  Symmetry plays a fundamental role in understanding complex quantum matter,
particularly in classifying topological quantum phases, which have attracted
great interests in the recent decade. An outstanding example is the
time-reversal invariant topological insulator, a symmetry-protected topological
(SPT) phase in the symplectic class of the Altland-Zirnbauer classification. We
report the observation for ultracold atoms of a noninteracting SPT band in a
one-dimensional optical lattice and study quench dynamics between topologically
distinct regimes. The observed SPT band can be protected by a magnetic group
and a nonlocal chiral symmetry, with the band topology being measured via Bloch
states at symmetric momenta. The topology also resides in far-from-equilibrium
spin dynamics, which are predicted and observed in experiment to exhibit
qualitatively distinct behaviors in quenching to trivial and nontrivial
regimes, revealing two fundamental types of spin-relaxation dynamics related to
bulk topology. This work opens the way to expanding the scope of SPT physics
with ultracold atoms and studying nonequilibrium quantum dynamics in these
exotic systems.
