Dynamics of Bose–Einstein condensates near Feshbach resonance in external potential

doi:10.1007/s11467-010-0150-3

Front. Phys.

2011, Vol. 6

Issue (1) : 46-60 https://doi.org/10.1007/s11467-010-0150-3

REVIEW ARTICLE

Dynamics of Bose–Einstein condensates near Feshbach resonance in external potential

Xiao-fei ZHANG (张晓斐)^1,2, Xing-hua HU (胡兴华)¹, Deng-shan WANG (王灯山)¹, Xun-xu LIU (刘循序)¹, Wu-ming LIU (刘伍明)¹(

)

1. Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China; 2. College of Science, Honghe University, Mengzi 661100, China

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Abstract

We review our recent theoretical advances in the dynamics of Bose–Einstein condensates with tunable interactions using Feshbach resonance and external potential. A set of analytic and numerical methods for Gross–Pitaevskii equations are developed to study the nonlinear dynamics of Bose– Einstein condensates. Analytically, we present the integrable conditions for the Gross–Pitaevskii equations with tunable interactions and external potential, and obtain a family of exact analytical solutions for one- and two-component Bose–Einstein condensates in one and two-dimensional cases. Then we apply these models to investigate the dynamics of solitons and collisions between two solitons. Numerically, the stability of the analytic exact solutions are checked and the phenomena, such as the dynamics and modulation of the ring dark soliton and vector-soliton, soliton conversion via Feshbach resonance, quantized soliton and vortex in quasi-two-dimensional are also investigated. Both the exact and numerical solutions show that the dynamics of Bose–Einstein condensates can be effectively controlled by the Feshbach resonance and external potential, which offer a good opportunity for manipulation of atomic matter waves and nonlinear excitations in Bose–Einstein condensates.

Keywords Bose–Einstein condensate Feshbach resonance soliton

Corresponding Author(s): null,Email:zr12345@163.com, wmliu@aphy.iphy.ac.cn

Issue Date: 05 March 2011

Cite this article:

Xiao-fei ZHANG (张晓斐),Xing-hua HU (胡兴华),Deng-shan WANG (王灯山), et al. Dynamics of Bose–Einstein condensates near Feshbach resonance in external potential[J]. Front. Phys. , 2011, 6(1): 46-60.

URL:

https://academic.hep.com.cn/fop/EN/10.1007/s11467-010-0150-3
https://academic.hep.com.cn/fop/EN/Y2011/V6/I1/46

