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 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.
Highlights
Large-spin atomic fermions displaying rich pairing structures and diverse many-body phenomena could be realized through controlling interactions in spin scattering channels
Fermionic alkaline-earth atoms can exhibit an exact SU(κ) symmetry with κ = 2I +1 [5, 6], where I is pure nuclear spin. Experimental explorations of these fermionic systems have been reported on the trimer state of 6Li atoms [7, 8, 9], the SU(10) symmetry fermionic gas of 87Sr atoms with I = 9/2 [10] and the two-orbital magnetism of SU(κ) symmetry in 87Sr atoms [11], the SU(2) ⊗ SU(6) symmetry fermionic atoms of 173Yb with its spin-1/2 isotope [12], the SU (6) Mott-insulator state of 173Yb atoms [13] and two-orbital Hubbard model [14], etc
Based on the exact solution, we find that the model has subtle spin pairing phases and exhibits Fulde-Ferrel-LarkinOvchinnikov (FFLO) like pair correlations
Summary
Large-spin atomic fermions displaying rich pairing structures and diverse many-body phenomena could be realized through controlling interactions in spin scattering channels. Fermionic alkaline-earth atoms can exhibit an exact SU(κ) symmetry with κ = 2I +1 [5, 6], where I is pure nuclear spin. For the present SO(4) symmetry model with either repulsive interaction (c > 0) or attractive interaction (c < 0), bound pairs could emerge in the ground state regardless of the sign of c.
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