Please wait a minute...
Chin. Phys. B, 2021, Vol. 30(3): 030302    DOI: 10.1088/1674-1056/abc53e
GENERAL Prev   Next  

Spin-orbit-coupled spin-1 Bose-Einstein condensates confined in radially periodic potential

Ji Li(李吉)1, Tianchen He(何天琛)1,†, Jing Bai(白晶)1, Bin Liu(刘斌)2, and Huan-Yu Wang(王寰宇)3
1 Department of Physics, Taiyuan Normal University, Jinzhong 030619, China; 2 Basic Teaching Department, Shanxi Institute of Energy, Jinzhong 030600, China; 3 Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
Abstract  We investigate the ground states of spin-1 Bose-Einstein condensates (BECs) with spin-orbit coupling in a radially periodic potential by numerically solving the coupled Gross-Pitaevskii equations. In the radially periodic potential, we first demonstrate that spin-orbit-coupled antiferromagnetic BECs support a multiring petal phase. Polar-core vortex can be observed from phase profiles, which is manifested as circularly symmetric distribution. We further show that spin-orbit coupling can induce multiring soliton structure in ferromagnetic BECs. It is confirmed especially that the wave-function phase of the ring corresponding to uniform distribution satisfies the rotational symmetry, and the wave-function phase of the ring corresponding to partial splitting breaks the rotational symmetry. Adjusting the spin-orbit coupling strength can control the number of petal in antiferromagnetic BECs and the winding numbers of wave-function in ferromagnetic BECs. Finally, we discuss effects of spin-independent and spin-dependent interactions on the ground states.
Keywords:  the spinor Bose-Einstein condensates      spin-orbit coupling      radially periodic potential  
Received:  07 August 2020      Revised:  01 October 2020      Accepted manuscript online:  28 October 2020
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.Hj (Bose-Einstein condensates in optical potentials)  
Fund: Project supported by the Scientific and Technologial Innovation Program of the Higher Education Institutions in Shanxi Province, China (Grant Nos. 2019L0813, 2019L0785, and 2019L0808).
Corresponding Authors:  Corresponding author. E-mail:   

Cite this article: 

Ji Li(李吉), Tianchen He(何天琛), Jing Bai(白晶), Bin Liu(刘斌), and Huan-Yu Wang(王寰宇) Spin-orbit-coupled spin-1 Bose-Einstein condensates confined in radially periodic potential 2021 Chin. Phys. B 30 030302

