Interaction Effects on Wannier Functions of a Bose-Einstein Condensate in an Optical Lattice and Implications for Bose-Hubbard Model

TL;DR

This paper develops a method to incorporate interaction effects into Wannier functions for a Bose-Einstein condensate in an optical lattice, leading to more accurate Bose-Hubbard model parameters that align with experimental data.

Contribution

It introduces interaction-dependent Wannier functions for BECs in optical lattices, improving the calculation of tunneling and on-site interaction parameters in the Bose-Hubbard model.

Findings

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

Calculated on-site interaction $U$ agrees with experimental measurements.

Enhanced modeling accuracy for Bose-Hubbard parameters.

Abstract

We show that one can properly take into account of the interaction effects and construct a set of orthonormal Wannier functions for a Bose-Einstein condensate in an optical lattice. These interaction-dependent Wannier functions are used to compute the tunneling rate $J$ and the on-site repulsion $U$ in the Bose-Hubbard model. Both parameters are found to be substantially different from ones calculated with the single-particle Wannier functions. Our numerical results of $U$ are found in good agreement with the measured on-site energy in a recent experiment [Campbell {\it et al.} Science {\bf 314}, 281 (2006)].