  We experimentally realized a time-periodically modulated 1D lattice for
ultracold atoms featuring a pair of linear bands, each associated with a
Floquet winding number: a topological invariant. These bands are spin-momentum
locked and almost perfectly linear everywhere in the Brillouin zone (BZ),
making this system a near-ideal realization of the 1D Dirac Hamiltonian. We
characterized the Floquet winding number using a form of quantum state
tomography, covering the BZ and following the micromotion through one Floquet
period. Lastly, we altered the modulation timing to lift the topological
protection, opening a gap at the Dirac point that grew in proportion to the
deviation from the topological configuration.
