中国物理B ›› 2024, Vol. 33 ›› Issue (10): 100304-100304.doi: 10.1088/1674-1056/ad6424

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Bessel vortices in spin-1 Bose-Einstein condensates with Zeeman splitting and spin-orbit coupling

Huan-Bo Luo(罗焕波)1,2, Xin-Feng Zhang(张鑫锋)2, Runhua Li(李润华)1, Yongyao Li(黎永耀)2, and Bin Liu(刘彬)2,†   

  1. 1 Department of Physics, South China University of Technology, Guangzhou 510640, China;
    2 School of Physics and Optoelectronic Engineering, Foshan University, Foshan 528000, China
  • 收稿日期:2024-06-14 修回日期:2024-07-16 接受日期:2024-07-17 发布日期:2024-09-21
  • 通讯作者: Bin Liu E-mail:binliu@fosu.edu.cn
  • 基金资助:
    Project supported by the Guangdong Basic and Applied Basic Research Foundation (Grant No. 2023A1515110198), the Natural Science Foundation of Guangdong Province, China (Grant Nos. 2024A1515030131 and 2021A1515010214), the National Natural Science Foundation of China (Grant Nos. 12274077, 11905032, and 12475014), the Research Fund of the Guangdong-Hong Kong-Macao Joint Laboratory for Intelligent Micro-Nano Optoelectronic Technology (Grant No. 2020B1212030010), and the Israel Science Foundation (Grant No. 1695/22).

Bessel vortices in spin-1 Bose-Einstein condensates with Zeeman splitting and spin-orbit coupling

Huan-Bo Luo(罗焕波)1,2, Xin-Feng Zhang(张鑫锋)2, Runhua Li(李润华)1, Yongyao Li(黎永耀)2, and Bin Liu(刘彬)2,†   

  1. 1 Department of Physics, South China University of Technology, Guangzhou 510640, China;
    2 School of Physics and Optoelectronic Engineering, Foshan University, Foshan 528000, China
  • Received:2024-06-14 Revised:2024-07-16 Accepted:2024-07-17 Published:2024-09-21
  • Contact: Bin Liu E-mail:binliu@fosu.edu.cn
  • Supported by:
    Project supported by the Guangdong Basic and Applied Basic Research Foundation (Grant No. 2023A1515110198), the Natural Science Foundation of Guangdong Province, China (Grant Nos. 2024A1515030131 and 2021A1515010214), the National Natural Science Foundation of China (Grant Nos. 12274077, 11905032, and 12475014), the Research Fund of the Guangdong-Hong Kong-Macao Joint Laboratory for Intelligent Micro-Nano Optoelectronic Technology (Grant No. 2020B1212030010), and the Israel Science Foundation (Grant No. 1695/22).

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摘要： We investigate the ground states of spin-orbit coupled spin-1 Bose-Einstein condensates in the presence of Zeeman splitting. By introducing the generalized momentum operator, the linear version of the system is solved exactly, yielding a set of Bessel vortices. Additionally, based on linear solution and using variational approximation, the solutions for the full nonlinear system and their ground state phase diagrams are derived, including the vortex states with quantum numbers $m=0$, 1, as well as mixed states. In this work, mixed states in spin-1 spin-orbit coupling (SOC) BEC are interpreted for the first time as weighted superpositions of three vortex states. Furthermore, the results also indicate that under strong Zeeman splitting, the system cannot form localized states. The variational solutions align well with numerical simulations, showing stable evolution and meeting the criteria for long-term observation in experiments.

关键词: spin-orbit coupling, Bessel vortices, variational method

Abstract: We investigate the ground states of spin-orbit coupled spin-1 Bose-Einstein condensates in the presence of Zeeman splitting. By introducing the generalized momentum operator, the linear version of the system is solved exactly, yielding a set of Bessel vortices. Additionally, based on linear solution and using variational approximation, the solutions for the full nonlinear system and their ground state phase diagrams are derived, including the vortex states with quantum numbers $m=0$, 1, as well as mixed states. In this work, mixed states in spin-1 spin-orbit coupling (SOC) BEC are interpreted for the first time as weighted superpositions of three vortex states. Furthermore, the results also indicate that under strong Zeeman splitting, the system cannot form localized states. The variational solutions align well with numerical simulations, showing stable evolution and meeting the criteria for long-term observation in experiments.

Key words: spin-orbit coupling, Bessel vortices, variational method

中图分类号:  (Tunneling, Josephson effect, Bose-Einstein condensates in periodic potentials, solitons, vortices, and topological excitations)

  • 03.75.Lm
71.70.Ej (Spin-orbit coupling, Zeeman and Stark splitting, Jahn-Teller effect) 75.70.Tj (Spin-orbit effects)