1	M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E.Wieman, and E. A. Cornell, Science , 1995, 269: 198 doi: 10.1126/science.269.5221.198
2	F. Dalfovo, S. Giorgini, L. P. Pitaevskii, and S. Stringari, Rev. Mod. Phys ., 1999, 71: 463 doi: 10.1103/RevModPhys.71.463
3	P. G. Drazin and R. S. Johnson, Solitons: An Introduction, Cambridge: Cambridge University Press , 1989
4	K. E. Strecker, G. B. Partridge, A. G. Truscoff, and R. G. Hulet, Nature (London) , 2002, 417: 150 doi: 10.1038/nature747
5	L. Khaykovich, F. Schreck, G. Ferrari, T. Bourdel, J. Cubizolles, L. D. Carr, Y. Castin, and C. Salomon, Science , 2002, 296: 1290 doi: 10.1126/science.1071021
6	C. Becker, S. Stellmer, P. Soltan-Panahi, S. D?orscher, M. Baumert, Eva-MariaRichter, JochenKronj?ager, K. Bongs, and K. Sengstock, Nature Phys ., 2008, 4: 496 doi: 10.1038/nphys962
7	B. Eiermann, Th. Anker, M. Albiez, M. Taglieber, P. Treutlein, K. P. Marzlin, and M. K. Oberthaler, Phys. Rev. Lett ., 2004, 92: 230401 doi: 10.1103/PhysRevLett.92.230401
8	D. L. Wang, X. H. Yan, and W. M. Liu, Phys. Rev. E , 2008, 78: 026606 doi: 10.1103/PhysRevE.78.026606
9	Z. W. Xie, W. P. Zhang, S. T. Chui, and W. M. Liu, Phys. Rev. A , 2004, 69: 053609 doi: 10.1103/PhysRevA.69.053609
10	Z. W. Xie, Z. X. Cao, E. I. Kats, and W. M. Liu, Phys. Rev. A , 2005, 71: 025601 doi: 10.1103/PhysRevA.71.025601
11	Z. D. Li and Q. Y. Li, Ann. Phys. (New York) , 2007, 322: 1961 doi: 10.1016/j.aop.2006.11.004
12	Q. Y. Li and Z. D. Li, Opt. Commun. , 2010, 283: 3361 doi: 10.1016/j.optcom.2010.04.039
13	A. J. Moerdijk, B. J. Verhaar, and A. Axelsson, Phys. Rev. A , 1995, 51: 4852 doi: 10.1103/PhysRevA.51.4852
14	J. L. Roberts, N. R. Claussen, James P. Burke, Jr., C. H. Greene, E. A. Cornell, and C. E.Wieman, Phys. Rev. Lett ., 1998, 81: 5109 doi: 10.1103/PhysRevLett.81.5109
15	J. Stenger, S. Inouye, M. R. Andrews, H. -J. Miesner, D. M. Stamper-Kurn, and W. Ketterle, Phys. Rev. Lett ., 1999, 82: 2422 doi: 10.1103/PhysRevLett.82.2422
16	S. Inouye, M. R. Andrews, J. Stenger, H. -J. Miesner, D. M. Stamper-Kurn, and W. Ketterle, Nature , 1998, 392: 151 doi: 10.1038/32354
17	S. L. Cornish, N. R. Claussen, J. L. Roberts, E. A. Cornell, and C. E. Wieman, Phys. Rev. Lett ., 2000, 85: 1795 doi: 10.1103/PhysRevLett.85.1795
18	E. A. Donley, N. R. Claussen, S. L. Cornish, J. L. Roberts, E. A. Cornell, and C. E. Wieman, Nature (London) , 2001, 412: 295 doi: 10.1038/35085500
19	C. A. Regal and D. S. Jin, Phys. Rev. Lett ., 2003, 90: 230404 doi: 10.1103/PhysRevLett.90.230404
20	T. Volz, S. Dürr, S. Ernst, A. Marte, and G. Rempe, Phys. Rev. A , 2003, 68: 010702 doi: 10.1103/PhysRevA.68.010702
21	F. K. Abdullaev, A. M. Kamchatnov, V. V. Konotop, and V. A. Brazhnyi, Phys. Rev. Lett ., 2003, 90: 230402 doi: 10.1103/PhysRevLett.90.230402
22	V. M. Péerez-García, V. V. Konotop, and V. A. Brazhnyi, Phys. Rev. Lett ., 2004, 92: 220403 doi: 10.1103/PhysRevLett.92.220403
23	Z. X. Liang, Z. D. Zhang, and W. M. Liu, Phys. Rev. Lett ., 2005, 94: 050402 doi: 10.1103/PhysRevLett.94.050402
24	H. Saito and M. Ueda, Phys. Rev. Lett ., 2003, 90: 040403 doi: 10.1103/PhysRevLett.90.040403
25	D. E. Pelinovsky, P. G. Kevrekidis, and D. J. Frantzeskakis, Phys. Rev. Lett ., 2003, 91: 240201 doi: 10.1103/PhysRevLett.91.240201
26	G. D. Montesinos, H. Michinel, and V. M. Perez-Garcia, Phys. Rev. Lett ., 2004, 92: 133901 doi: 10.1103/PhysRevLett.92.133901
27	V. V. Konotop and P. Pacciani, Phys. Rev. Lett ., 2005, 94: 240405 doi: 10.1103/PhysRevLett.94.240405
28	G. Thalhammer, G. Barontini, L. De Sarlo, J. Catani, F. Minardi, and M. Inguscio, Phys. Rev. Lett ., 2008, 100: 210402 doi: 10.1103/PhysRevLett.100.210402
29	H. W. Xiong, S. J. Liu, W. P. Zhang, and M. S. Zhan, Phys. Rev. Lett ., 2005, 95: 120401 doi: 10.1103/PhysRevLett.95.120401
30	C. J. Myatt, E. A. Burt, R. W. Ghrist, E. A. Cornell, and C. E. Wieman, Phys. Rev. Lett ., 1997, 78: 586 doi: 10.1103/PhysRevLett.78.586
