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Ground state of spin-orbit coupled rotating two-component Bose-Einstein condensate in gradient magnetic field

Li Ji Liu Wu-Ming

Ground state of spin-orbit coupled rotating two-component Bose-Einstein condensate in gradient magnetic field

Li Ji, Liu Wu-Ming
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  • Two-component Bose-Einstein condensate offers an ideal platform for investigating many intriguing topological defects due to the interplay between intraspecies and interspecies interactions. The recent realization of spin-orbit coupling in two-component Bose-Einstein condensate, owing to coupling between the spin and the centre-of-mass motion of the atom, provides possibly new opportunities to search for novel quantum states. In particular, the gradient magnetic field in the Bose-Einstein condensate has brought a new way to create topologically nontrivial structures including Dirac monopoles and quantum knots. Previous studies of the gradient magnetic field effect in the Bose-Einstein condensate mainly focused on the three-component case. However, it remains unclear how the gradient magnetic field affects the ground state configuration in the rotating two-component Bose-Einstein condensate with spin-orbit coupling. In this work, by using quasi two-dimensional Gross-Pitaevskii equations, we study the ground state structure of a rotating two-component Bose-Einstein condensate with spin-orbit coupling and gradient magnetic field. We concentrate on the effects of the spin-orbit coupling and the gradient magnetic field on the ground state. The numerical results show that increasing the strength of the spin-orbit coupling can induce a phase transition from skyrmion lattice to skyrmion chain in the presence of the gradient magnetic field. Unlike the study of skyrmion in rotating two-component Bose-Einstein condensate with only spin-orbit coupling, the skyrmion chain can occur under the isotropic spin-orbit coupling when the gradient magnetic field is considered. It is worth noting that the skyrmion chain here is arrayed along the diagonal direction. Next we examine the effect of the gradient magnetic field on spin-orbit coupled two-component Bose-Einstein condensate. For the case of weak spin-orbit coupling and the slow rotation, a phase transition from a single plane-wave to half-skyrmion is found through increasing magnetic field gradient strength. For the case of strong spin-orbit coupling and the fast rotation, the nature of the ground state is shown to support the formation of a hidden vortex as the gradient magnetic field is enhanced. These hidden vortices have no visible cores in density distributions but have phase singularities in phase distributions, which are arrayed along the diagonal direction. This result confirms a new method of creating the hidden vortices in the two-component Bose-Einstein condensate. These topological structures can be detected by using the time-of-flight absorption imaging technique. Our results illustrate that the gradient magnetic field not only provides an opportunity to explore the exotic topological structures in spin-orbit coupled spinor Bose-Einstein condensate, but also is crucial for realizing the phase transitions among different ground states. This work paves the way for the future exploring of topological defect and the corresponding dynamical stability in quantum systems subjected to a gradient magnetic field.
      Corresponding author: Li Ji, liji2015@iphy.ac.cn
    • Funds: Project supported by the NKRDP, China (Grant No. 2016YFA0301500) and the National Natural Science Foundation of China (Grant Nos. 11434015, KZ201610005011).
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    Dalfovo F, Stringari S 1996 Phys. Rev. A 53 2477

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    Bao W Z, Du Q 2004 SIAM J. Sci. Comput. 25 1674

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    Wen L H, Xiong H W, Wu B 2010 Phys. Rev. A 82 053627

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    Mithun T, Porsezian K, Dey B 2014 Phys. Rev. A 89 053625

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    Barnett R, Boyd G R, Galitski V 2012 Phys. Rev. Lett. 109 235308

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    Liu C F, Wan W J, Zhang G Y 2013 Acta Phys. Sin. 62 200306(in Chinese) [刘超飞, 万文娟, 张赣源 2013 物理学报 62 200306]

  • [1]

    Hall D S, Matthews M R, Ensher J R, Wieman C E, Cornell E A 1998 Phys. Rev. Lett. 81 1539

    [2]

