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

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.

Keywords

Bose–Einstein condensate / spinor / vortex lattice / soliton / spin–orbit coupling

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

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

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

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

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

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

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

[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

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

[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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[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

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

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

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

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

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

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

[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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[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

[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

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

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

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

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

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

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

[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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[110] U. K. Röβer, A. N. Bogdanov, and C. P.eiderer, Nature, 2006, 442(7104): 797

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

[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

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

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

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

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

[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

[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

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

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

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

RIGHTS & PERMISSIONS

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg