Effect of the Singlet Pairing Force on the Spin Structures of 3-Species Bose-Einstein Condensates with Spin-1 Atoms

• Published in: Journal of low temperature physics 2022, Vol.206 (3-4), p.167-181
• Main Authors: He, Y. Z., Liu, Y. M., Bao, C. G.
• Format: Article
• Language: English
• Subjects: Atomic structure; Bose-Einstein condensates; Characterization and Evaluation of Materials; Condensed Matter Physics; Eigenvectors; Low temperature physics; Magnetic Materials; Magnetism; Parameter sensitivity; Physics; Physics and Astronomy; Spin structure
• ISSN: 0022-2291; 1573-7357
• DOI: 10.1007/s10909-021-02647-y

The spin structures of Bose-Einstein condensates (BEC) with three kinds of spin-1 atoms are studied. The many-body Hamiltonian is diagonalized in the spin space via a strict numerical approach to obtain eigen-energies and eigen-states. The emphasis is to clarify the effect of the singlet pairing force with the strength Γ. This force has been neglected in previous studies on 3-species BEC. We found that the classification scheme for the phases of the ground state (g.s.) found previously with Γ = 0 remains to be valid if the total spin of each species (which is conserved previously but not now) is replaced by its average S J ¯ . Accordingly, the phase-diagrams for the g.s. remain qualitatively unchanged except for a shift of the boundaries (critical surfaces) separating the zones (each for a phase). However, neighboring to the critical surface which designates the breakdown of the ppp-phase (all the three species are in the polar phase), we found that there is a narrow zone in which the spin structure is extremely sensitive to the variation of the parameters if Γ is negative. It implies that, once the ppp-phase is broken, a great adjustment in spin structure will follow. This highly sensitive narrow zone does not exist if Γ = 0 .