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Ground states, solitons and spin textures in spin-1 Bose-Einstein condensates

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Abstract

We present an overview of our recent theoretical studies on the quantum phenomena of the spin-1 Bose-Einstein condensates, including the phase diagram, soliton solutions and the formation of the topological spin textures. A brief exploration of the effects of spin-orbit coupling on the ground-state properties is given. We put forward proposals by using the transmission spectra of an optical cavity to probe the quantum ground states: the ferromagnetic and polar phases. Quasi-one-dimension solitons and ring dark solitons are studied. It is predicted that characteristics of the magnetic solitons in optical lattice can be tuned by controlling the long-range light-induced and static magnetic dipoledipole interactions; solutions of single-component magnetic and single-, two-, three-components polar solitons are found; ring dark solitons in spin-1 condensates are predicted to live longer lifetimes than that in their scalar counterparts. In the formation of spin textures, we have considered the theoretical model of a rapidly quenched and fast rotating trapped spin-1 Bose-Einstein condensate, whose dynamics can be studied by solving the stochastic projected Gross-Pitaevskii equations. Spontaneous generation of nontrivial topological defects, such as the hexagonal lattice skyrmions and square lattice of half-quantized vortices was predicted. In particular, crystallization of merons (half skyrmions) can be generated in the presence of spin-orbit coupling.

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References

  1. D. M. Stamper-Kurn, M. R. Andrews, A. P. Chikkatur, S. Inouye, H. J. Miesner, J. Stenger, and W. Ketterle, Phys. Rev. Lett., 1998, 80(10): 2027

    Article  ADS  Google Scholar 

  2. T. Ohmi and K. Machida, J. Phys. Soc. Jpn., 1998, 67(6): 1822

    Article  ADS  Google Scholar 

  3. T. L. Ho, Phys. Rev. Lett., 1998, 81(4): 742

    Article  ADS  Google Scholar 

  4. J. Stenger, S. Inouye, D. M. Stamper-Kurn, H. J. Miesner, A. P. Chikkatur, and W. Ketterle, Nature, 1998, 396(6709): 345

    Article  ADS  Google Scholar 

  5. C. K. Law, H. Pu, and N. P. Bigelow, Phys. Rev. Lett., 1998, 81(24): 5257

    Article  ADS  Google Scholar 

  6. M. Koashi and M. Ueda, Phys. Rev. Lett., 2000, 84(6): 1066

    Article  ADS  Google Scholar 

  7. T. L. Ho and L. Yin, Phys. Rev. Lett., 2000, 84(11): 2302

    Article  ADS  Google Scholar 

  8. H. J. Miesner, D. M. Stamper-Kurn, J. Stenger, S. Inouye, A. P. Chikkatur, and W. Ketterle, Phys. Rev. Lett., 1999, 82(11): 2228

    Article  ADS  Google Scholar 

  9. H. Pu, C. K. Law, S. Raghavan, J. H. Eberly, and N. P. Bigelow, Phys. Rev. A, 1999, 60(2): 1463

    Article  ADS  Google Scholar 

  10. M. S. Chang, C. D. Hamley, M. D. Barrett, J. A. Sauer, K. M. Fortier, W. Zhang, L. You, and M. S. Chapman, Phys. Rev. Lett., 2004, 92(14): 140403