    Matthews M R, Anderson B P, Haljan P C, Hall D S, Wieman C E, Cornell E A 1999 Phys. Rev. Lett. 83 2498

    [3]

    Anderson B P, Haljan P C, Regal C A, Feder D L, Collins L A, Clark C W, Cornell E A 2001 Phys. Rev. Lett. 86 2926

    [4]

    Kasamatsu K, Tsubota M 2004 Phys. Rev. Lett. 93 100402

    [5]

    Qu C L, Pitaevskii L P, Stringari S 2016 Phys. Rev. Lett. 116 160402

    [6]

    Williams J E, Holland M J 1999 Nature 401 568

    [7]

    hberg P, Santos L 2001 Phys. Rev. Lett. 86 2918

    [8]

    Kasamatsu K, Tsubota M, Ueda M 2004 Phys. Rev. Lett. 93 250406

    [9]

    Schweikhard V, Coddington I, Engels P, Tung S, Cornell E A 2004 Phys. Rev. Lett. 93 210403

    [10]

    Cipriani M, Nitta M 2013 Phys. Rev. Lett. 111 170401

    [11]

    Kasamatsu K, Tsubota M, Ueda M 2003 Phys. Rev. Lett. 91 150406

    [12]

    Battye R A, Cooper N R, Sutcliffe P M 2002 Phys. Rev. Lett. 88 080401

    [13]

    Martikainen J P, Collin A, Suominen K A 2002 Phys. Rev. Lett. 88 090404

    [14]

    Lin Y J, Garca K J, Spielman I B 2011 Nature 471 83

    [15]

    Ji S C, Zhang J Y, Zhang L, Du Z D, Zheng W, Deng Y J, Zhai H, Chen S, Pan J W 2014 Nature Phys. 10 314

    [16]

    Wu Z, Zhang L, Sun W, Xu X T, Wang B Z, Ji S C, Deng Y J, Chen S, Liu X J, Pan J W 2016 Science 354 83

    [17]

    Huang L H, Meng Z M, Wang P J, Peng P, Zhang S L, Chen L C, Li D H, Zhou Q, Zhang J 2016 Nature Phys. 12 540

    [18]

    Ruseckas J, Juzelinas G, hberg P, Fleischhauer M 2005 Phys. Rev. Lett. 95 010404

    [19]

    Campbell D L, Juzelinas G, Spielman I B 2011 Phys. Rev. A 84 025602

    [20]

    Zhang J Y, Ji S C, Chen Z, Zhang L, Du Z D, Yan B, Pan G S, Zhao B, Deng Y J, Zhai H, Chen S, Pan J W 2012 Phys. Rev. Lett. 109 115301

    [21]

    Liu X J, Borunda M F, Liu X, Sinova J 2009 Phys. Rev. Lett. 102 046402

    [22]

    Anderson B M, Spielman I B, Juzelinas G 2013 Phys. Rev. Lett. 111 125301

    [23]

    Anderson B M, Juzelinas G, Galitski V M, Spielman I B 2012 Phys. Rev. Lett. 108 235301

    [24]

    Cheuk L M, Sommer A T, Hadzibabic Z, Yefsah T, Bakr W S, Zwierlein1 M W 2012 Phys. Rev. Lett. 109 095302

    [25]

    Wang P J, Yu Z Q, Fu Z K, Miao J, Huang L H, Chai S J, Zhai H, Zhang J 2012 Phys. Rev. Lett. 109 095301

    [26]

    Lan Z H, hberg P 2014 Phys. Rev. A 89 023630

    [27]

    Wang C J, Gao C, Jian C M, Zhai H 2010 Phys. Rev. Lett. 105 160403

    [28]

    Sinha S, Nath R, Santos L 2011 Phys. Rev. Lett. 107 270401

    [29]

    Hu H, Ramachandhran B, Pu H, Liu X J 2012 Phys. Rev. Lett. 108 010402

    [30]

