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

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.

15 pages, 12 figures, and 6 tables

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Cited by in corpus (6)

• The SU(N) Fermi-Hubbard Model on two sites: Bethe Ansatz solution and Quantum Phase Transition of the Lipkin-Meshkov-Glick Model in the large-N limit
• Unit-density SU(3) Fermi-Hubbard Model with Spin Flavor Imbalance
• Static impurity in a mesoscopic system of SU($N$) fermionic matter-waves
• Strongly dipolar molecular Bose-Einstein condensates: From few- to many-body physics
• Trion formation and ordering in the attractive SU(3) Fermi-Hubbard model
• Fluctuation-induced first-order superfluid transition in unitary $\mathrm{SU}(N)$ Fermi gases