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Chin. Phys. B, 2016, Vol. 25(4): 040305    DOI: 10.1088/1674-1056/25/4/040305
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Weakly interacting spinor Bose-Einstein condensates with three-dimensional spin-orbit coupling

Shu-Wei Song(宋淑伟)1,2,3, Rui Sun(孙蕊)1,2,3, Hong Zhao(赵洪)1,2,3, Xuan Wang(王暄)1,2,3, Bao-Zhong Han(韩宝忠)1,2,3
1 State Key Laboratory Breeding Base of Dielectrics Engineering, Harbin University of Science and Technology, Harbin 150080, China;
2 Key Laboratory of Engineering Dielectrics and Its Application, Ministry of Education, Harbin University of Science and Technology, Harbin 150080, China;
3 College of Electrical and Electronic Engineering, Harbin University of Science and Technology, Harbin 150080, China
Abstract  

Starting from the Hamiltonian of the second quantization form, the weakly interacting Bose-Einstein condensate with spin-orbit coupling of Weyl type is investigated. It is found that the SU(2) nonsymmetric term, i.e., the spin-dependent interaction, can lift the degeneracy of the ground states with respect to the z component of the total angular momentum Jz, casting the ground condensate state into a configuration of zero Jz. This ground state density profile can also be affirmed by minimizing the full Gross-Pitaevskii energy functional. The spin texture of the zero Jz state indicates that it is a knot structure, whose fundamental group is π3(M)π3(S2)=Z.

Keywords:  Bose-Einstein condensate      spin-orbit coupling      knot  
Received:  06 November 2015      Revised:  16 December 2015      Accepted manuscript online: 
PACS:  03.75.Lm (Tunneling, Josephson effect, Bose-Einstein condensates in periodic potentials, solitons, vortices, and topological excitations)  
  03.75.Mn (Multicomponent condensates; spinor condensates)  
  67.85.Fg (Multicomponent condensates; spinor condensates)  
  67.85.Jk (Other Bose-Einstein condensation phenomena)  
Fund: 

Project supported by the National Natural Science Foundation of China (Grant No. 11447178).

Corresponding Authors:  Shu-Wei Song     E-mail:  japical@live.cn

Cite this article: 

Shu-Wei Song(宋淑伟), Rui Sun(孙蕊), Hong Zhao(赵洪), Xuan Wang(王暄), Bao-Zhong Han(韩宝忠) Weakly interacting spinor Bose-Einstein condensates with three-dimensional spin-orbit coupling 2016 Chin. Phys. B 25 040305

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