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

doi:10.1007/s11467-013-0350-8

Front. Phys.

2013, Vol. 8

Issue (3) : 302-318 https://doi.org/10.1007/s11467-013-0350-8

REVIEW ARTICLE

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

Shu-Wei Song¹, Lin Wen¹, Chao-Fei Liu², S.-C. Gou³, Wu-Ming Liu¹(

)

1. Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China; 2. School of Science, Jiangxi University of Science and Technology, Ganzhou 341000, China; 3. Department of Physics, National Changhua University of Education, Changhua 50058, Taiwan, China

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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.

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

Corresponding Author(s): Liu Wu-Ming,Email:mliu@aphy.iphy.ac.cn

Issue Date: 01 June 2013

Cite this article:

Shu-Wei Song,Lin Wen,Chao-Fei Liu, et al. Ground states, solitons and spin textures in spin-1 Bose–Einstein condensates[J]. Front. Phys. , 2013, 8(3): 302-318.

URL:

https://academic.hep.com.cn/fop/EN/10.1007/s11467-013-0350-8
https://academic.hep.com.cn/fop/EN/Y2013/V8/I3/302

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 doi: 10.1103/PhysRevLett.80.2027
2	T. Ohmi and K. Machida, J. Phys. Soc. Jpn. , 1998, 67(6): 1822 doi: 10.1143/JPSJ.67.1822
3	T. L. Ho, Phys. Rev. Lett. , 1998, 81(4): 742 doi: 10.1103/PhysRevLett.81.742
4	J. Stenger, S. Inouye, D. M. Stamper-Kurn, H. J. Miesner, P. Chikkatur, and W. Ketterle, Nature , 1998, 396(6709): 345 doi: 10.1038/24567
5	C. K. Law, H. Pu, and N. P. Bigelow, Phys. Rev. Lett. , 1998, 81(24): 5257 doi: 10.1103/PhysRevLett.81.5257
6	M. Koashi and M. Ueda, Phys. Rev. Lett. , 2000, 84(6): 1066 doi: 10.1103/PhysRevLett.84.1066
7	T. L. Ho and L. Yin, Phys. Rev. Lett. , 2000, 84(11): 2302 doi: 10.1103/PhysRevLett.84.2302
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 doi: 10.1103/PhysRevLett.82.2228
9	H. Pu, C. K. Law, S. Raghavan, J. H. Eberly, and N. P. Bigelow, Phys. Rev. A , 1999, 60(2): 1463 doi: 10.1103/PhysRevA.60.1463
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 doi: 10.1103/PhysRevLett.92.140403
11	A. Widera, F. Gerbier, S. F?lling, T. Gericke, O. Mandel, and I. Bloch, New J. Phys. , 2006, 8(8): 152 doi: 10.1088/1367-2630/8/8/152
12	N. Klausen, J. Bohn, and C. Greene, Phys. Rev. A , 2001, 64(5): 053602 doi: 10.1103/PhysRevA.64.053602
13	F. Zhou, Phys. Rev. Lett. , 2001, 87(8): 080401 doi: 10.1103/PhysRevLett.87.080401
14	G. W. Semenoff and F. Zhou, Phys. Rev. Lett. , 2007, 98(10): 100401 doi: 10.1103/PhysRevLett.98.100401
15	T. Isoshima, K. Machida, and T. Ohmi, J. Phys. Soc. Jpn. , 2001, 70(6): 1604 doi: 10.1143/JPSJ.70.1604
16	T. Mizushima, K. Machida, and T. Kita, Phys. Rev. Lett. , 2002, 89(3): 030401 doi: 10.1103/PhysRevLett.89.030401
17	U. Leonhardt and G. E. Volovik, JETP Lett. , 2000, 72(2): 46 doi: 10.1134/1.1312008
18	T. Isoshima and K. Machida, Phys. Rev. A , 2002, 66(2): 023602 doi: 10.1103/PhysRevA.66.023602
20	H. T. C. Stoof, E. Vliegen, and U. Al Khawaja, Phys. Rev. Lett. , 2001, 87(12): 120407 doi: 10.1103/PhysRevLett.87.120407
21	J. Ruostekoski and J. R. Anglin, Phys. Rev. Lett. , 2003, 91(19): 190402 doi: 10.1103/PhysRevLett.91.190402
22	J. Ieda, T. Miyakawa, and M. Wadati, Phys. Rev. Lett. , 2004, 93(19): 194102 doi: 10.1103/PhysRevLett.93.194102
23	E. V. Doktorov, J. Wang, and J. Yang, Phys. Rev. A , 2008, 77(4): 043617 doi: 10.1103/PhysRevA.77.043617
