Effective Orbital Ordering In Multiwell Optical Lattices With Fermionic Atoms

We consider the behavior of Fermi atoms on optical superlattices with two-well structure for each node. Fermions on such lattices serve as an analog simulator of the Fermi-type Hamiltonian. We derive a mapping between fermion quantum ordering in the optical superlattices and the spin-orbital physics developed for degenerate d-electron compounds. The appropriate effective spin-orbital model appears to be a modification of the Kugel-Khomskii Hamiltonian. We show how different ground states of this Hamiltonian correspond to particular spin-pseudospin arrangement patterns of fermions on the lattice. The dependence of the fermion arrangement on phases of complex hopping amplitudes is illustrated.