1 Ho T L Phys. Rev. Lett. 81 742
2 Klausen N N, Bohn J L and Greene C H Phys. Rev. A 64 053602
3 G\"orlitz A, Gustavson T L, Leanhardt A E, L\"ow R, Chikkatur A P, Gupta S, Inouye S, Pritchard D E and Ketterle W Phys. Rev. Lett. 90 090401
4 Bloch I, Dalibard J and Zwerger W Rev. Mod. Phys. 80 885
5 Stamper-Kurn D M and Ueda M Rev. Mod. Phys. 85 1191
6 Li L, Li Z D, Malomed B A, Mihalache D and Liu W M Phys. Rev. A 72 033611
7 Isoshima T, Machida K and Ohmi T J. Phys. Soc. Jpn. 70 1604
8 Tuchiya S J and Kurihara S J. Phys. Soc. Jpn. 70 1182
9 Kasamatsu K, Tsubota M and Ueda M Int. J. Mod. Phys. B 19 1835
10 Mizushima T, Machida K and Kita T Phys. Rev. A 66 053610
11 Martikainen J P, Collin A and Suominen K A Phys. Rev. A 66 053604
12 Mizushima T, Kobayashi N and Machida K Phys. Rev. A 70 043613
13 Ji A C, Liu W M, Song J L and Zhou F Phys. Rev. Lett. 101 010402
14 Seo S W, Kang S J, Kwon W J and Shin Y Phys. Rev. Lett. 115 015301
15 Seo S W, Kwon W J, Kang S J and Shin Y Phys. Rev. Lett. 116 185301
16 Orlova N V, Kuopanportti P and Milo\vsevi\'cM V Phys. Rev. A 94 023617
17 Lin Y J, Jim\'enez-Garc\'ía K and Spielman I B Nature 471 83
18 Ji S C, Zhang J Y, Zhang L, Du Z D, Zheng W, Deng Y J, Zhai H, Chen S and Pan J W Nat. Phys. 10 314
19 Wu Z, Zhang L, Sun W, 1 Xu X T, Wang B Z, Ji S C, Deng Y J, Chen S, Liu X J and Pan J W Science 354 83
20 Huang L H, Meng Z M, Wang P J, Peng P, Zhang S L, Chen L C, Li D H, Zhou Q and Zhang J Nat. Phys. 12 540
21 Wang P J, Yu Z Q, Fu Z K, Miao J, Huang L H, Chai S J, Zhai H and Zhang J Phys. Rev. Lett. 109 095301
22 Campbell D L, Juzeli\'unas G and Spielman I B Phys. Rev. A 84 025602
23 Zhang J Y, Ji S C, Chen Z, Zhang L, Du Z D, Yan B, Pan J S, Zhao B, Deng Y J, Zhai H, Chen S and Pan J W Phys. Rev. Lett. 109 115301
24 Liu X J, Borunda M F, Liu X and Sinova J Phys. Rev. Lett. 102 046402
25 Anderson B M, Spielman I B and Juzeli\'unas G Phys. Rev. Lett. 111 125301
26 Anderson B M, Juzeli\'unas G, Galitski V M and Spielman I B Phys. Rev. Lett. 108 235301
27 Cheuk L W, Sommer A T, Hadzibabic Z, Yefsah T, Bakr W S and Zwierlein M W Phys. Rev. Lett. 109 095302
28 Ruseckas J, Juzeli\'unas G, \"Ohberg P and Fleischhauer M Phys. Rev. Lett. 95 010404
29 Lan Z H and \"Ohberg P Phys. Rev. A 89 023630
30 Wang C J, Gao C, Jian C M and Zhai H Phys. Rev. Lett. 105 160403
31 Su S W, Liu I K, Tsai Y C, Liu W M and Gou S C Phys. Rev. A 86 023601
32 Sinha S, Nath R and Santos L Phys. Rev. Lett. 107 270401
33 Hu H, Ramachandhran B, Pu H and Liu X J Phys. Rev. Lett. 108 010402
34 Li J, Yu Y M, Zhuang L and Liu W M Phys. Rev. A 95 043633
35 Li J, Zhang X F and Liu W M Ann. Phys.-New York 396 87
36 Gopalakrishnan S, Martin I and Demler E A Phys. Rev. Lett. 111 185304
37 Mason P and Berloff N G Phys. Rev. A 79 043620
38 Ryu C, Andersen M F, Clad\'e P, Natarajan V, Helmerson K and Phillips W D Phys. Rev. Lett. 99 260401
39 Abad M, Guilleumas M, Mayol R and Pi M Phys. Rev. A 81 043619
40 Zhang X F, Kato M, Han W, Zhang S G and Saito H Phys. Rev. A 95 033620
41 White A C, Zhang Y P and Busch T Phys. Rev. A 95 041604(R)
42 Karabulut E \"O, Malet F, Fetter A L, Kavoulakis G M and Reimann S M New J. Phys. 18 015013
43 Wang J G, Xu L L and Yang S J Phys. Rev. A 96 033629
44 Kartashov Y V and Zezyulin D A Phys. Rev. Lett. 122 123201
45 Baizakov B B, Malomed B A and Salerno M Phys. Rev. E 74 066615
46 Song S W, Sun R, Zhao H, Wang X and Han B Z Chin. Phys. B 25 040305
