Resonance Scattering in Optical Lattices and Molecules: Interband versus Intraband Effects

We study the low-energy two-body scattering in optical lattices with higher-band effects included in an effective potential, using a renormalization group approach. The approach captures the most dominating higher-band effects as well as all multiple scattering processes in the lowest band. For an arbitrary negative free space scattering length (a(s)), a resonance of low-energy scattering occurs as the lattice potential depths reach a critical value v(c); these resonances, with continuously tunable positions v(c) and widths W, can be mainly driven either by intraband or both intra-and interband effects depending on the magnitude of a(s). We have also studied the scattering amplitudes and the formation of molecules when interband effects are dominating, and discussed an intimate relation between molecules for negative a(s) and repulsively bound states pioneered by Winkler et al. [Nature (London) 441, 853 (2006)].