Extended molecules and geometric scattering resonances in optical lattices

TL;DR

This paper develops a theory for low-energy neutral atom scattering in optical lattices, revealing how interactions and resonances depend on lattice parameters and microscopic scattering lengths.

Contribution

It introduces a novel theoretical framework describing scattering resonances and effective interactions in optical lattices, including geometric resonances and bound states.

Findings

Effective scattering amplitude approaches a lattice-dependent limit for repulsive interactions.

A geometric resonance occurs for attractive interactions before reaching the limit.

Near resonance, the effective interaction becomes repulsive and supports extended bound states.

Abstract

We develop a theory describing neutral atoms scattering at low energies in an optical lattice. We show that for a repulsive interaction, as the microscopic scattering length increases, the effective scattering amplitude approaches a limiting value which depends only on the lattice parameters. In the case of attractive interaction a geometric resonance occurs before reaching this limit. Close to the resonance, the effective interaction becomes repulsive and supports a weakly bound state, which can extend over several lattice sites.