  A dynamical Hopf insulator is experimentally synthesized with a quenched
two-dimensional quantum anomalous Hall system on a square Raman lattice. The
quench dynamics for the quasimomentum-time-dependent Bloch vectors defines a
Hopf map from $(q_x,q_y,t)\in T^3$ to the Bloch sphere $S^2$. In this Hopf map,
a dynamical Hopf number can be defined, and it exactly equals the Chern number
of the post-quench Hamiltonian. We experimentally measure the Hopf link between
the fibers for the North and South Poles on $S^2$, which are the trajectories
in $(q_x,q_y,t)$ space with maximal spin polarization, to extract the
topological Chern number of the post-quench Hamiltonian. We also observe the
structure of Hopf fibration for the mutually nested Hopf tori. Our study sheds
some new light on the interplay between topology (Hopf number) and geometry
(fiber bundle) in quantum dynamics.