    Yu Z Q 2013 Phys. Rev. A 87 051606

    [31]

    Bhat I A, Mithun T, Malomed B A, Porsezian K 2015 Phys. Rev. A 92 063606

    [32]

    Li Y, Zhou X F, Wu C J 2016 Phys. Rev. A 93 033628

    [33]

    Kato M, Zhang X F, Saito H 2017 Phys. Rev. A 95 043605

    [34]

    Xu X Q, Han J H 2011 Phys. Rev. Lett. 107 200401

    [35]

    Liu C F, Fan H, Zhang Y C, Wang D S, Liu W M 2012 Phys. Rev. A 86 053616

    [36]

    Zhou X F, Zhou J, Wu C J 2011 Phys. Rev. A 84 063624

    [37]

    Sakaguchi H, Umeda K 2016 J. Phys. Soc. Jpn. 85 064402

    [38]

    Zhang X F, Gao R S, Wang X, Dong R F, Liu T, Zhang S G 2013 Phys. Lett. A 377 1109

    [39]

    Wang X, Tan R B, Du Z J, Zhao W Y, Zhang X F, Zhang S G 2014 Chin. Phys. B 23 070308

    [40]

    Wang H, Wen L H, Yang H, Shi C X, Li J H 2017 J. Phys. B: At. Mol. Opt. Phys. 50 155301

    [41]

    Radić J, Sedrakyan T A, Spielman I B, Galitski V 2011 Phys. Rev. A 84 063604

    [42]

    Fetter A L 2014 Phys. Rev. A 89 023629

    [43]

    Chen G P 2015 Acta Phys. Sin. 64 030302(in Chinese) [陈光平 2015 物理学报 64 030302]

    [44]

    Liu C F, Liu W M 2012 Phys. Rev. A 86 033602

    [45]

    Kennedy C J, Siviloglou G A, Miyake H, Burton W C, Ketterle W 2013 Phys. Rev. Lett. 111 225301

    [46]

    Ray M W, Ruokokoski E, Kandel S, Mttnen M, Hall D S 2014 Nature 505 657

    [47]

    Ray M W, Ruokokoski E, Tiurev K, Mttnen M, Hall D S 2015 Science 348 544

    [48]

    Hall D S, Ray M W, Tiurev K, Ruokokoski E, Gheorghe A H, Mttnen M 2016 Nature Phys. 12 478

    [49]

    Kawaguchi Y, Nitta M, Ueda M 2008 Phys. Rev. Lett. 100 180403

    [50]

    Li J, Yu Y M, Zhuang L, Liu W M 2017 Phys. Rev. A 95 043633

    [51]

    Liu J S, Li J, Liu W M 2017 Acta Phys. Sin. 66 130305(in Chinese) [刘静思, 李吉, 刘伍明 2017 物理学报 66 130305]

    [52]

    Leanhardt A E, Grlitz A, Chikkatur A P, Kielpinski D, Shin Y, Pritchard D E, Ketterle W 2002 Phys. Rev. Lett. 89 190403

    [53]

    Pritchard D E 1983 Phys. Rev. Lett. 51 1336

    [54]

    Leanhardt A E, Shin Y, Kielpinski D, Pritchard D E, Ketterle W 2003 Phys. Rev. Lett. 90 140403

    [55]

    Han W, Zhang S Y, Jin J J, Liu W M 2012 Phys. Rev. A 85 043626

    [56]

    Dalfovo F, Stringari S 1996 Phys. Rev. A 53 2477

    [57]

    Zhang X F, Dong R F, Liu T, Liu W M, Zhang S G 2012 Phys. Rev. A 86 063628

    [58]

    Bao W Z, Du Q 2004 SIAM J. Sci. Comput. 25 1674

    [59]

    Wen L H, Xiong H W, Wu B 2010 Phys. Rev. A 82 053627

    [60]

    Mithun T, Porsezian K, Dey B 2014 Phys. Rev. A 89 053625

    [61]

