Floquet engineering topological Dirac bands

We experimentally realize a time-periodically modulated 1D lattice for ultracold atoms featuring a pair of linear bands, each protected by 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\delete{, covering the BZ and following the micromotion in 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.