Effective orbital ordering in multiwell optical lattices with fermionic   atoms
  We consider the behavior of Fermi atoms on optical superlattices with two-well structure of each node. Fermions on such lattices serve as an analog simulator of 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 the 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 fermion arrangement on phases of complex hopping amplitudes is illustrated. 
A.M. Belemuk, N.M. Chtchelkatchev, and A.V. Mikheyenkov
cond-mat.mes-hall quant-ph