Molecular wavefunction and tunneling properties of a bound pair of Fermi atoms in an optical lattice

We investigate tunneling properties of a bound pair of Fermi atoms in an optical lattice. Including a realistic cosine-shape optical lattice potential, we calculate the molecular wavefunction ψ. Starting from the weak-coupling regime, we show how ψ shrinks as one increases the strength of a pairing interaction between atoms. When the molecular size becomes comparable to the lattice constant in the intermediate coupling regime, we find from the spatial structure of ψ that the molecular tunneling between lattice sites is accompanied by virtual dissociation. This phenomenon is shown to be suppressed in the strong-coupling regime due to very strong binding energy. We point out that, while the molecular tunneling accompanied by virtual dissociation can be described by the Hubbard model, it cannot describe the molecular tunneling with no virtual dissociation in the strong-coupling regime.