  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.
