玻色-爱因斯坦凝聚中的环状暗孤子动力学

郭慧; 王雅君; 王林雪; 张晓斐

doi:10.7498/aps.69.20191424

摘要

环状暗孤子最早是在非线性光学系统中理论预言并实验实现的一种二维孤子类型. 跟通常的二维孤子(如条纹孤子)相比, 环状暗孤子具有更好的稳定性和更加丰富的动力学行为. 玻色-爱因斯坦凝聚由于其高度可调控性为研究环状暗孤子提供了一个全新的平台. 本文结合玻色-爱因斯坦凝聚和孤子研究的现状, 综述玻色-爱因斯坦凝聚中环状暗孤子的解析解、稳定性调控及其衰变动力学等方面的研究进展. 首先介绍了一套变换方法将均匀系统中非线性系数不随时间变化的环状暗孤子解析解推广到谐振子外势下非线性系数随时间变化的环状暗孤子解析解; 然后讨论在形变扰动下环状暗孤子的稳定性相图, 并介绍了如何利用周期调制的非线性来增强环状暗孤子的稳定性; 此外, 还重点讨论了环状暗孤子衰变导致的涡旋极子动力学以及斑图形成.

关键词:

Abstract

Soliton is an exotic topological excitation, and it widely exists in various nonlinear systems, such as nonlinear optics, Bose-Einstein condensates, classical and quantum fluids, plasma, magnetic materials, etc. A stable soliton can propagate with constant amplitude and velocity, and maintain its shape. Two-dimensional and three-dimensional solitons are usually hard to stabilize, and how to realize stable two-dimensional or three-dimensional solitons has aroused the great interest of the researchers. Ring dark soliton is a kind of two-dimensional soliton, which was first theoretically predicted and experimentally realized in nonlinear optical systems. Compared with the usual two-dimensional solitons, ring dark solitons have good stability and rich dynamical behaviors. Owing to their highly controllable capability, Bose-Einstein condensates provide a new platform for studying the ring dark solitons. Based on the recent progress in Bose-Einstein condensates and solitons, this paper reviews the research on the analytic solutions, stability, as well as the decay dynamics of ring dark solitons in Bose-Einstein condensates. A transform method is introduced, which generalizes the analytic solutions of ring dark solitons from a homogeneous system with time-independent nonlinearity to a harmonically trapped inhomogeneous system with time-dependent nonlinearity. The stability phase diagram of the ring dark soliton under deformation perturbations is discussed by numerically solving the Gross-Pitaevskii equations in the mean-field theory. A method of enhancing the stability of ring dark solitons by periodically modulating the nonlinear coefficients is introduced. It is also shown that the periodically modulated nonlinear coefficient can be experimentally realized by the Feshbach resonance technology. In addition, we discuss the dynamics of the decay of ring dark solitons. It is found that the ring dark soliton can decay into various vortex clusters composed of vortices and antivortices. This opens a new avenue to the investigation of vortex dynamics and quantum turbulence. It is also found that the ring dark solitons combined with periodic modulated nonlinearity can give rise to the pattern formation, which is an interesting nonlinear phenomenon widely explored in all the fields of nature. Finally, some possible research subjects about ring dark solitons in future research are also discussed.

Keywords:

作者及机构信息

1.
中国科学院国家授时中心时间频率基准重点实验室, 西安　710600

2.
中国科学院大学天文与空间科学学院, 北京　100049

3.
陕西科技大学文理学院, 西安　710021

通信作者: 张晓斐, xfzhang@ntsc.ac.cn

基金项目: 国家自然科学基金(批准号: 11775253, 11704383)和陕西省自然科学基础研究计划(批准号: 2019JQ-058)资助的课题

Authors and contacts

1.
Key Laboratory of Time and Frequency Primary Standards, National Time Service Center, Chinese Academy of Sciences, Xi’an 710600, China

2.
School of Astronomy and Space Science, University of Chinese Academy of Sciences, Beijing 100049, China

3.
Department of Arts and Sciences, Shaanxi University of Science and Technology, Xi’an 710021, China

Corresponding author: Zhang Xiao-Fei, xfzhang@ntsc.ac.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11775253, 11704383) and the Natural Science Basic Research Plan in Shaanxi Province of China (Grant No. 2019JQ-058)

