  While 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. Here 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 possesses various degrees of
freedom about 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 physics of flat band with a highly controllable
quantum system.