    Article  ADS  Google Scholar 

  11. A. Widera, F. Gerbier, S. Fölling, T. Gericke, O. Mandel, and I. Bloch, New J. Phys., 2006, 8(8): 152

    Article  ADS  Google Scholar 

  12. N. Klausen, J. Bohn, and C. Greene, Phys. Rev. A, 2001, 64(5): 053602

    Article  ADS  Google Scholar 

  13. F. Zhou, Phys. Rev. Lett., 2001, 87(8): 080401

    Article  ADS  Google Scholar 

  14. G. W. Semenoff and F. Zhou, Phys. Rev. Lett., 2007, 98(10): 100401

    Article  MathSciNet  ADS  Google Scholar 

  15. T. Isoshima, K. Machida, and T. Ohmi, J. Phys. Soc. Jpn., 2001, 70(6): 1604

    Article  ADS  MATH  Google Scholar 

  16. T. Mizushima, K. Machida, and T. Kita, Phys. Rev. Lett., 2002, 89(3): 030401

    Article  ADS  Google Scholar 

  17. U. Leonhardt and G. E. Volovik, JETP Lett., 2000, 72(2): 46

    Article  ADS  Google Scholar 

  18. T. Isoshima and K. Machida, Phys. Rev. A, 2002, 66(2): 023602

    Article  ADS  Google Scholar 

  19. T. Isoshima, K. Machida, and T. Ohmi, J. Phys. Soc. Jpn., 2001, 70(6): 1604

    Article  ADS  Google Scholar 

  20. H. T. C. Stoof, E. Vliegen, and U. Al Khawaja, Phys. Rev. Lett., 2001, 87(12): 120407

    Article  ADS  Google Scholar 

  21. J. Ruostekoski and J. R. Anglin, Phys. Rev. Lett., 2003, 91(19): 190402

    Article  ADS  Google Scholar 

  22. J. Ieda, T. Miyakawa, and M. Wadati, Phys. Rev. Lett., 2004, 93(19): 194102

    Article  ADS  Google Scholar 

  23. E. V. Doktorov, J. Wang, and J. Yang, Phys. Rev. A, 2008, 77(4): 043617

    Article  ADS  Google Scholar 

  24. H. E. Nistazakis, D. J. Frantzeskakis, P. G. Kevrekidis, B. A. Malomed, and R. Carretero-González, Phys. Rev. A, 2008, 77(3): 033612

    Article  ADS  Google Scholar 

  25. M. Ueda and Y. Kawaguchi, Phys. Rep., 2012, 520: 253

    Article  MathSciNet  ADS  Google Scholar 

  26. W. Z. Bao and Y. Z. Zhang, Methods Appl. Anal., 2010, 17: 049

    MathSciNet  Google Scholar 

  27. A. S. Bradley, C. Gardiner, and M. Davis, Phys. Rev. A, 2008, 77(3): 033616

    Article  ADS  Google Scholar 

  28. S. J. Rooney, A. S. Bradley, and P. B. Blakie, Phys. Rev. A, 2010, 81(2): 023630

    Article  ADS  Google Scholar 

  29. S. J. Rooney, P. B. Blakie, B. P. Anderson, and A. S. Bradley, Phys. Rev. A, 2011, 84(2): 023637

    Article  ADS  Google Scholar 

  30. A. Sinatra, C. Lobo, and Y. Castin, J. Phys. B, 2002, 35(17): 3599

    Article  ADS  Google Scholar 

  31. C. W. Gardiner and P. Zoller, Phys. Rev. A, 1998, 58(1): 1050

    Article  Google Scholar 

  32. C. W. Gardiner and P. Zoller, Phys. Rev. A, 2000, 61(3): 033601

    Article  ADS  Google Scholar 

  33. S. W. Su, C. H. Hsueh, I. K. Liu, T. L. Horng, Y. C. Tsai, S. C. Gou, and W. M. Liu, Phys. Rev. A, 2011, 84(2): 023601

    Article  ADS  Google Scholar 

  34. Y. Hao, Y. Zhang, J. Q. Liang, and S. Chen, Phys. Rev. A, 2006, 73(5): 053605

    Article  ADS  Google Scholar 

  35. L. Li, Z. Li, B. A. Malomed, D. Mihalache, and W. M. Liu, Phys. Rev. A, 2005, 72(3): 033611

    Article  ADS  Google Scholar 

  36. N. P. Robins, W. Zhang, E. A. Ostrovskaya, and Y. S. Kivshar, Phys. Rev. A, 2001, 64(2): 021601

    Article  ADS  Google Scholar 

  37. W. Zhang, D. L. Zhou, M. S. Chang, M. S. Chapman, and L. You, Phys. Rev. Lett., 2005, 95(18): 180403

    Article  ADS  Google Scholar 

  38. H. Saito, Y. Kawaguchi, and M. Ueda, Phys. Rev. Lett., 2006, 96(6): 065302

    Article  ADS  Google Scholar 

  39. S. Murakami, N. Nagaosa, and S. C. Zhang, Phys. Rev. B, 2004, 69(23): 235206

    Article  ADS  Google Scholar 

  40. Y. J. Lin, R. L. Compton, A. R. Perry, W. D. Phillips, J. V. Porto, and I. B. Spielman, Phys. Rev. Lett., 2009, 102(13): 130401