文章全文 : translate this paragraph

参考文献

[1]	Zabusky N J, Kruskal M D 1965 Phys. Rev. Lett. 15 240
[2]	Kartashov Y V, Malomed B A, Torner L 2011 Rev. Mod. Phys. 83 247 Google Scholar
[3]	Kivshar Y S, Malomed B A 1989 Rev. Mod. Phys. 61 763 Google Scholar
[4]	Fan S T, Zhang Y Y, Yan L L, Guo W G, Zhang S G, Jiang H F 2019 Chin. Phys. B 28 064204 Google Scholar
[5]	Zhao L C, Yang Z Y, Yang W L 2019 Chin. Phys. B 28 010501 Google Scholar
[6]	Shou Q, Liu D W, Zhang X, Hu W, Guo Q 2014 Chin. Phys. B 23 084204 Google Scholar
[7]	Lei Y, Lou S Y 2013 Chin. Phys. Lett. 30 060202 Google Scholar
[8]	Li Q Y, Zhao F, He P B, Li Z D 2015 Chin. Phys. B 24 037508 Google Scholar
[9]	Qi W, Li H F, Liang Z X 2019 Chin. Phys. Lett. 36 040501 Google Scholar
[10]	Lai X J, Cai X O, Zhang J F 2015 Chin. Phys. B 24 070503 Google Scholar
[11]	Anderson M H, Ensher J R, Matthews M R, Wieman C E, Cornell E A 1995 Science 269 198 Google Scholar
[12]	Davis K B, Mewes M O, Andrews M R, Druten N J, Durfee D S, Kurn D M, Ketterle W 1995 Phys. Rev. Lett. 75 3969 Google Scholar
[13]	Bradley C C, Sackett C A, Tollett J J, Hulet R G 1995 Phys. Rev. Lett. 75 1687 Google Scholar
[14]	Bradley C C, Sackett C A, Hulet R G 1997 Phys. Rev. Lett. 78 985 Google Scholar
[15]	Dalfovo F, Giorgini S, Pitaevskii L P, Stringari S 1999 Rev. Mod. Phys. 71 463 Google Scholar
[16]	Leggett A J 2001 Rev. Mod. Phys. 73 307 Google Scholar
[17]	Morsch O, Oberthaler M 2006 Rev. Mod. Phys. 78 179 Google Scholar
[18]	Fetter A L 2009 Rev. Mod. Phys. 81 647 Google Scholar
[19]	Chin C, Grimm R, Julienne P, Tiesinga E 2010 Rev. Mod. Phys. 82 1225 Google Scholar
[20]	Stamper-Kurn D M, Ueda M 2013 Rev. Mod. Phys. 85 1191 Google Scholar
[21]	Goldman N, Juzeliūnas G, Öhberg P, Spielman I B 2014 Rep. Prog. Phys. 77 126401 Google Scholar
[22]	Balakrishnan R, Satija I I 2011 Pramana J. Phys. 77 929 Google Scholar
[23]	Carretero-González R, Frantzeskakis D J, Kevrekidis P G 2008 Nonlinearity 21 R139 Google Scholar
[24]	Frantzeskakis D J 2010 J. Phys. A: Math. Theor. 43 213001 Google Scholar
[25]	Kevrekidis P G, Frantzeskakis D J, Carretero-González R 2008 Emergent Nonlinear Phenomena in Bose-Einstein Condensates: Theory and Experiment (Berlin: Springer Press)
[26]	Ruprecht P A, Holland M J, Burnett K, Edwards M 1995 Phys. Rev. A 51 4704 Google Scholar
[27]	Denschlag J, Simsarian J E, Feder D L, Clark C W, Collins L A, Cubizolles J, Deng L, Hagley E W, Helmerson K, Reinhardt W P, Rolston S L, Schneider B I, Phillips W D 2000 Science 287 97 Google Scholar
[28]	Sanpera A, Shlyapnikov G V, Lewenstein M 1999 Phys. Rev. Lett. 83 5198 Google Scholar
[29]	Tiesinga E, Verhaar B J, Stoof H T C 1993 Phys. Rev. A 47 4114 Google Scholar
[30]	Inouye S, Andrews M R, Stenger J, Miesner H J, Stamper-Kurn D M, Ketterle W 1998 Nature 392 151 Google Scholar
[31]	Strecker K E, Partridge G B, Truscott A G, Hulet R G 2002 Nature 417 150 Google Scholar
[32]	Khaykovich L, Schreck F, Ferrari G, Bourdel T, Cubizolles J, Carr L D, Castin Y, Salomon C 2002 Science 296 1290 Google Scholar
[33]	Cornish S L, Thompson S T, Wieman C E 2006 Phys. Rev. Lett. 96 170401 Google Scholar
[34]	Malomed B A 2016 Eur. Phys. J. Special Topics 225 2507 Google Scholar
[35]	Kivshar Y S, Luther-Davies B 1998 Phys. Rep. 298 81 Google Scholar
[36]	Reinhardt W P, Clark C W 1997 J. Phys. B: At. Mol. Opt. Phys. 30 L785 Google Scholar