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 doi: 10.1103/PhysRevA.77.033612
25	M. Ueda and Y. Kawaguchi, Phys. Rep. , 2012, 520: 253 doi: 10.1016/j.physrep.2012.07.005
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 doi: 10.1103/PhysRevA.77.033616
28	S. J. Rooney, A. S. Bradley, and P. B. Blakie, Phys. Rev. A , 2010, 81(2): 023630 doi: 10.1103/PhysRevA.81.023630
29	S. J. Rooney, P. B. Blakie, B. P. Anderson, and A. S. Bradley, Phys. Rev. A , 2011, 84(2): 023637 doi: 10.1103/PhysRevA.84.023637
30	A. Sinatra, C. Lobo, and Y. Castin, J. Phys. B , 2002, 35(17): 3599 doi: 10.1088/0953-4075/35/17/301
31	C. W. Gardiner and P. Zoller, Phys. Rev. A , 1998, 58(1): 1050 doi: 10.1103/PhysRevA.58.536
32	C. W. Gardiner and P. Zoller, Phys. Rev. A , 2000, 61(3): 033601 doi: 10.1103/PhysRevA.61.033601
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 doi: 10.1103/PhysRevA.84.023601
34	Y. Hao, Y. Zhang, J. Q. Liang, and S. Chen, Phys. Rev. A , 2006, 73(5): 053605 doi: 10.1103/PhysRevA.73.053605
35	L. Li, Z. Li, B. A. Malomed, D. Mihalache, and W. M. Liu, Phys. Rev. A , 2005, 72(3): 033611 doi: 10.1103/PhysRevA.72.033611
36	N. P. Robins, W. Zhang, E. A. Ostrovskaya, and Y. S. Kivshar, Phys. Rev. A , 2001, 64(2): 021601 doi: 10.1103/PhysRevA.64.021601
37	W. Zhang, D. L. Zhou, M. S. Chang, M. S. Chapman, and L. You, Phys. Rev. Lett. , 2005, 95(18): 180403 doi: 10.1103/PhysRevLett.95.180403
38	H. Saito, Y. Kawaguchi, and M. Ueda, Phys. Rev. Lett. , 2006, 96(6): 065302 doi: 10.1103/PhysRevLett.96.065302
39	S. Murakami, N. Nagaosa, and S. C. Zhang, Phys. Rev. B , 2004, 69(23): 235206 doi: 10.1103/PhysRevB.69.235206
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 doi: 10.1103/PhysRevLett.102.130401
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 doi: 10.1038/nphys1954
42	Y. J. Lin, K. Jiménez-Garíc, and I. B. Spielman, Nature , 2011, 471(7336): 83 doi: 10.1038/nature09887
43	M. Aidelsburger, M. Atala, S. Nascimbene, S. Trotzky, Y. A. Chen, and I. Bloch, Phys. Rev. Lett. , 2011, 107(25): 255301 doi: 10.1103/PhysRevLett.107.255301
44	Z. Fu, P. Wang, S. Chai, L. Huang, and J. Zhang, Phys. Rev. A , 2011, 84(4): 043609 doi: 10.1103/PhysRevA.84.043609
45	D. L. Campbell, G. Juzeliūnas, and I. B. Spielman, Phys. Rev. A , 2011, 84(2): 025602 doi: 10.1103/PhysRevA.84.025602
46	T. D. Stanescu, B. Anderson, and V. Galitski, Phys. Rev. A , 2008, 78(2): 023616 doi: 10.1103/PhysRevA.78.023616
47	S. Gopalakrishnan, A. Lamacraft, and P. M. Goldbart, Phys. Rev. A , 2011, 84(6): 061604 doi: 10.1103/PhysRevA.84.061604
48	S. Sinha, R. Nath, and L. Santos, Phys. Rev. Lett. , 2011, 107(27): 270401 doi: 10.1103/PhysRevLett.107.270401
49	H. Hu, B. Ramachandhran, H. Pu, and X. J. Liu, Phys. Rev. Lett. , 2012, 108(1): 010402 doi: 10.1103/PhysRevLett.108.010402
50	J. Radi?, T. A. Sedrakyan, I. B. Spielman, and V. Galitski, Phys. Rev. A , 2011, 84(6): 063604 doi: 10.1103/PhysRevA.84.063604
51	H. Hu and X. J. Liu, Phys. Rev. A , 2012, 85(1): 013619 doi: 10.1103/PhysRevA.85.013619
52	D. W. Zhang, Z. Y. Xue, H. Yan, Z. D. Wang, and S. L. Zhu, Phys. Rev. A , 2012, 85(1): 013628 doi: 10.1103/PhysRevA.85.013628
53	B. Ramachandhran, B. Opanchuk, X. J. Liu, H. Pu, P. D. Drummond, and H. Hu, Phys. Rev. A , 2012, 85(2): 023606 doi: 10.1103/PhysRevA.85.023606
54	R. Barnett, S. Powell, T. Grass, M. Lewenstein, and S. Das-Sarma, Phys. Rev. A , 2012, 85(2): 023615 doi: 10.1103/PhysRevA.85.023615
55	W. Zheng and Z. B. Li, Phys. Rev. A , 2012, 85(5): 053607 doi: 10.1103/PhysRevA.85.053607
56	C. M. Jian and H. Zhai, Phys. Rev. B , 2011, 84(6): 060508 doi: 10.1103/PhysRevB.84.060508
57	Y. X. Du, H. Yan, D. W. Zhang, C. J. Shan, and S. L. Zhu, Phys. Rev. A , 2012, 85(4): 043619 doi: 10.1103/PhysRevA.85.043619
58	M. Merkl, A. Jacob, F. E. Zimmer, P. ?hberg, and L. Santos, Phys. Rev. Lett. , 2010, 104(7): 073603 doi: 10.1103/PhysRevLett.104.073603
59	Y. P. Zhang, L. Mao, and C. W. Zhang, Phys. Rev. Lett. , 2012, 108(3): 035302 doi: 10.1103/PhysRevLett.108.035302
60	Y. Deng, J. Cheng, H. Jing, C. P. Sun, and S. Yi, Phys. Rev. Lett. , 2012, 108(12): 125301 doi: 10.1103/PhysRevLett.108.125301
61	X. Q. Xu and J. H. Han, Phys. Rev. Lett. , 2011, 107(20): 200401 doi: 10.1103/PhysRevLett.107.200401
62	X. F. Zhou, J. Zhou, and C. J. Wu, Phys. Rev. A , 2011, 84(6): 063624 doi: 10.1103/PhysRevA.84.063624
63	Z. F. Xu, R. Lü, and L. You, Phys. Rev. A , 2011, 83(5): 053602 doi: 10.1103/PhysRevA.83.053602
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 doi: 10.1103/PhysRevLett.109.095301
65	G. Juzeliūnas, J. Ruseckas, and J. Dalibard, Phys. Rev. A , 2010, 81(5): 053403 doi: 10.1103/PhysRevA.81.053403
66	T. L. Ho and S. Z. Zhang, Phys. Rev. Lett. , 2011, 107(15): 150403 doi: 10.1103/PhysRevLett.107.150403
67	C. J. Wang, C. Gao, C. M. Jian, and H. Zhai, Phys. Rev. Lett. , 2010, 105(16): 160403 doi: 10.1103/PhysRevLett.105.160403
68	S. K. Yip, Phys. Rev. A , 2011, 83(4): 043616 doi: 10.1103/PhysRevA.83.043616
69	M. S. Chang, Q. S. Qin, W. X. Zhang, L. You, and M. S. Chapman, Nat. Phys. , 2005, 1(2): 111 doi: 10.1038/nphys153
70	K. Murata, H. Saito, and M. Ueda, Phys. Rev. A , 2007, 75(1): 013607 doi: 10.1103/PhysRevA.75.013607
71	L. Wen, Q. Sun, H. Q. Wang, A. C. Ji, and W. M. Liu, Phys. Rev. A , 2012, 86(4): 043602 doi: 10.1103/PhysRevA.86.043602
72	I. B. Mekhov, C. Maschler, and H. Ritsch, Nat. Phys. , 2007, 3(5): 319 doi: 10.1038/nphys571
73	S. Ashhab and A. J. Leggett, Phys. Rev. A , 2002, 65(2): 023604 doi: 10.1103/PhysRevA.65.023604
74	F. Brennecke, T. Donner, S. Ritter, T. Bourdel, M. K?hl, and T. Esslinger, Nature , 2007, 450(7167): 268 doi: 10.1038/nature06120
75	Y. Colombe, T. Steinmetz, G. ubois, F. Linke, D. Hunger, and J. Reichel, Nature , 2007, 450(7167): 272 doi: 10.1038/nature06331
76	J. M. Zhang, S. Cui, H. Jing, D. L. Zhou, and W. M. Liu, Phys. Rev. A , 2009, 80(4): 043623 doi: 10.1103/PhysRevA.80.043623
77	J. Kronj?ger, C. Becker, P. Navez, K. Bongs, and K. Sengstock, Phys. Rev. Lett. , 2006, 97(11): 110404 doi: 10.1103/PhysRevLett.97.110404
78	Z. W. Xie, W. Zhang, S. T. Chui, and W. M. Liu, Phys. Rev. A , 2004, 69(5): 053609 doi: 10.1103/PhysRevA.69.053609
79	H. Pu, W. P. Zhang, and P. Meystre, Phys . Rev. Lett. , 2001, 87(14): 140405 doi: 10.1103/PhysRevLett.87.140405
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 doi: 10.1103/PhysRevLett.88.060401
82	D. I. Pushkarov and Kh. I. Pushkarov, Phys. Lett. A , 1977, 61(5): 339 doi: 10.1016/0375-9601(77)90635-1
83	V. V. Konotop, M. Salerno, and S. Takeno, Phys. Rev. E , 1997, 56(6): 7240 doi: 10.1103/PhysRevE.56.7240
84	T. Bergeman, M. G. Moore, and M. Olshanii, Phys. Rev. Lett. , 2003, 91(16): 163201 doi: 10.1103/PhysRevLett.91.163201
85	M. Olshanii, Phys. Rev. Lett. , 1998, 81(5): 938 doi: 10.1103/PhysRevLett.81.938
86	C. Becker, S. Stellmer, P. Soltan-Panahi, S. D?rscher, M. Baumert, E. Richter, J. Kronj?ger, K. Bongs, and K. Sengstock, Nat. Phys. , 2008, 4(6): 496 doi: 10.1038/nphys962
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 doi: 10.1103/PhysRevLett.101.130401
88	G. X. Huang, V. A. Makarov, and M. G. Velarde, Phys. Rev. A , 2003, 67(2): 023604 doi: 10.1103/PhysRevA.67.023604
89	Y. S. Kivshar and X. Yang, Phys. Rev. E , 1994, 50(1): R40 doi: 10.1103/PhysRevE.50.R40
90	H. E. Nistazakis, D. J. Frantzeskakis, B. A. Malomed, and P. G. Kevrekidis, Phys. Lett. A , 2001, 285(3–4): 157 doi: 10.1016/S0375-9601(01)00320-6
91	A. Dreischuh, D. Neshev, G. G. Paulus, F. Grasbon, and H. Walther, Phys. Rev. E , 2002, 66(6): 066611 doi: 10.1103/PhysRevE.66.066611
92	S. W. Song, D. S. Wang, H. Wang, and W. M. Liu, Phys. Rev. A , 2012, 85(6): 063617 doi: 10.1103/PhysRevA.85.063617
93	L. Dobrek, M. Gajda, M. Lewenstein, K. Sengstock, G. Birkl, and W. Ertmer, Phys. Rev. A , 1999, 60(5): R3381 doi: 10.1103/PhysRevA.60.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 doi: 10.1126/science.287.5450.97
95	Z. Dutton, M. Budde, C. Slowe, and L. V. Hau, Science , 2001, 293(5530): 663 doi: 10.1126/science.1062527
96	N. S. Ginsberg, J. Brand, and L. V. Hau, Phys. Rev. Lett. , 2005, 94(4): 040403 doi: 10.1103/PhysRevLett.94.040403
97	I. Shomroni, E. Lahoud, S. Levy, and J. Steinhauer, Nat. Phys. , 2009, 5(3): 193 doi: 10.1038/nphys1177
98	K. C. Wright, L. S. Leslie, A. Hansen, and N. P. Bigelow, Phys. Rev. Lett. , 2009, 102(3): 030405 doi: 10.1103/PhysRevLett.102.030405
99	X. H. Hu, X. F. Zhang, D. Zhao, H. G. Luo, and W. M. Liu, Phys. Rev. A , 2009, 79(2): 023619 doi: 10.1103/PhysRevA.79.023619
100	G. Theocharis, D. J. Frantzeskakis, P. G. Kevrekidis, B. A. Malomed, and Y. S. Kivshar, Phys. Rev. Lett. , 2003, 90(12): 120403 doi: 10.1103/PhysRevLett.90.120403
101	X. F. Zhang, X. H. Hu, D. S. Wang, X. X. Liu, and W. M. Liu, Front. Phys. , 2011, 6(1): 46 doi: 10.1007/s11467-010-0150-3
102	V. V. Konotop and L. Pitaevskii, Phys. Rev. Lett. , 2004, 93(24): 240403 doi: 10.1103/PhysRevLett.93.240403
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 doi: 10.1038/32354
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 doi: 10.1103/PhysRevA.86.023601
107	C. F. Liu and W. M. Liu, Phys. Rev. A , 2012, 86(3): 033602 doi: 10.1103/PhysRevA.86.033602
108	A. Y. Cherny, J. S. Caux, and J. Brand, Front. Phys. , 2012, 7(1): 54 doi: 10.1007/s11467-011-0211-2
109	T. L. Horng, C. H. Hsueh, S. W. Su, Y. M. Kao, and S. C. Gou, Phys. Rev. A , 2009, 80(2): 023618 doi: 10.1103/PhysRevA.80.023618
110	U. K. R?βer, A. N. Bogdanov, and C. P.eiderer, Nature , 2006, 442(7104): 797 doi: 10.1038/nature05056
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 doi: 10.1038/nature09124
113	D. A. Ivanov, Phys. Rev. Lett. , 2001, 86(2): 268 doi: 10.1103/PhysRevLett.86.268
114	A. Actor, Rev. Mod. Phys. , 1979, 51(3): 461 doi: 10.1103/RevModPhys.51.461
115	L. Brey, H. A. Fertig, R. Cote, and A. H. MacDonald, Phys. Rev. B , 1996, 54(23): 16888 doi: 10.1103/PhysRevB.54.16888
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 doi: 10.1103/PhysRevLett.79.5058
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 doi: 10.1103/PhysRevLett.93.125301
119	A. E. Leanhardt, Y. Shin, D. Kielpinski, D. E. Pritchard, and W. Ketterle, Phys. Rev. Lett. , 2003, 90(14): 140403 doi: 10.1103/PhysRevLett.90.140403
120	T. Mizushima, K. Machida, and T. Kita, Phys. Rev. A , 2002, 66(5): 053610 doi: 10.1103/PhysRevA.66.053610
121	T. Kita, T. Mizushima, and K. Machida, Phys. Rev. A , 2002, 66: 061601(R) doi: 10.1103/PhysRevA.66.061601

