Exact theoretical description of two ultracold atoms in a single site of a 3D optical lattice using realistic interatomic interaction potentials

TL;DR

This paper presents an exact numerical method for describing two ultracold atoms in a 3D optical lattice, accounting for realistic interatomic potentials and coupling effects, with implications for experimental molecule formation.

Contribution

It introduces a configuration-interaction approach that explicitly considers center-of-mass and relative motion coupling in a realistic potential framework.

Findings

Deviations from harmonic approximation are quantified for heteronuclear pairs.

The method accurately predicts binding energies near Feshbach resonances.

Results inform analysis of radio-frequency association experiments.

Abstract

A theoretical approach was developed for an exact numerical description of a pair of ultracold atoms interacting via a central potential that are trapped in a three-dimensional optical lattice. The coupling of center-of-mass and relative-motion coordinates is explicitly considered using a configuration-interaction (exact-diagonalization) technique. Deviations from the harmonic approximation are discussed for several heteronuclear alkali-metal atom pairs trapped in a single site of an optical lattice. The consequences are discussed for the analysis of a recent experiment [C. Ospelkaus et al, Phys. Rev. Lett. 97, 120402 (2006)] in which radio-frequency association was used to create diatomic molecules from a fermionic and a bosonic atom and to measure their binding energies close to a magnetic Feshbach resonance.