[37]	Feder D L, Pindzola M S, Collins L A, Schneider B I, Clark C W 2000 Phys. Rev. A 62 053606 Google Scholar
[38]	Brand J, Reinhardt W P 2002 Phys. Rev. A 65 043612 Google Scholar
[39]	Huang G, Makarov V A, Velarde M G 2003 Phys. Rev. A 67 023604 Google Scholar
[40]	Dutton Z, Budde M, Slowe C, Hau L V 2001 Science 293 663 Google Scholar
[41]	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 Google Scholar
[42]	Tikhonenko V, Christou J, Luther-Davies B, Kivshar Y S 1996 Opt. Lett. 21 1129 Google Scholar
[43]	Kuznetsov E, Turitsyn S 1998 Zh. Eksp. Teor. Fiz. 94 119
[44]	Theocharis G, Frantzeskakis D J, Kevrekidis P G, Malomed B A, Kivshar Y S 2003 Phys. Rev. Lett. 90 120403 Google Scholar
[45]	Kivshar Y S, Yang X 1994 Phys. Rev. E 50 R40 Google Scholar
[46]	Kivshar Y S, Yang X 1994 Chaos, Solitons Fractals 4 1745 Google Scholar
[47]	Baluschev S, Dreischuh A, Velchev I, Dinev S, Marazov O 1995 Appl. Phys. B: Lasers Opt. 61 121 Google Scholar
[48]	Baluschev S, Dreischuh A, Velchev I, Dinev S, Marazov O 1995 Phys. Rev. E 52 5517 Google Scholar
[49]	Yang S J, Wu Q S, Zhang S N, Feng S, Guo W, Wen Y C, Yu Y 2007 Phys. Rev. A 76 063606 Google Scholar
[50]	Yang S J, Wu Q S, Feng S, Wen Y C, Yu Y 2008 Phys. Rev. A 77 035602 Google Scholar
[51]	Hu X H, Zhang X F, Zhao D, Luo H G, Liu W M 2009 Phys. Rev. A 79 023619 Google Scholar
[52]	Barenghi C F, Donnelly R J, Vinen W F 2001 Quantized Vortex Dynamics and Superfluid Turbulence (Berlin: Springer Press)
[53]	Halperin W P, Tsubota M 2009 Progress in Low Temperature Physics: Quantum Turbulence (Amsterdam: Elsevier Press)
[54]	Kusumura T, Tsubota M, Takeuchi H 2012 J. Phys. Conf. Ser. 400 012038 Google Scholar
[55]	Khamehchi M A, Hossain K, Mossman M E, Zhang Y, Busch T, Forbes M M, Engels P 2017 Phys. Rev. Lett. 118 155301 Google Scholar
[56]	Dalibard J, Gerbier F, Juzeliūnas G, Öhberg P 2011 Rev. Mod. Phys. 83 1523 Google Scholar
[57]	Han W, Zhang X F, Song S W, Saito H, Zhang W, Liu W M, Zhang S G 2016 Phys. Rev. A 94 033629 Google Scholar
[58]	Fedichev P O, Kagan Y, Shlyapnikov G V, Walraven J T M 1996 Phys. Rev. Lett. 77 2913 Google Scholar
[59]	Theis M, Thalhammer G, Winkler K, Hellwig M, Ruff G, Grimm R, Denschlag J H 2004 Phys. Rev. Lett. 93 123001 Google Scholar
[60]	Olshanii M 1998 Phys. Rev. Lett. 81 938 Google Scholar
[61]	Haller E, Gustavsson M, Mark M J, Danzl J G, Hart R, Pupillo G, Nägerl H C 2009 Science 325 1224 Google Scholar
[62]	Zhang R, Cheng Y, Zhai H, Zhang P 2015 Phys. Rev. Lett. 115 135301 Google Scholar
[63]	Pagano G, Mancini M, Cappellini G, Livi L, Sias C, Catani J, Inguscio M, Fallani L 2015 Phys. Rev. Lett. 115 265301 Google Scholar
[64]	Claussen N R, Donley E A, Thompson S T, Wieman C E 2002 Phys. Rev. Lett. 89 010401 Google Scholar
[65]	Kevrekidis P G, Theocharis G, Frantzeskakis D J, Malomed B A 2003 Phys. Rev. Lett. 90 230401 Google Scholar
[66]	Greiner M, Regal C A, Jin D S 2005 Phys. Rev. Lett. 94 070403 Google Scholar
[67]	Yamazaki R, Taie S, Sugawa S, Takahashi Y 2010 Phys. Rev. Lett. 105 050405 Google Scholar
[68]	Qi R, Zhai H 2011 Phys. Rev. Lett. 106 163201 Google Scholar
[69]	Infeld E, Rowlands G 1990 Nonlinear Waves, Solitons and Chaos (Cambridge: Cambridge University Press)
[70]	Hirota R 1979 J. Phys. Soc. Jpn. 46 1681 Google Scholar
[71]	Nakamura A 1980 J. Phys. Soc. Jpn. 49 2380 Google Scholar
