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

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 the spin-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). ⊗. 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.