Tunnelling couplings in discrete lattices, single particle band structure and eigenstates of interacting atom pairs

TL;DR

This paper explores how extending tunnelling couplings beyond nearest neighbors in discrete lattice models can accurately replicate the lowest energy band of continuous periodic potentials, impacting the behavior of interacting atom pairs.

Contribution

It introduces the inclusion of longer-range tunnelling couplings in lattice models, revealing their significant effects on scattering and bound states of atom pairs in periodic potentials.

Findings

Extended tunnelling couplings reproduce the lowest energy band of continuous potentials.

Longer-range couplings significantly influence atom pair scattering.

Bound state properties are affected by the inclusion of these couplings.

Abstract

By adjusting the tunnelling couplings over longer than nearest neighbor distances it is possible in discrete lattice models to reproduce the properties of the lowest energy band of a real, continuous periodic potential. We propose to include such terms in problems with interacting particles and we show that they have significant consequences for scattering and bound states of atom pairs in periodic potentials.