[72]	Nakamura A, Chen H H 1981 J. Phys. Soc. Jpn. 50 711 Google Scholar
[73]	Johnson R S 1999 Wave Motion 30 1 Google Scholar
[74]	Ko K, Kuehl H 1979 Phys. Fluids 22 1343 Google Scholar
[75]	Malomed B A 2006 Soliton Management in Periodic Systems (Berlin: Springer Press)
[76]	Pelinovsky D E, Kevrekidis P G, Frantzeskakis D J, Zharnitsky V 2004 Phys. Rev. E 70 047604 Google Scholar
[77]	Kevrekidis P G, Pelinovsky D E, Stefanov A 2006 J. Phys. A: Math. Gen. 39 479 Google Scholar
[78]	Saito H, Ueda M 2003 Phys. Rev. Lett. 90 040403 Google Scholar
[79]	Abdullaev F K, Caputo J G, Kraenkel R A, Malomed B A 2003 Phys. Rev. A 67 013605 Google Scholar
[80]	Liang Z X, Zhang Z D, Liu W M 2005 Phys. Rev. Lett. 94 050402 Google Scholar
[81]	Cross M C, Hohenberg P C 1993 Rev. Mod. Phys. 65 851 Google Scholar
[82]	Abid M, Huepe C, Metens S, Nore C, Pham C T, Tuckerman L S, Brachet M E 2003 Fluid Dyn. Res. 33 509 Google Scholar
[83]	Cuypers Y, Maurel A, Petitjeans P 2003 Phys. Rev. Lett. 91 194502 Google Scholar
[84]	Yang T, Hu Z Q, Zou S, Liu W M 2016 Sci. Rep. 6 29066 Google Scholar
[85]	Busch T, Anglin J R 2001 Phys. Rev. Lett. 87 010401 Google Scholar
[86]	Wang L X, Dai C Q, Wen L, Liu T, Jiang H F, Saito H, Zhang S G, Zhang X F 2018 Phys. Rev. A 97 063607 Google Scholar
[87]	See Supplemental Material of Ref.[86] at http://link.aps.org/supplemental/10.1103/PhysRevA.97.063607 for movies of the vortex dipole dynamics.
[88]	Kawaguchi Y, Ueda M 2012 Phys. Rep. 520 253 Google Scholar
[89]	Arecchi F T, Boccaletti S, Ramazza P 1999 Phys. Rep. 318 1 Google Scholar
[90]	Seiden G, Thomas P J 2011 Rev. Mod. Phys. 83 1323 Google Scholar
[91]	Schwabe M, Konopka U, Bandyopadhyay P, Morfill G E 2011 Phys. Rev. Lett. 106 215004 Google Scholar
[92]	Langer J S 1980 Rev. Mod. Phys. 52 1 Google Scholar
[93]	Xu Z F, Lü R, You L 2011 Phys. Rev. A 83 053602 Google Scholar
[94]	He Z M, Wen L, Wang Y J, Chen G P, Tan R B, Dai C Q, Zhang X F 2019 Phys. Rev. E 99 062216 Google Scholar
[95]	Pethick C J, Smith H 2008 Bose-Einstein Condensation in Dilute Gases (Cambridge: Cambridge University Press)
[96]	Pitaevskii L, Stringari S 2003 Bose-Einstein Condensation (New York: Oxford University Press)
[97]	Thalhammer G, Barontini G, Sarlo L D, Catani J, Minardi F, Inguscio M 2008 Phys. Rev. Lett. 100 210402 Google Scholar
[98]	Papp S B, Pino J M, Wieman C E 2008 Phys. Rev. Lett. 101 040402 Google Scholar
[99]	Galitski V, Spielman I B 2013 Nature 494 49 Google Scholar
[100]	Ferrier-Barbut I, Pfau T 2018 Science 359 274 Google Scholar
[101]	Kartashov Y V, Astrakharchik G E, Malomed B A, Torner L 2019 Nat. Rev. Phys. 1 185 Google Scholar
[102]	Sakaguchi H, Li B, Malomed B A 2014 Phys. Rev. E 89 032920 Google Scholar
[103]	Zhang Y C, Zhou Z W, Malomed B A, Pu H 2015 Phys. Rev. Lett. 115 253902 Google Scholar
[104]	Wu C J, Ian M S, Zhou X F 2011 Chin. Phys. Lett. 28 097102 Google Scholar
[105]	Wang C, Gao C, Jian C M, Zhai H 2010 Phys. Rev. Lett. 105 160403 Google Scholar
[106]	Sinha S, Nath R, Santos L 2011 Phys. Rev. Lett. 107 270401 Google Scholar
[107]	Hu H, Ramachandhran B, Pu H, Liu X J 2012 Phys. Rev. Lett. 108 010402 Google Scholar
[108]	Xu Z F, Kawaguchi Y, You L, Ueda M 2012 Phys. Rev. A 86 033628 Google Scholar
[109]	Xu Z F, Kobayashi S, Ueda M 2013 Phys. Rev. A 88 013621 Google Scholar

