Frustrated tunneling of ultracold atoms in a state-dependent optical lattice

We propose a general method to realize frustrated tunneling of ultracold atoms in a state-dependent optical lattice. Two typical lattice configurations are considered, the square lattice with competing interaction and the kagom\'e lattice with geometrical frustration. The ideal can be extended to implement frustrated tunneling of ultracold atoms in various geometries, which enable us to investigate the physics of frustration in both bosonic and spin systems. We study the mean-field phase diagrams of the considered models and the experimental situations are also discussed.