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

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Abstract

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 \(\Gamma =0\) remains to be valid if the total spin of each species (which is conserved previously but not now) is replaced by its average \(\overline{S_\mathrm{J}}\). 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 \(\Gamma \) 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 \(\Gamma =0\).

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Acknowledgements

Supported by the National Natural Science Foundation of China under Grants No.11874432, 11372122, 11274393, 11574404, and 11275279; the Open Project Program of State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, China (No.Y4KF201CJ1); the National Basic Research Program of China (2013CB933601); and the Natural Science Foundation of Guangdong of China (2016A030313313).

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Authors and Affiliations

  1. School of Physics, Sun Yat-Sen University, Guangzhou, 510275, People’s Republic of China

    Y. Z. He & C. G. Bao

  2. Department of Physics, Shaoguan University, Shaoguan, 510205, People’s Republic of China

    Y. M. Liu

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  1. Y. Z. He
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  3. C. G. Bao
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Correspondence to C. G. Bao.

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He, Y.Z., Liu, Y.M. & Bao, C.G. Effect of the Singlet Pairing Force on the Spin Structures of 3-Species Bose-Einstein Condensates with Spin-1 Atoms. J Low Temp Phys 206, 167–181 (2022). https://doi.org/10.1007/s10909-021-02647-y

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