[1] Spin-orbit coupling adjusting topological superfluid of mass-imbalanced Fermi gas
Jian Feng(冯鉴), Wei-Wei Zhang(张伟伟), Liang-Wei Lin(林良伟), Qi-Peng Cai(蔡启鹏), Yi-Cai Zhang(张义财), Sheng-Can Ma(马胜灿), and Chao-Fei Liu(刘超飞). Chin. Phys. B, 2022, 31(9): 090305.
[2] Influence of Rashba spin-orbit coupling on Josephson effect in triplet superconductor/two-dimensional semiconductor/triplet superconductor junctions
Bin-Hao Du(杜彬豪), Man-Ni Chen(陈嫚妮), and Liang-Bin Hu(胡梁宾). Chin. Phys. B, 2022, 31(7): 077201.
[3] Anderson localization of a spin-orbit coupled Bose-Einstein condensate in disorder potential
Huan Zhang(张欢), Sheng Liu(刘胜), and Yongsheng Zhang(张永生). Chin. Phys. B, 2022, 31(7): 070305.
[4] Gap solitons of spin-orbit-coupled Bose-Einstein condensates in $\mathcal{PT}$ periodic potential
S Wang(王双), Y H Liu(刘元慧), and T F Xu(徐天赋). Chin. Phys. B, 2022, 31(7): 070306.
[5] Gate tunable Rashba spin-orbit coupling at CaZrO3/SrTiO3 heterointerface
Wei-Min Jiang(姜伟民), Qiang Zhao(赵强), Jing-Zhuo Ling(凌靖卓), Ting-Na Shao(邵婷娜), Zi-Tao Zhang(张子涛), Ming-Rui Liu(刘明睿), Chun-Li Yao(姚春丽), Yu-Jie Qiao(乔宇杰), Mei-Hui Chen(陈美慧), Xing-Yu Chen(陈星宇), Rui-Fen Dou(窦瑞芬), Chang-Min Xiong(熊昌民), and Jia-Cai Nie(聂家财). Chin. Phys. B, 2022, 31(6): 066801.
[6] Vortex chains induced by anisotropic spin-orbit coupling and magnetic field in spin-2 Bose-Einstein condensates
Hao Zhu(朱浩), Shou-Gen Yin(印寿根), and Wu-Ming Liu(刘伍明). Chin. Phys. B, 2022, 31(6): 060305.
[7] Asymmetric Fraunhofer pattern in Josephson junctions from heterodimensional superlattice V5S8
Juewen Fan(范珏雯), Bingyan Jiang(江丙炎), Jiaji Zhao(赵嘉佶), Ran Bi(毕然), Jiadong Zhou(周家东), Zheng Liu(刘政), Guang Yang(杨光), Jie Shen(沈洁), Fanming Qu(屈凡明), Li Lu(吕力), Ning Kang(康宁), and Xiaosong Wu(吴孝松). Chin. Phys. B, 2022, 31(5): 057402.
[8] Manipulating vortices in F=2 Bose-Einstein condensates through magnetic field and spin-orbit coupling
Hao Zhu(朱浩), Shou-Gen Yin(印寿根), and Wu-Ming Liu(刘伍明). Chin. Phys. B, 2022, 31(4): 040306.
[9] SU(3) spin-orbit coupled fermions in an optical lattice
Xiaofan Zhou(周晓凡), Gang Chen(陈刚), and Suo-Tang Jia(贾锁堂). Chin. Phys. B, 2022, 31(1): 017102.
[10] Spin and spin-orbit coupling effects in nickel-based superalloys: A first-principles study on Ni3Al doped with Ta/W/Re
Liping Liu(刘立平), Jin Cao(曹晋), Wei Guo(郭伟), and Chongyu Wang(王崇愚). Chin. Phys. B, 2022, 31(1): 016105.
[11] Highly accurate theoretical study on spectroscopic properties of SH including spin-orbit coupling
Shu-Tao Zhao(赵书涛), Xin-Peng Liu(刘鑫鹏), Rui Li(李瑞), Hui-Jie Guo(国慧杰), and Bing Yan(闫冰). Chin. Phys. B, 2021, 30(7): 073104.
[12] Dynamics of bright soliton in a spin-orbit coupled spin-1 Bose-Einstein condensate
Hui Guo(郭慧), Xu Qiu(邱旭), Yan Ma(马燕), Hai-Feng Jiang(姜海峰), and Xiao-Fei Zhang(张晓斐). Chin. Phys. B, 2021, 30(6): 060310.
[13] Tunable valley filter efficiency by spin-orbit coupling in silicene nanoconstrictions
Yi-Jian Shi(施一剑), Yuan-Chun Wang(王园春), and Peng-Jun Wang(汪鹏君). Chin. Phys. B, 2021, 30(5): 057201.
[14] Configuration interaction study on low-lying states of AlCl molecule
Xiao-Ying Ren(任笑影), Zhi-Yu Xiao(肖志宇), Yong Liu(刘勇), and Bing Yan(闫冰). Chin. Phys. B, 2021, 30(5): 053101.
[15] Adjustable half-skyrmion chains induced by SU(3) spin-orbit coupling in rotating Bose-Einstein condensates
Li Wang(王力), Ji Li(李吉), Xiao-Lin Zhou(周晓林), Xiang-Rong Chen(陈向荣), and Wu-Ming Liu(刘伍明). Chin. Phys. B, 2021, 30(11): 110312.
No Suggested Reading articles found!