SU($N$) symmetry with ultracold alkali dimers: weak dependence of scattering properties on hyperfine state

TL;DR

This paper explores the use of ultracold alkali diatomic molecules for implementing SU(N) symmetric many-body quantum systems, demonstrating weak dependence of scattering properties on hyperfine states and low inelastic collision rates.

Contribution

It introduces new computational methods for large basis sets and shows that selected molecules exhibit properties suitable for SU(N) symmetry with minimal spin dependence.

Findings

Scattering lengths are weakly dependent on hyperfine states.

All studied molecules have predominantly elastic collisions.

Spin-changing inelastic collision rates are very low.

Abstract

We investigate the prospect of using ultracold alkali diatomic molecules to implement many-body quantum systems with SU($N$) symmetry. Experimentally accessible molecules offer large $N$ for both bosonic and fermionic systems, with both attractive and repulsive interactions. We carry out coupled-channel scattering calculations on pairs of NaK, NaRb and NaCs molecules that are shielded from destructive collisions with static electric fields. We develop new methods to handle the very large basis sets required to include nuclear spins. We show that all the molecules studied have the properties required for SU($N$) symmetry: the collisions are principally elastic, and the scattering lengths depend only weakly on the spin states of the molecules. The rates of spin-changing inelastic collisions are very low. We develop and test a semiclassical model of the spin dependence and find that it performs well.