    Article  ADS  Google Scholar 

  41. Y. J. Lin, R. L. Compton, K. Jiménez-García, W. D. Phillips, J. V. Porto, and I. B. Spielman, Nat. Phys., 2011, 7(7): 531

    Article  Google Scholar 

  42. Y. J. Lin, K. Jiménez-García, and I. B. Spielman, Nature, 2011, 471(7336): 83

    Article  ADS  Google Scholar 

  43. M. Aidelsburger, M. Atala, S. Nascimbene, S. Trotzky, Y. A. Chen, and I. Bloch, Phys. Rev. Lett., 2011, 107(25): 255301

    Article  ADS  Google Scholar 

  44. Z. Fu, P. Wang, S. Chai, L. Huang, and J. Zhang, Phys. Rev. A, 2011, 84(4): 043609

    Article  ADS  Google Scholar 

  45. D. L. Campbell, G. Juzeliūnas, and I. B. Spielman, Phys. Rev. A, 2011, 84(2): 025602

    Article  ADS  Google Scholar 

  46. T. D. Stanescu, B. Anderson, and V. Galitski, Phys. Rev. A, 2008, 78(2): 023616

    Article  ADS  Google Scholar 

  47. S. Gopalakrishnan, A. Lamacraft, and P. M. Goldbart, Phys. Rev. A, 2011, 84(6): 061604

    Article  ADS  Google Scholar 

  48. S. Sinha, R. Nath, and L. Santos, Phys. Rev. Lett., 2011, 107(27): 270401

    Article  Google Scholar 

  49. H. Hu, B. Ramachandhran, H. Pu, and X. J. Liu, Phys. Rev. Lett., 2012, 108(1): 010402

    Article  ADS  Google Scholar 

  50. J. Radić, T. A. Sedrakyan, I. B. Spielman, and V. Galitski, Phys. Rev. A, 2011, 84(6): 063604

    Article  ADS  Google Scholar 

  51. H. Hu and X. J. Liu, Phys. Rev. A, 2012, 85(1): 013619

    Article  ADS  Google Scholar 

  52. D. W. Zhang, Z. Y. Xue, H. Yan, Z. D. Wang, and S. L. Zhu, Phys. Rev. A, 2012, 85(1): 013628

    Article  ADS  Google Scholar 

  53. B. Ramachandhran, B. Opanchuk, X. J. Liu, H. Pu, P. D. Drummond, and H. Hu, Phys. Rev. A, 2012, 85(2): 023606

    Article  ADS  Google Scholar 

  54. R. Barnett, S. Powell, T. Grass, M. Lewenstein, and S. Das-Sarma, Phys. Rev. A, 2012, 85(2): 023615

    Article  ADS  Google Scholar 

  55. W. Zheng and Z. B. Li, Phys. Rev. A, 2012, 85(5): 053607

    Article  MathSciNet  ADS  Google Scholar 

  56. C. M. Jian and H. Zhai, Phys. Rev. B, 2011, 84(6): 060508

    Article  ADS  Google Scholar 

  57. Y. X. Du, H. Yan, D. W. Zhang, C. J. Shan, and S. L. Zhu, Phys. Rev. A, 2012, 85(4): 043619

    Article  ADS  Google Scholar 

  58. M. Merkl, A. Jacob, F. E. Zimmer, P. Öhberg, and L. Santos, Phys. Rev. Lett., 2010, 104(7): 073603

    Article  ADS  Google Scholar 

  59. Y. P. Zhang, L. Mao, and C. W. Zhang, Phys. Rev. Lett., 2012, 108(3): 035302

    Article  MathSciNet  ADS  Google Scholar 

  60. Y. Deng, J. Cheng, H. Jing, C. P. Sun, and S. Yi, Phys. Rev. Lett., 2012, 108(12): 125301

    Article  ADS  Google Scholar 

