Resonant Scattering and Microscopic Model of Spinless Fermi Gases in One-dimensional Optical Lattices

We study the effective Bloch-wave scattering of a spinless Fermi gas in one-dimensional (1D) optical lattices. By tuning the odd-wave scattering length, we find multiple resonances of Bloch-waves scattering at the bottom (and the top) of the lowest band, beyond which an attractive (and a repulsive) two-body bound state starts to emerge. These resonances exhibit comparable widths in the deep lattice limit, and the finite interaction range plays an essential role in determining their locations. Based on the exact two-body solutions, we construct an effective microscopic model for the low-energy scattering of fermions. The model can reproduce not only the scattering amplitudes of Bloch-waves at the lowest band bottom/top, but also the attractive/repulsive bound states within a reasonably large energy range below/above the band. These results lay the foundation for quantum simulating topological states in cold Fermi gases confined in 1D optical lattices.