Quantum mechanics

Optical lattice

Theoretical physics

Superfluidity

Quantum phases

Topological degeneracy

Ultracold atom

Symmetry protected topological order

Physics

Topological order

Mathematics

Fermion

Topological insulator

Geometry

Quantum

Combinatorics

Symmetry (geometry)

Topology (electrical circuits)

Quantum phase transition

Science Advances

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.

Observation of symmetry-protected topological band with ultracold fermions