  Fermions in an optical lattice near a wide Feshbach resonance are expected to
be described by an effective Hamiltonian of the general Hubbard model with
particle-assisted tunneling rates resulting from the strong atomic interaction
[Phys. Rev. Lett. 95, 243202 (2005)]. Here, we propose a scheme to
unambiguously test the predictions of this effective Hamiltonian through
manipulation of ultracold atoms in an inhomogeneous optical superlattice. The
structure of the low-energy Hilbert space as well as the particle assisted
tunneling rates can be inferred from measurements of the time-of-flight images.
