High-precision analysis of Feshbach resonances in a Mott insulator

TL;DR

This paper develops a simple effective model combined with coupled-channels calculations to accurately analyze Feshbach resonances in a Mott insulator, improving upon standard Hubbard-model interpretations and matching high-precision experimental data.

Contribution

It introduces an easy-to-use effective description of on-site interaction energy that works across various interaction strengths, enabling precise resonance position determination.

Findings

Accurate resonance positions for $^7$Li Feshbach resonances were determined.

The model is validated against rigorous numerical treatments.

Earlier experimental data are consistent with the new analysis.

Abstract

We show that recent high-precision measurements of relative on-site interaction energies $\Delta U$ in a Mott insulator require a theoretical description beyond the standard Hubbard-model interpretation, when combined with an accurate coupled-channels calculation. In contrast to more sophisticated lattice models, which can be elaborate especially for parameter optimization searches, we introduce an easy to use effective description of $U$ valid over a wide range of interaction strengths modeling atomic pairs confined to single lattice sites. This concise model allows for a straightforward combination with a coupled-channels analysis. With this model we perform such a coupled-channels analysis of high-precision $^7$Li spectroscopic data on the on-site interaction energy $U$, which spans over four Feshbach resonances and provide an accurate and consistent determination of the associated resonance positions. Earlier experiments on three of the Feshbach resonances are consistent with this new analysis. Moreover, we verify our model with a more rigorous numerical treatment of the two atom system in an optical lattice.