Theoretical description of two ultracold atoms in finite 3D optical lattices using realistic interatomic interaction potentials

TL;DR

This paper presents an exact numerical method for modeling two ultracold atoms in a finite 3D optical lattice, accounting for realistic interatomic potentials and symmetry considerations.

Contribution

It introduces a comprehensive theoretical framework using exact diagonalization to accurately describe atom interactions in finite optical lattices with symmetry considerations.

Findings

Accurate numerical treatment of atom pairs in finite lattices.

Inclusion of realistic interatomic potentials.

Explicit consideration of lattice symmetry and particle statistics.

Abstract

A theoretical approach is described for an exact numerical treatment of a pair of ultracold atoms interacting via a central potential that are trapped in a finite three-dimensional optical lattice. The coupling of center-of-mass and relative-motion coordinates is treated using an exact diagonalization (configuration-interaction) approach. The orthorhombic symmetry of an optical lattice with three different but orthogonal lattice vectors is explicitly considered as is the Fermionic or Bosonic symmetry in the case of indistinguishable particles.