Ultracold atoms in Lieb lattices

Ultracold atoms in optical lattices have been attracted much interest for its application to quantum simulation, in which non-trivial theoretical models are simulated by well-controllable quantum systems instead of getting hardly-computable numerical solutions. Optical lattices provide a unique opportunity to simulate strongly correlated solid electrons, especially those described by the Hubbard model.
Lattice structure is one of the most important properties of strongly correlated systems which determines the ground state quantum phases. With optical lattices, variety of lattice structures can be realized by changing laser configurations. We have realized an optical Lieb lattice which has a flat energy dispersion in the first excited band. By tuning intensities and relative phases of lattice laser beams, lattice parameters such as tunneling and energy offset of each sublattice can be fully controllable. The dynamical control of these parameters allows us to load both Bose condensates and degenerate fermions into the flat band. The band flatness is confirmed by observing the frozen motion of matter waves. The band structure is further investigated by inducing oscillation modes of condensates and the interaction effect on the flat dispersion is successfully observed. For fermions, the loading process can be regarded as a realization of "spatial adiabatic passage", in which quantum particles are transported between spaticaly isolated states without being observed at the intermediate region. In this talk, I will report these series of experiments and future possibilities of approaching exotic magnetic states with the optical Lieb lattice.