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While kinetic energy of a massive particle generally has quadratic dependenceon its momentum, a flat, dispersionless energy band is realized in crystalswith specific lattice structures. Such macroscopic degeneracy causes theemergence of localized eigenstates and has been a key concept in the context ofitinerant ferromagnetism. Here we report the realization of a "Lieb lattice"configuration with an optical lattice, which has a flat energy band as thefirst excited state. Our optical lattice potential possesses various degrees offreedom about its manipulation, which enables coherent transfer of aBose-Einstein condensate into the flat band. In addition to measuring lifetimeof the flat band population for different tight-binding parameters, weinvestigate the inter-sublattice dynamics of the system by projecting thesublattice population onto the band population. This measurement clearly showsthe formation of the localized state with the specific sublattice decoupled inthe flat band, and even detects the presence of flat-band breakingperturbations, resulting in the delocalization. Our results will open up thepossibilities of exploring physics of flat band with a highly controllablequantum system.

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