  61. X. Q. Xu and J. H. Han, Phys. Rev. Lett., 2011, 107(20): 200401

    Article  ADS  Google Scholar 

  62. X. F. Zhou, J. Zhou, and C. J. Wu, Phys. Rev. A, 2011, 84(6): 063624

    Article  ADS  Google Scholar 

  63. Z. F. Xu, R. Lü, and L. You, Phys. Rev. A, 2011, 83(5): 053602

    Article  ADS  Google Scholar 

  64. P. Wang, Z. Q. Yu, Z. Fu, J. Miao, L. Huang, S. Chai, H. Zhai, and J. Zhang, Phys. Rev. Lett., 2012, 109(9): 095301

    Article  ADS  Google Scholar 

  65. G. Juzeliūnas, J. Ruseckas, and J. Dalibard, Phys. Rev. A, 2010, 81(5): 053403

    Article  ADS  Google Scholar 

  66. T. L. Ho and S. Z. Zhang, Phys. Rev. Lett., 2011, 107(15): 150403

    Article  ADS  Google Scholar 

  67. C. J. Wang, C. Gao, C. M. Jian, and H. Zhai, Phys. Rev. Lett., 2010, 105(16): 160403

    Article  ADS  Google Scholar 

  68. S. K. Yip, Phys. Rev. A, 2011, 83(4): 043616

    Article  MathSciNet  ADS  Google Scholar 

  69. M. S. Chang, Q. S. Qin, W. X. Zhang, L. You, and M. S. Chapman, Nat. Phys., 2005, 1(2): 111

    Article  Google Scholar 

  70. K. Murata, H. Saito, and M. Ueda, Phys. Rev. A, 2007, 75(1): 013607

    Article  ADS  Google Scholar 

  71. L. Wen, Q. Sun, H. Q. Wang, A. C. Ji, and W. M. Liu, Phys. Rev. A, 2012, 86(4): 043602

    Article  ADS  Google Scholar 

  72. I. B. Mekhov, C. Maschler, and H. Ritsch, Nat. Phys., 2007, 3(5): 319

    Article  Google Scholar 

  73. S. Ashhab and A. J. Leggett, Phys. Rev. A, 2002, 65(2): 023604

    Article  ADS  Google Scholar 

  74. F. Brennecke, T. Donner, S. Ritter, T. Bourdel, M. Köhl, and T. Esslinger, Nature, 2007, 450(7167): 268

    Article  ADS  Google Scholar 

  75. Y. Colombe, T. Steinmetz, G. Dubois, F. Linke, D. Hunger, and J. Reichel, Nature, 2007, 450(7167): 272

    Article  ADS  Google Scholar 

  76. J. M. Zhang, S. Cui, H. Jing, D. L. Zhou, and W. M. Liu, Phys. Rev. A, 2009, 80(4): 043623

    Article  ADS  Google Scholar 

  77. J. Kronjäger, C. Becker, P. Navez, K. Bongs, and K. Sengstock, Phys. Rev. Lett., 2006, 97(11): 110404

    Article  ADS  Google Scholar 

  78. Z. W. Xie, W. Zhang, S. T. Chui, and W. M. Liu, Phys. Rev. A, 2004, 69(5): 053609

    Article  ADS  Google Scholar 

  79. H. Pu, W. P. Zhang, and P. Meystre, Phys. Rev. Lett., 2001, 87(14): 140405

    Article  ADS  Google Scholar 

  80. K. Cross, C. P. Search, H. Pu, W. P. Zhang, and P. Meystre, Phys. Rev. Lett., 2002, 88: 033603

    Google Scholar 

  81. W. Zhang, H. Pu, C. P. Search, and P. Meystre, Phys. Rev. Lett., 2002, 88(6): 060401

    Article  ADS  Google Scholar 

  82. D. I. Pushkarov and Kh. I. Pushkarov, Phys. Lett. A, 1977, 61(5): 339

