Interaction-Driven Shift and Distortion of a Flat Band in an Optical Lieb Lattice

We report the momentum-resolved measurement of Bloch bands in an optical Lieb lattice for a Bose-Einstein condensate (BEC). A BEC in the lattice is transported to a desired quasimomentum by applying a constant force. The energy dispersion of the lowest band is obtained by integrating measured group velocities. We also measure the gap from the lowest band to the higher bands with the same quasimomentum, which can be extracted from the oscillation of the sublattice populations after preparing a superposition of the band eigenstates. We show that the experimental results agree with a band calculation based on the Bogoliubov approximation. It is revealed that the second band, which should be flat in a single-particle description, is shifted and, in particular, distorted around the Brillouin zone edge as the interaction strength increases.