31	D. S. Hall, M. R. Matthews, J. R. Ensher, C. E. Wieman, and E. A. Cornell, Phys. Rev. Lett ., 1998, 81: 1539 doi: 10.1103/PhysRevLett.81.1539
32	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: 2027 doi: 10.1103/PhysRevLett.80.2027
33	T. S. Raju, P. K. Panigrahi, and K. Porsezian, Phys. Rev. A , 2005, 71: 035601 doi: 10.1103/PhysRevA.71.035601
34	G. Modugno, G. Ferrari, G. Roati, R. J. Brecha, A. Simoni, and M. Inguscio, Science , 2001, 294: 1320 doi: 10.1126/science.1066687
35	H. A. Cruz, V. A. Brazhnyi, V. V. Konotop, G. L. Alfimov, and M. Salerno, Phys. Rev. A , 2007, 76: 013603 doi: 10.1103/PhysRevA.76.013603
36	Q. Y. Li, Z. D. Li, S. F. Yao, L. Li, and G. S. Fu, Chin. Phys. B, 2010, 19: 080501 doi: 10.1088/1674-1056/19/8/080501
37	V. M. Péerez-García and V. Vekslerchik, Phys. Rev. E , 2003, 67: 061804 doi: 10.1103/PhysRevE.67.061804
38	V. A. Brazhnyi and V. V. Konotop, Phys. Rev. E , 2005, 72: 026616 doi: 10.1103/PhysRevE.72.026616
39	J. K. Xue, G. Q. Li, A. X. Zhang, and P. Peng, Phys. Rev. E , 2008, 77: 016606 doi: 10.1103/PhysRevE.77.016606
40	L. Li, B. A. Malomed, D. Mihalache, and W. M. Liu, Phys. Rev. E , 2006, 73: 066610 doi: 10.1103/PhysRevE.73.066610
41	L. Salasnich and B. A. Malomed, Phys. Rev. A , 2006, 74: 053610 doi: 10.1103/PhysRevA.74.053610
42	P. ?hberg and L. Santos, J. Phys. B2001, 34: 4721 doi: 10.1088/0953-4075/34/23/316
43	S. K. Adhikari, Phys. Lett. A , 2005, 346: 179 doi: 10.1016/j.physleta.2005.07.044
44	S. B. Papp, J. M. Pino, and C. E. Wieman, Phys. Rev. Lett ., 2008, 101: 040402 doi: 10.1103/PhysRevLett.101.040402
45	A. P. Sheppard and Y. S. Kivshar, Phys. Rev. E , 1997, 55: 4773 doi: 10.1103/PhysRevE.55.4773
46	D. J. Kaup and B. A. Malomed, Phys. Rev. A , 1993, 48: 599 doi: 10.1103/PhysRevA.48.599
47	Th. Busch and J. R. Anglin, Phys. Rev. Lett ., 2001, 87: 010401 doi: 10.1103/PhysRevLett.87.010401
48	X. F. Zhang, Q. Yang, J. F. Zhang, X. Z. Chen, and W.M. Liu, Phys. Rev. A , 2008, 77: 023613
49	C. Sulem and P. L. Sulem, The Nonlinear Schr?dinger Equation, New York: Springer-Verlag, 1999
50	B. Li, X. F. Zhang, Y. Q. Li, Y. Chen, and W. M. Liu, Phys. Rev. A , 2008, 78: 023608 doi: 10.1103/PhysRevA.78.023608
51	Y. Kagan, A. E. Muryshev, and G. V. Shlyapnikov, Phys. Rev. Lett ., 1998, 81: 933 doi: 10.1103/PhysRevLett.81.933
52	S. V. Manakov, Sov. Phys. JETP, 1974, 38: 248
53	R. Radhakrishnan and M. Lakshmanan, J. Phys. A, 1995, 28: 2683 doi: 10.1088/0305-4470/28/9/025
54	P. ?hberg and L. Santos, Phys. Rev. Lett ., 2001, 86: 2918 doi: 10.1103/PhysRevLett.86.2918
55	X. F. Zhang, X. H. Hu, X. X. Liu, and W. M. Liu, Phys. Rev. A , 2009, 79: 33630 doi: 10.1103/PhysRevA.79.033630
56	H. Pu and N. P. Bigelow, Phys. Rev. Lett ., 1998, 80: 1130 doi: 10.1103/PhysRevLett.80.1130
57	X. X. Liu, H. Pu, B. Xiong, W. M. Liu, and J. B. Gong, Phys. Rev. A , 2009, 79: 013423 doi: 10.1103/PhysRevA.79.013423
58	D. S. Wang, X. H. Hu, and W. M. Liu, Phys. Rev. A , 2010, 82: 023612 doi: 10.1103/PhysRevA.82.023612
59	K. Kasamatsu and M. Tsubota, Phys. Rev. A 74, 013617 (2006). doi: 10.1103/PhysRevA.74.013617
60	X. H. Hu, X. F. Zhang, D. Zhao, H. G. Luo, and W. M. Liu, Phys. Rev. A , 2009, 79: 023619 doi: 10.1103/PhysRevA.79.023619
61	J. Belmonte-Beitia, V. M. Péerez-García, and V. Vekslerchik, Phys. Rev. Lett ., 2007, 98: 064102 doi: 10.1103/PhysRevLett.98.064102
62	M. Abramowitz and I. Stegun, Handbook of Mathematical Functions, New York: Dover, 1965
63	D. S. Wang, X. H. Hu, J. P. Hu, and W. M. Liu, Phys. Rev. A , 2010, 81: 025604
64	E. T. Whittaker and G. N. Watson, A Course in Modern Analysis , 4th Ed., Cambridge, UK: Cambridge University Press, 1990
65	L. Wu, L. Li, J. F. Zhang, D. Mihalache, B. A. Malomed, and W. M. Liu, Phys. Rev. A , 2010, 81: 061805(R) doi: 10.1103/PhysRevA.81.061805

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