Effective multi-body induced tunneling and interactions in the Bose-Hubbard model of the lowest dressed band of an optical lattice

TL;DR

This paper develops an extended Bose-Hubbard model incorporating interaction-induced multibody effects and tunneling processes, providing a more accurate low-energy description of ultracold bosons in optical lattices.

Contribution

It introduces a systematic construction of an effective single-band model using ladder operators for correlated states, capturing multibody interactions and tunneling effects beyond traditional models.

Findings

Multibody interactions and tunneling processes are enhanced near Feshbach resonances.

Correlations significantly influence the energy reduction mechanism in local lattice sites.

The model aligns with experimental parameters for ultracold bosonic atoms in optical lattices.

Abstract

We construct the effective lowest-band Bose-Hubbard model incorporating interaction-induced on-site correlations. The model is based on ladder operators for local correlated states, which deviate from the usual Wannier creation and annihilation, allowing for a systematic construction of the most appropriate single-band low-energy description in the form of the extended Bose-Hubbard model. A formulation of this model in terms of ladder operators not only naturally contains the previously found effective multibody interactions, but also contains multibody-induced single-particle tunneling, pair tunneling, and nearest-neighbor interaction processes of higher orders. An alternative description of the same model can be formulated in terms of occupation-dependent Bose-Hubbard parameters. These multiparticle effects can be enhanced using Feshbach resonances, leading to corrections which are well within experimental reach and of significance to the phase diagram of ultracold bosonic atoms in an optical lattice. We analyze the energy-reduction mechanism of interacting atoms on a local lattice site and show that this cannot be explained only by a spatial broadening of Wannier orbitals on a single-particle level, which neglects correlations.