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Chin. Phys. B, 2021, Vol. 30(3): 030302    DOI: 10.1088/1674-1056/abc53e
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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: tywlxdh@qq.com   

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
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