施引文献

图 1 形变扰动下环状暗孤子的稳定性相图^[51]

Fig. 1. Stability phase diagram of ring dark solitons under deformation perturbation.

下载: 全尺寸图片幻灯片

图 2 单分量BEC中形变扰动下环状暗孤子的衰变行为^[51]

Fig. 2. Decay of the ring dark soliton under deformation perturbation in a single-component BEC.

下载: 全尺寸图片幻灯片

图 3 两分量BEC中相同深度环状暗孤子的衰变行为^[86]

Fig. 3. Decay of the ring dark solitons with the same depth in two-component BECs.

下载: 全尺寸图片幻灯片

图 4 四组涡旋极子在两分量BEC中的动力学演化^[86]

Fig. 4. Evolution of four vortex dipoles in two-component BECs.

下载: 全尺寸图片幻灯片

图 5 两分量BEC中不同深度环状暗孤子的衰变行为^[86]

Fig. 5. Decay of the ring dark solitons with different depths in two-component BECs.

下载: 全尺寸图片幻灯片

图 6 周期调制相互作用系统中环状暗孤子衰变引起的斑图形成^[94]

Fig. 6. Pattern formation induced by the decay of ring dark solitons in a system with periodically modulated interactions.

下载: 全尺寸图片幻灯片

图 7 斑图在周期调制相互作用系统中的演化^[94]

Fig. 7. Evolution of the pattern in a system with periodically modulated interactions.

下载: 全尺寸图片幻灯片

表 1 环状暗孤子寿命随相互作用振荡频率的变化^[51]

Table 1. Life of the ring dark soliton as a function of the interaction oscillation frequency.

相互作用振荡频率$\omega$/$\varOmega$	环状暗孤子寿命t/ms
$ < 0.5$	$ < 15$
0.6	17
0.8	43
1.0	45
1.5	16
$ > 1.7$	$ < 15$
注1: 原子间相互作用$g(t) = 1-\sin{\omega t}$, 环状暗孤子深度$\cos{\phi(0)} = 0.76$.

