Lattice model parameters for ultracold nonreactive molecules: chaotic scattering and its limitations

TL;DR

This paper calculates and analyzes the parameters of a many-channel Hubbard model for ultracold nonreactive molecules in optical lattices, examining the validity of approximations and connecting model parameters to underlying physical assumptions.

Contribution

It extends previous models by going beyond initial approximations, providing a detailed analysis of the model parameters and their experimental implications.

Findings

Quantitative estimates of model parameters for ultracold molecules.

Assessment of the validity regime of the approximations used.

Connection between transition state theory and experimental observables.

Abstract

We calculate the parameters of the recently-derived many-channel Hubbard model that is predicted to describe ultracold nonreactive molecules in an optical lattice, going beyond the approximations used in Do\c{c}aj \textit{et al.}~[Phys. Rev. Lett. \textbf{116}, 135301 (2016)]. Although those approximations are expected to capture the qualitative structure of the model parameters, finer details and quantitative values are less certain. To set expectations for experiments, whose results depend on the model parameters, we describe the approximations' regime of validity and the likelihood that experiments will be in this regime, discuss the impact that the failure of these approximations would have on the predicted model, and develop theories going beyond these approximations. Not only is it necessary to know the model parameters in order to describe experiments, but the connection that we elucidate between these parameters and the underlying assumptions that are used to derive them will allow molecule experiments to probe new physics. For example, transition state theory, which is used across chemistry and chemical physics, plays a key role in our determination of lattice parameters, thus connecting its physical assumptions to highly accurate experimental investigation.