Two-channel Bose-Hubbard model of atoms at a Feshbach resonance

TL;DR

This paper introduces a refined two-channel Bose-Hubbard model that accurately describes two atoms at a Feshbach resonance in an optical lattice, addressing convergence issues with traditional models and validated against non-perturbative calculations.

Contribution

It presents a new Bose-Hubbard model incorporating a small number of Bloch bands for Feshbach resonances, improving accuracy over previous models.

Findings

Model accurately predicts stationary states and dynamics during lattice acceleration.

Comparison shows good agreement with non-perturbative calculations.

Introduces a square-well potential for realistic Feshbach resonance modeling.

Abstract

Based on the analytic model of Feshbach resonances in harmonic traps described in Phys. Rev. A 83, 030701 (2011) a Bose-Hubbard model is introduced that provides an accurate description of two atoms in an optical lattice at a Feshbach resonance with only a small number of Bloch bands. The approach circumvents the problem that the eigenenergies in the presence of a delta-like coupling do not converge to the correct energies, if an uncorrelated basis is used. The predictions of the Bose-Hubbard model are compared to non-perturbative calculations for both the stationary states and the time-dependent wavefunction during an acceleration of the lattice potential. For this purpose, a square-well interaction potential is introduced, which allows for a realistic description of Feshbach resonances within non-perturbative single-channel calculations.