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

## TL;DR

This paper investigates low-energy two-body scattering in optical lattices, revealing resonance phenomena driven by interband and intraband effects, with implications for molecule behavior upon release from the lattice.

## Contribution

It introduces a renormalization group approach to include higher-band effects in scattering, identifying conditions for resonances and analyzing energy dependence in optical lattices.

## Key findings

- Resonances occur at specific potential depths even with short-range interactions.
- Interband and intraband effects can independently or jointly drive resonances.
- The scattering matrix in lattices shows stronger energy dependence than in free space.

## Abstract

We study the low-energy two-body scattering in optical lattices with all higher-band effects included in an effective potential, using a renormalization group approach. As the potential depth reaches a certain value, a resonance of low energy scattering occurs even when the negative s-wave scattering length $(a_s)$ is much shorter than the lattice constant. These resonances can be mainly driven either by interband or intraband effects or by both, depending on the magnitude of $a_s$. Furthermore the low-energy scattering matrix in optical lattices has a much stronger energy-dependence than that in free space. We also investigate the momentum distribution for molecules when released from optical lattices.