experimentally measured evolving state through the Hopf map, which are close to the theoretical values marked by yellow and green arrows. c, d Quench dynamics for the trivial postquench Hamiltonian H(k) with m = 3. The vectors a(k) have a topologically trivial distribution and the inverse images of \({\hat{{{{{{{{\boldsymbol{p}}}}}}}}}}_{1}\) and \({\hat{{{{{{{{\boldsymbol{p}}}}}}}}}}_{2}\) do not link with each other. In a and c, the color bar describes az, the component of the vectors a(k) along the z direction.
