Microscopic derivation of multi-channel Hubbard models for ultracold nonreactive molecules in an optical lattice

TL;DR

This paper rigorously derives a multi-channel Hubbard model for ultracold nonreactive molecules in optical lattices, confirming its robustness and extending its applicability to include multiple internal states, thus advancing the theoretical understanding of complex molecular quantum gases.

Contribution

It provides an exact derivation of the multi-channel Hubbard model from first principles and extends the model to include multiple internal molecular states.

Findings

The multi-channel Hubbard model is robust against previous approximations.

The derivation connects ab initio molecular physics to many-body lattice models.

The model can incorporate multiple internal states like hyperfine or rotational levels.

Abstract

Recent experimental advances in the cooling and manipulation of bialkali dimer molecules have enabled the production of gases of ultracold molecules that are not chemically reactive. It has been presumed in the literature that in the absence of an electric field the low-energy scattering of such nonreactive molecules (NRMs) will be similar to atoms, in which a single $s$-wave scattering length governs the collisional physics. However, in Ref. [1], it was argued that the short-range collisional physics of NRMs is much more complex than for atoms, and that this leads to a many-body description in terms of a multi-channel Hubbard model. In this work, we show that this multi-channel Hubbard model description of NRMs in an optical lattice is robust against the approximations employed in Ref. [1] to estimate its parameters. We do so via an exact, albeit formal, derivation of a multi-channel resonance model for two NRMs from an ab initio description of the molecules in terms of their constituent atoms. We discuss the regularization of this two-body multi-channel resonance model in the presence of a harmonic trap, and how its solutions form the basis for the many-body model of Ref. [1]. We also generalize the derivation of the effective lattice model to include multiple internal states (e.g., rotational or hyperfine). We end with an outlook to future research.