Floquet engineering topological Dirac bands

TL;DR

This paper reports the experimental realization of a 1D Floquet topological system with ultracold atoms, demonstrating linear Dirac bands, topological invariants, and the ability to control topological protection via modulation timing.

Contribution

The study introduces a novel experimental setup for Floquet engineering of topological Dirac bands in a 1D lattice with ultracold atoms, including measurement of topological invariants and control over topological protection.

Findings

Realized a 1D Floquet topological lattice with ultracold atoms.

Measured Floquet winding number using quantum state tomography.

Controlled topological protection by adjusting modulation timing.

Abstract

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.