下载: 导出CSV

[1]	Zabusky N J, Kruskal M D 1965 Phys. Rev. Lett. 15 240
[2]	Kartashov Y V, Malomed B A, Torner L 2011 Rev. Mod. Phys. 83 247 Google Scholar
[3]	Kivshar Y S, Malomed B A 1989 Rev. Mod. Phys. 61 763 Google Scholar
[4]	Fan S T, Zhang Y Y, Yan L L, Guo W G, Zhang S G, Jiang H F 2019 Chin. Phys. B 28 064204 Google Scholar
[5]	Zhao L C, Yang Z Y, Yang W L 2019 Chin. Phys. B 28 010501 Google Scholar
[6]	Shou Q, Liu D W, Zhang X, Hu W, Guo Q 2014 Chin. Phys. B 23 084204 Google Scholar
[7]	Lei Y, Lou S Y 2013 Chin. Phys. Lett. 30 060202 Google Scholar
[8]	Li Q Y, Zhao F, He P B, Li Z D 2015 Chin. Phys. B 24 037508 Google Scholar
[9]	Qi W, Li H F, Liang Z X 2019 Chin. Phys. Lett. 36 040501 Google Scholar
[10]	Lai X J, Cai X O, Zhang J F 2015 Chin. Phys. B 24 070503 Google Scholar
[11]	Anderson M H, Ensher J R, Matthews M R, Wieman C E, Cornell E A 1995 Science 269 198 Google Scholar
[12]	Davis K B, Mewes M O, Andrews M R, Druten N J, Durfee D S, Kurn D M, Ketterle W 1995 Phys. Rev. Lett. 75 3969 Google Scholar
[13]	Bradley C C, Sackett C A, Tollett J J, Hulet R G 1995 Phys. Rev. Lett. 75 1687 Google Scholar
[14]	Bradley C C, Sackett C A, Hulet R G 1997 Phys. Rev. Lett. 78 985 Google Scholar
[15]	Dalfovo F, Giorgini S, Pitaevskii L P, Stringari S 1999 Rev. Mod. Phys. 71 463 Google Scholar
[16]	Leggett A J 2001 Rev. Mod. Phys. 73 307 Google Scholar
[17]	Morsch O, Oberthaler M 2006 Rev. Mod. Phys. 78 179 Google Scholar
[18]	Fetter A L 2009 Rev. Mod. Phys. 81 647 Google Scholar
[19]	Chin C, Grimm R, Julienne P, Tiesinga E 2010 Rev. Mod. Phys. 82 1225 Google Scholar
[20]	Stamper-Kurn D M, Ueda M 2013 Rev. Mod. Phys. 85 1191 Google Scholar
[21]	Goldman N, Juzeliūnas G, Öhberg P, Spielman I B 2014 Rep. Prog. Phys. 77 126401 Google Scholar
[22]	Balakrishnan R, Satija I I 2011 Pramana J. Phys. 77 929 Google Scholar
[23]	Carretero-González R, Frantzeskakis D J, Kevrekidis P G 2008 Nonlinearity 21 R139 Google Scholar
[24]	Frantzeskakis D J 2010 J. Phys. A: Math. Theor. 43 213001 Google Scholar
[25]	Kevrekidis P G, Frantzeskakis D J, Carretero-González R 2008 Emergent Nonlinear Phenomena in Bose-Einstein Condensates: Theory and Experiment (Berlin: Springer Press)
[26]	Ruprecht P A, Holland M J, Burnett K, Edwards M 1995 Phys. Rev. A 51 4704 Google Scholar
[27]	Denschlag J, Simsarian J E, Feder D L, Clark C W, Collins L A, Cubizolles J, Deng L, Hagley E W, Helmerson K, Reinhardt W P, Rolston S L, Schneider B I, Phillips W D 2000 Science 287 97 Google Scholar
[28]	Sanpera A, Shlyapnikov G V, Lewenstein M 1999 Phys. Rev. Lett. 83 5198 Google Scholar
[29]	Tiesinga E, Verhaar B J, Stoof H T C 1993 Phys. Rev. A 47 4114 Google Scholar
[30]	Inouye S, Andrews M R, Stenger J, Miesner H J, Stamper-Kurn D M, Ketterle W 1998 Nature 392 151 Google Scholar
[31]	Strecker K E, Partridge G B, Truscott A G, Hulet R G 2002 Nature 417 150 Google Scholar
[32]	Khaykovich L, Schreck F, Ferrari G, Bourdel T, Cubizolles J, Carr L D, Castin Y, Salomon C 2002 Science 296 1290 Google Scholar
[33]	Cornish S L, Thompson S T, Wieman C E 2006 Phys. Rev. Lett. 96 170401 Google Scholar
[34]	Malomed B A 2016 Eur. Phys. J. Special Topics 225 2507 Google Scholar
[35]	Kivshar Y S, Luther-Davies B 1998 Phys. Rep. 298 81 Google Scholar
[36]	Reinhardt W P, Clark C W 1997 J. Phys. B: At. Mol. Opt. Phys. 30 L785 Google Scholar
[37]	Feder D L, Pindzola M S, Collins L A, Schneider B I, Clark C W 2000 Phys. Rev. A 62 053606 Google Scholar
[38]	Brand J, Reinhardt W P 2002 Phys. Rev. A 65 043612 Google Scholar
[39]	Huang G, Makarov V A, Velarde M G 2003 Phys. Rev. A 67 023604 Google Scholar
[40]	Dutton Z, Budde M, Slowe C, Hau L V 2001 Science 293 663 Google Scholar
[41]	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 Google Scholar
[42]	Tikhonenko V, Christou J, Luther-Davies B, Kivshar Y S 1996 Opt. Lett. 21 1129 Google Scholar
[43]	Kuznetsov E, Turitsyn S 1998 Zh. Eksp. Teor. Fiz. 94 119
[44]	Theocharis G, Frantzeskakis D J, Kevrekidis P G, Malomed B A, Kivshar Y S 2003 Phys. Rev. Lett. 90 120403 Google Scholar
[45]	Kivshar Y S, Yang X 1994 Phys. Rev. E 50 R40 Google Scholar
[46]	Kivshar Y S, Yang X 1994 Chaos, Solitons Fractals 4 1745 Google Scholar
[47]	Baluschev S, Dreischuh A, Velchev I, Dinev S, Marazov O 1995 Appl. Phys. B: Lasers Opt. 61 121 Google Scholar
[48]	Baluschev S, Dreischuh A, Velchev I, Dinev S, Marazov O 1995 Phys. Rev. E 52 5517 Google Scholar
[49]	Yang S J, Wu Q S, Zhang S N, Feng S, Guo W, Wen Y C, Yu Y 2007 Phys. Rev. A 76 063606 Google Scholar
[50]	Yang S J, Wu Q S, Feng S, Wen Y C, Yu Y 2008 Phys. Rev. A 77 035602 Google Scholar
[51]	Hu X H, Zhang X F, Zhao D, Luo H G, Liu W M 2009 Phys. Rev. A 79 023619 Google Scholar
[52]	Barenghi C F, Donnelly R J, Vinen W F 2001 Quantized Vortex Dynamics and Superfluid Turbulence (Berlin: Springer Press)
[53]	Halperin W P, Tsubota M 2009 Progress in Low Temperature Physics: Quantum Turbulence (Amsterdam: Elsevier Press)
[54]	Kusumura T, Tsubota M, Takeuchi H 2012 J. Phys. Conf. Ser. 400 012038 Google Scholar
