Twonniers: Interaction-induced effects on Bose-Hubbard parameters

TL;DR

This paper introduces two-particle Wannier functions, called Twonniers, to incorporate interaction effects into Bose-Hubbard parameters, revealing significant differences from traditional single-particle calculations and emphasizing the importance of density effects in experiments.

Contribution

The study develops a method to include interaction effects in Wannier functions, providing more accurate Bose-Hubbard parameters for ultracold atoms in optical lattices.

Findings

Interaction-dependent Wannier functions differ significantly from single-particle ones.

Density effects are important across various lattice depths.

Results impact precision in ultracold atom experiments.

Abstract

We study the effects of the repulsive on-site interactions on the broadening of the localized Wannier functions used for calculating the parameters to describe ultracold atoms in optical lattices. For this, we replace the common single-particle Wannier functions, which do not contain any information about the interactions, by two-particle Wannier functions ("Twonniers") obtained from an exact solution which takes the interactions into account. We then use these interaction-dependent basis functions to calculate the Bose--Hubbard model parameters, showing that they are substantially different both at low and high lattice depths, from the ones calculated using single-particle Wannier functions. Our results suggest that density effects are not negligible for many parameter ranges and need to be taken into account in metrology experiments.