Coherent driving and freezing of bosonic matter wave in an optical Lieb lattice.

Although kinetic energy of a massive particle generally has quadratic dependence on its momentum, a flat, dispersionless energy band is realized in crystals with specific lattice structures. Such macroscopic degeneracy causes the emergence of localized eigenstates and has been a key concept in the context of itinerant ferromagnetism. We report the realization of a "Lieb lattice" configuration with an optical lattice, which has a flat energy band as the first excited state. Our optical lattice potential has various degrees of freedom in its manipulation, which enables coherent transfer of a Bose-Einstein condensate into the flat band. In addition to measuring lifetime of the flat band population for different tight-binding parameters, we investigate the inter-sublattice dynamics of the system by projecting the sublattice population onto the band population. This measurement clearly shows the formation of the localized state with the specific sublattice decoupled in the flat band, and even detects the presence of flat-band breaking perturbations, resulting in the delocalization. Our results will open up the possibilities of exploring the physics of flat bands with a highly controllable quantum system.