[55]	Khamehchi M A, Hossain K, Mossman M E, Zhang Y, Busch T, Forbes M M, Engels P 2017 Phys. Rev. Lett. 118 155301 Google Scholar
[56]	Dalibard J, Gerbier F, Juzeliūnas G, Öhberg P 2011 Rev. Mod. Phys. 83 1523 Google Scholar
[57]	Han W, Zhang X F, Song S W, Saito H, Zhang W, Liu W M, Zhang S G 2016 Phys. Rev. A 94 033629 Google Scholar
[58]	Fedichev P O, Kagan Y, Shlyapnikov G V, Walraven J T M 1996 Phys. Rev. Lett. 77 2913 Google Scholar
[59]	Theis M, Thalhammer G, Winkler K, Hellwig M, Ruff G, Grimm R, Denschlag J H 2004 Phys. Rev. Lett. 93 123001 Google Scholar
[60]	Olshanii M 1998 Phys. Rev. Lett. 81 938 Google Scholar
[61]	Haller E, Gustavsson M, Mark M J, Danzl J G, Hart R, Pupillo G, Nägerl H C 2009 Science 325 1224 Google Scholar
[62]	Zhang R, Cheng Y, Zhai H, Zhang P 2015 Phys. Rev. Lett. 115 135301 Google Scholar
[63]	Pagano G, Mancini M, Cappellini G, Livi L, Sias C, Catani J, Inguscio M, Fallani L 2015 Phys. Rev. Lett. 115 265301 Google Scholar
[64]	Claussen N R, Donley E A, Thompson S T, Wieman C E 2002 Phys. Rev. Lett. 89 010401 Google Scholar
[65]	Kevrekidis P G, Theocharis G, Frantzeskakis D J, Malomed B A 2003 Phys. Rev. Lett. 90 230401 Google Scholar
[66]	Greiner M, Regal C A, Jin D S 2005 Phys. Rev. Lett. 94 070403 Google Scholar
[67]	Yamazaki R, Taie S, Sugawa S, Takahashi Y 2010 Phys. Rev. Lett. 105 050405 Google Scholar
[68]	Qi R, Zhai H 2011 Phys. Rev. Lett. 106 163201 Google Scholar
[69]	Infeld E, Rowlands G 1990 Nonlinear Waves, Solitons and Chaos (Cambridge: Cambridge University Press)
[70]	Hirota R 1979 J. Phys. Soc. Jpn. 46 1681 Google Scholar
[71]	Nakamura A 1980 J. Phys. Soc. Jpn. 49 2380 Google Scholar
[72]	Nakamura A, Chen H H 1981 J. Phys. Soc. Jpn. 50 711 Google Scholar
[73]	Johnson R S 1999 Wave Motion 30 1 Google Scholar
[74]	Ko K, Kuehl H 1979 Phys. Fluids 22 1343 Google Scholar
[75]	Malomed B A 2006 Soliton Management in Periodic Systems (Berlin: Springer Press)
[76]	Pelinovsky D E, Kevrekidis P G, Frantzeskakis D J, Zharnitsky V 2004 Phys. Rev. E 70 047604 Google Scholar
[77]	Kevrekidis P G, Pelinovsky D E, Stefanov A 2006 J. Phys. A: Math. Gen. 39 479 Google Scholar
[78]	Saito H, Ueda M 2003 Phys. Rev. Lett. 90 040403 Google Scholar
[79]	Abdullaev F K, Caputo J G, Kraenkel R A, Malomed B A 2003 Phys. Rev. A 67 013605 Google Scholar
[80]	Liang Z X, Zhang Z D, Liu W M 2005 Phys. Rev. Lett. 94 050402 Google Scholar
[81]	Cross M C, Hohenberg P C 1993 Rev. Mod. Phys. 65 851 Google Scholar
[82]	Abid M, Huepe C, Metens S, Nore C, Pham C T, Tuckerman L S, Brachet M E 2003 Fluid Dyn. Res. 33 509 Google Scholar
[83]	Cuypers Y, Maurel A, Petitjeans P 2003 Phys. Rev. Lett. 91 194502 Google Scholar
[84]	Yang T, Hu Z Q, Zou S, Liu W M 2016 Sci. Rep. 6 29066 Google Scholar
[85]	Busch T, Anglin J R 2001 Phys. Rev. Lett. 87 010401 Google Scholar
[86]	Wang L X, Dai C Q, Wen L, Liu T, Jiang H F, Saito H, Zhang S G, Zhang X F 2018 Phys. Rev. A 97 063607 Google Scholar
[87]	See Supplemental Material of Ref.[86] at http://link.aps.org/supplemental/10.1103/PhysRevA.97.063607 for movies of the vortex dipole dynamics.
[88]	Kawaguchi Y, Ueda M 2012 Phys. Rep. 520 253 Google Scholar
[89]	Arecchi F T, Boccaletti S, Ramazza P 1999 Phys. Rep. 318 1 Google Scholar
[90]	Seiden G, Thomas P J 2011 Rev. Mod. Phys. 83 1323 Google Scholar
[91]	Schwabe M, Konopka U, Bandyopadhyay P, Morfill G E 2011 Phys. Rev. Lett. 106 215004 Google Scholar
[92]	Langer J S 1980 Rev. Mod. Phys. 52 1 Google Scholar
[93]	Xu Z F, Lü R, You L 2011 Phys. Rev. A 83 053602 Google Scholar
[94]	He Z M, Wen L, Wang Y J, Chen G P, Tan R B, Dai C Q, Zhang X F 2019 Phys. Rev. E 99 062216 Google Scholar
[95]	Pethick C J, Smith H 2008 Bose-Einstein Condensation in Dilute Gases (Cambridge: Cambridge University Press)
[96]	Pitaevskii L, Stringari S 2003 Bose-Einstein Condensation (New York: Oxford University Press)
[97]	Thalhammer G, Barontini G, Sarlo L D, Catani J, Minardi F, Inguscio M 2008 Phys. Rev. Lett. 100 210402 Google Scholar
[98]	Papp S B, Pino J M, Wieman C E 2008 Phys. Rev. Lett. 101 040402 Google Scholar
[99]	Galitski V, Spielman I B 2013 Nature 494 49 Google Scholar
[100]	Ferrier-Barbut I, Pfau T 2018 Science 359 274 Google Scholar
[101]	Kartashov Y V, Astrakharchik G E, Malomed B A, Torner L 2019 Nat. Rev. Phys. 1 185 Google Scholar
[102]	Sakaguchi H, Li B, Malomed B A 2014 Phys. Rev. E 89 032920 Google Scholar
[103]	Zhang Y C, Zhou Z W, Malomed B A, Pu H 2015 Phys. Rev. Lett. 115 253902 Google Scholar
[104]	Wu C J, Ian M S, Zhou X F 2011 Chin. Phys. Lett. 28 097102 Google Scholar
[105]	Wang C, Gao C, Jian C M, Zhai H 2010 Phys. Rev. Lett. 105 160403 Google Scholar
[106]	Sinha S, Nath R, Santos L 2011 Phys. Rev. Lett. 107 270401 Google Scholar
[107]	Hu H, Ramachandhran B, Pu H, Liu X J 2012 Phys. Rev. Lett. 108 010402 Google Scholar
[108]	Xu Z F, Kawaguchi Y, You L, Ueda M 2012 Phys. Rev. A 86 033628 Google Scholar
[109]	Xu Z F, Kobayashi S, Ueda M 2013 Phys. Rev. A 88 013621 Google Scholar