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[10]	Yu-Ren Shi (石玉仁), Xue-Ling Wang (王雪玲), Guang-Hui Wang (王光辉), Cong-Bo Liu (刘丛波), Zhi-Gang Zhou (周志刚), Hong-Juan Yang(杨红娟). Analytical solutions for the spin-1 Bose–Einstein condensate in a harmonic trap[J]. Front. Phys. , 2013, 8(3): 319-327.
[11]	Na Zhang, Shuai Dong, Jun-Ming Liu. Ferroelectricity generated by spin–orbit and spin–lattice couplings in multiferroic DyMnO₃[J]. Front. Phys. , 2012, 7(4): 408-417.
[12]	Yao-hua Chen, Wei Wu, Guo-cai Liu, Hong-shuai Tao, Wu-ming Liu. Quantum phase transition of cold atoms trapped in optical lattices[J]. Front. Phys. , 2012, 7(2): 223-234.
[13]	Yong-qing Li, Ke-hui Wu, Jun-ren Shi, Xin-cheng Xie. Electron transport properties of three-dimensional topological insulators[J]. Front. Phys. , 2012, 7(2): 165-174.
[14]	Margaret D. Reid, Qiong-Yi He, Peter D. Drummond. Entanglement and nonlocality in multi-particle systems[J]. Front. Phys. , 2012, 7(1): 72-85.
[15]	Alice Sinatra, Jean-Christophe Dornstetter, Yvan Castin. Spin squeezing in Bose–Einstein condensates: Limits imposed by decoherence and non-zero temperature[J]. Front. Phys. , 2012, 7(1): 86-97.

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