    Article  ADS  Google Scholar 

  83. V. V. Konotop, M. Salerno, and S. Takeno, Phys. Rev. E, 1997, 56(6): 7240

    Article  ADS  Google Scholar 

  84. T. Bergeman, M. G. Moore, and M. Olshanii, Phys. Rev. Lett., 2003, 91(16): 163201

    Article  ADS  Google Scholar 

  85. M. Olshanii, Phys. Rev. Lett., 1998, 81(5): 938

    Article  ADS  Google Scholar 

  86. C. Becker, S. Stellmer, P. Soltan-Panahi, S. Dörscher, M. Baumert, E. Richter, J. Kronjäger, K. Bongs, and K. Sengstock, Nat. Phys., 2008, 4(6): 496

    Article  Google Scholar 

  87. A. Weller, J. P. Ronzheimer, C. Gross, J. Esteve, M. K. Oberthaler, G. Theocharis, and P. G. Kevrekidis, Phys. Rev. Lett., 2008, 101(13): 130401

    Article  ADS  Google Scholar 

  88. G. X. Huang, V. A. Makarov, and M. G. Velarde, Phys. Rev. A, 2003, 67(2): 023604

    Article  ADS  Google Scholar 

  89. Y. S. Kivshar and X. Yang, Phys. Rev. E, 1994, 50(1): R40

    Article  MathSciNet  ADS  Google Scholar 

  90. H. E. Nistazakis, D. J. Frantzeskakis, B. A. Malomed, and P. G. Kevrekidis, Phys. Lett. A, 2001, 285(3–4): 157

    Article  ADS  MATH  Google Scholar 

  91. A. Dreischuh, D. Neshev, G. G. Paulus, F. Grasbon, and H. Walther, Phys. Rev. E, 2002, 66(6): 066611

    Article  ADS  Google Scholar 

  92. S. W. Song, D. S. Wang, H. Wang, and W. M. Liu, Phys. Rev. A, 2012, 85(6): 063617

    Article  MathSciNet  ADS  Google Scholar 

  93. L. Dobrek, M. Gajda, M. Lewenstein, K. Sengstock, G. Birkl, and W. Ertmer, Phys. Rev. A, 1999, 60(5): R3381

    Article  ADS  Google Scholar 

  94. J. Denschlag, J. E. Simsarian, D. L. Feder, C. W. Clark, L. A. Collins, J. Cubizolles, L. Deng, E. W. Hagley, K. Helmerson, W. P. Reinhardt, S. L. Rolston, B. I. Schneider, and W. D. Phillips, Science, 2000, 287(5450): 97

    Article  ADS  Google Scholar 

  95. Z. Dutton, M. Budde, C. Slowe, and L. V. Hau, Science, 2001, 293(5530): 663

    Article  ADS  Google Scholar 

  96. N. S. Ginsberg, J. Brand, and L. V. Hau, Phys. Rev. Lett., 2005, 94(4): 040403

    Article  ADS  Google Scholar 

  97. I. Shomroni, E. Lahoud, S. Levy, and J. Steinhauer, Nat. Phys., 2009, 5(3): 193

    Article  Google Scholar 

  98. K. C. Wright, L. S. Leslie, A. Hansen, and N. P. Bigelow, Phys. Rev. Lett., 2009, 102(3): 030405

    Article  ADS  Google Scholar 

  99. X. H. Hu, X. F. Zhang, D. Zhao, H. G. Luo, and W. M. Liu, Phys. Rev. A, 2009, 79(2): 023619

    Article  ADS  Google Scholar 

  100. G. Theocharis, D. J. Frantzeskakis, P. G. Kevrekidis, B. A. Malomed, and Y. S. Kivshar, Phys. Rev. Lett., 2003, 90(12): 120403

