Observation of compact localized states in synthetic Floquet-Lieb topological photonic lattices

Abstract Flat bands are unique quantum states in translationally-invariant lattices that are characterized by dispersionless energy bands and compact localized Wannier functions. In static, tight-binding systems, topologically nontrivial and gapped, perfectly flat bands require infinite hopping range, making these systems difficult to realize. By introducing periodic driving into the system, it is possible to achieve flat bands embedded in topologically nontrivial bandgaps while requiring only nearest neighbor couplings. Here we realize perfectly flat bands in a Floquet-Lieb microring lattice in which the periodic circulation of light around the rings emulates a synthetic time-like dimension. Near-infrared imaging of the scattered light allows direct observation of the compact localized state, which confirms the cyclic trajectory of the Wannier function of the flat band. In addition to a symmetry-protected flat band, the dispersive bands of the lattice can also be flattened by tuning the geometric phase of the cyclically-evolving Wannier function, leading to light localization effect which may be called Aharonov-Anandan caging. The Aharonov-Anandan phase can be directly measured from the frequency displacement of the flat-band resonance. These results suggest that flat band modes in lattices with periodic synthetic dimension could provide a versatile platform for studying novel phenomena in strongly correlated quantum systems.