    Ruokokoski E, Huhtamki J A M, Mttnen M 2012 Phys. Rev. A 86 051607

    [62]

    Barnett R, Boyd G R, Galitski V 2012 Phys. Rev. Lett. 109 235308

    [63]

    Chen G J, Chen L, Zhang Y B 2016 New J. Phys. 18 063010

    [64]

    Zhang X F, Zhang P, Chen G P, Dong B, Tan R B, Zhang S G 2015 Acta Phys. Sin. 64 060302(in Chinese) [张晓斐, 张培, 陈光平, 董彪, 谭仁兵, 张首刚 2015 物理学报 64 060302]

    [65]

    Liu C F, Wan W J, Zhang G Y 2013 Acta Phys. Sin. 62 200306(in Chinese) [刘超飞, 万文娟, 张赣源 2013 物理学报 62 200306]

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  • Received Date:  26 March 2018
  • Accepted Date:  09 April 2018
  • Published Online:  05 June 2018

Ground state of spin-orbit coupled rotating two-component Bose-Einstein condensate in gradient magnetic field

    Corresponding author: Li Ji, liji2015@iphy.ac.cn
  • 1. Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China;
  • 2. School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
Fund Project:  Project supported by the NKRDP, China (Grant No. 2016YFA0301500) and the National Natural Science Foundation of China (Grant Nos. 11434015, KZ201610005011).

Abstract: Two-component Bose-Einstein condensate offers an ideal platform for investigating many intriguing topological defects due to the interplay between intraspecies and interspecies interactions. The recent realization of spin-orbit coupling in two-component Bose-Einstein condensate, owing to coupling between the spin and the centre-of-mass motion of the atom, provides possibly new opportunities to search for novel quantum states. In particular, the gradient magnetic field in the Bose-Einstein condensate has brought a new way to create topologically nontrivial structures including Dirac monopoles and quantum knots. Previous studies of the gradient magnetic field effect in the Bose-Einstein condensate mainly focused on the three-component case. However, it remains unclear how the gradient magnetic field affects the ground state configuration in the rotating two-component Bose-Einstein condensate with spin-orbit coupling. In this work, by using quasi two-dimensional Gross-Pitaevskii equations, we study the ground state structure of a rotating two-component Bose-Einstein condensate with spin-orbit coupling and gradient magnetic field. We concentrate on the effects of the spin-orbit coupling and the gradient magnetic field on the ground state. The numerical results show that increasing the strength of the spin-orbit coupling can induce a phase transition from skyrmion lattice to skyrmion chain in the presence of the gradient magnetic field. Unlike the study of skyrmion in rotating two-component Bose-Einstein condensate with only spin-orbit coupling, the skyrmion chain can occur under the isotropic spin-orbit coupling when the gradient magnetic field is considered. It is worth noting that the skyrmion chain here is arrayed along the diagonal direction. Next we examine the effect of the gradient magnetic field on spin-orbit coupled two-component Bose-Einstein condensate. For the case of weak spin-orbit coupling and the slow rotation, a phase transition from a single plane-wave to half-skyrmion is found through increasing magnetic field gradient strength. For the case of strong spin-orbit coupling and the fast rotation, the nature of the ground state is shown to support the formation of a hidden vortex as the gradient magnetic field is enhanced. These hidden vortices have no visible cores in density distributions but have phase singularities in phase distributions, which are arrayed along the diagonal direction. This result confirms a new method of creating the hidden vortices in the two-component Bose-Einstein condensate. These topological structures can be detected by using the time-of-flight absorption imaging technique. Our results illustrate that the gradient magnetic field not only provides an opportunity to explore the exotic topological structures in spin-orbit coupled spinor Bose-Einstein condensate, but also is crucial for realizing the phase transitions among different ground states. This work paves the way for the future exploring of topological defect and the corresponding dynamical stability in quantum systems subjected to a gradient magnetic field.

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