    Article  ADS  Google Scholar 

  101. X. F. Zhang, X. H. Hu, D. S. Wang, X. X. Liu, and W. M. Liu, Front. Phys., 2011, 6(1): 46

    Article  Google Scholar 

  102. V. V. Konotop and L. Pitaevskii, Phys. Rev. Lett., 2004, 93(24): 240403

    Article  ADS  Google Scholar 

  103. L. P. Pitaevskii and E. M. Lifshitz, Statistical Physics (part 2), 3rd Ed., Oxford: Pergamon, 1980, section 29

    Google Scholar 

  104. S. Inouye, M. Andrews, J. Stenger, H. Miesner, D. Stamper-Kurn, and W. Ketterle, Nature, 1998, 392: 151

    Article  ADS  Google Scholar 

  105. C. Chin, R. Grimm, P. Julienne, and E. Tiesinga, Rev. Mod. Phys., 1998, 70: 1003

    Article  Google Scholar 

  106. S. W. Su, I. K. Liu, Y. C. Tsai, W. M. Liu, and S. C. Gou, Phys. Rev. A, 2012, 86(2): 023601

    Article  ADS  Google Scholar 

  107. C. F. Liu and W. M. Liu, Phys. Rev. A, 2012, 86(3): 033602

    Article  ADS  Google Scholar 

  108. A. Y. Cherny, J. S. Caux, and J. Brand, Front. Phys., 2012, 7(1): 54

    Article  Google Scholar 

  109. T. L. Horng, C. H. Hsueh, S. W. Su, Y. M. Kao, and S. C. Gou, Phys. Rev. A, 2009, 80(2): 023618

    Article  ADS  Google Scholar 

  110. U. K. Rößler, A. N. Bogdanov, and C. Pfleiderer, Nature, 2006, 442(7104): 797

    Article  ADS  Google Scholar 

  111. S. Mühlbauer, B. Binz, F. Jonietz, C. Pfleiderer, A. Rosch, A. Neubauer, R. Georgii, and P. Boni, Science, 2009, 323(5916): 915

    Article  ADS  Google Scholar 

  112. X. Z. Yu, Y. Onose, N. Kanazawa, J. H. Park, J. H. Han, Y. Matsui, N. Nagaosa, and Y. Tokura, Nature, 2010, 465(7300): 901

    Article  ADS  Google Scholar 

  113. D. A. Ivanov, Phys. Rev. Lett., 2001, 86(2): 268

    Article  ADS  Google Scholar 

  114. A. Actor, Rev. Mod. Phys., 1979, 51(3): 461

    Article  MathSciNet  ADS  Google Scholar 

  115. L. Brey, H. A. Fertig, R. Cote, and A. H. MacDonald, Phys. Rev. B, 1996, 54(23): 16888

    Article  ADS  Google Scholar 

  116. G. E. Brown and M. Rho, The Multifaced Skyrmion, Singapore: World Scientific, 2010

    Book  Google Scholar 

  117. V. M. H. Ruutu, J. Kopu, M. Krusius, U. Parts, B. Placais, E. V. Thuneberg, and W. Xu, Phys. Rev. Lett., 1997, 79(25): 5058

    Article  ADS  Google Scholar 

  118. R. Ishiguro, O. Ishikawa, M. Yamashita, Y. Sasaki, K. Fukuda, M. Kubota, H. Ishimoto, R. Packard, T. Takagi, T. Ohmi, and T. Mizusaki, Phys. Rev. Lett., 2004, 93(12): 125301

    Article  ADS  Google Scholar 

  119. A. E. Leanhardt, Y. Shin, D. Kielpinski, D. E. Pritchard, and W. Ketterle, Phys. Rev. Lett., 2003, 90(14): 140403

    Article  ADS  Google Scholar 

  120. T. Mizushima, K. Machida, and T. Kita, Phys. Rev. A, 2002, 66(5): 053610

    Article  ADS  Google Scholar 

  121. T. Kita, T. Mizushima, and K. Machida, Phys. Rev. A, 2002, 66: 061601(R)

    Article  ADS  Google Scholar 

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Song, SW., Wen, L., Liu, CF. et al. Ground states, solitons and spin textures in spin-1 Bose-Einstein condensates. Front. Phys. 8, 302–318 (2013). https://doi.org/10.1007/s11467-013-0350-8

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