Exotic pairing in 1D spin-3/2 atomic gases with $SO(4)$ symmetry

TL;DR

This paper discovers an integrable $SO(4)$ symmetric model for 1D spin-3/2 fermionic gases, providing exact solutions and detailed phase diagrams, revealing complex pairing and shell structures in trapped ultracold atomic systems.

Contribution

It introduces a novel $SO(4)$ symmetry integrable point for spin-3/2 fermions and derives exact solutions, expanding understanding of pairing and phase behavior in these systems.

Findings

Exact Bethe ansatz solution for the $SO(4)$ symmetric model.

Full phase diagrams including pair correlations and quantum criticality.

Predicted shell structures in density profiles of trapped gases.

Abstract

Tuning interactions in the spin singlet and quintet channels of two colliding atoms could change the symmetry of the one-dimensional spin-3/2 fermionic systems of ultracold atoms while preserving the integrability. Here we find a novel $SO(4)$ symmetry integrable point in thespin-3/2 Fermi gas and derive the exact solution of the model using the Bethe ansatz. In contrast to the model with $SU(4)$ and $SO(5)$ symmetries, the present model with $SO(4)$ symmetry preserves spin singlet and quintet Cooper pairs in two sets of $SU(2)\otimes SU(2)$ spin subspaces. We obtain full phase diagrams, including the Fulde-Ferrel-Larkin-Ovchinnikov like pair correlations, spin excitations and quantum criticality through the generalized Yang-Yang thermodynamic equations. In particular, various correlation functions are calculated by using finite-size corrections in the frame work of conformal field theory. Moreover, within the local density approximation, we further find that spin singlet and quintet pairs form subtle multiple shell structures in density profiles of the trapped gas.