[1]	邢健崇, 张文静, 杨涛. 玻色-爱因斯坦凝聚中的非正则涡旋态及其动力学. 物理学报, 2023, 72(10): 100306. doi: 10.7498/aps.72.20222289
[2]	贾瑞煜, 方乒乒, 高超, 林机. 玻色-爱因斯坦凝聚体中的淬火孤子与冲击波. 物理学报, 2021, 70(18): 180303. doi: 10.7498/aps.70.20210564
[3]	唐娜, 杨雪滢, 宋琳, 张娟, 李晓霖, 周志坤, 石玉仁. 三体相互作用下准一维玻色-爱因斯坦凝聚体中的带隙孤子及其稳定性. 物理学报, 2020, 69(1): 010301. doi: 10.7498/aps.69.20191278
[4]	文林, 梁毅, 周晶, 余鹏, 夏雷, 牛连斌, 张晓斐. 线性塞曼劈裂对自旋-轨道耦合玻色-爱因斯坦凝聚体中亮孤子动力学的影响. 物理学报, 2019, 68(8): 080301. doi: 10.7498/aps.68.20182013
[5]	何章明, 张志强. 玻色-爱因斯坦凝聚体中的双孤子相互作用操控. 物理学报, 2016, 65(11): 110502. doi: 10.7498/aps.65.110502
[6]	张晓斐, 张培, 陈光平, 董彪, 谭仁兵, 张首刚. 共心双环外势中两分量偶极玻色-爱因斯坦凝聚体的基态结构研究. 物理学报, 2015, 64(6): 060302. doi: 10.7498/aps.64.060302
[7]	宋立军, 严冬, 刘烨. 玻色-爱因斯坦凝聚系统的量子Fisher信息与混沌. 物理学报, 2011, 60(12): 120302. doi: 10.7498/aps.60.120302
[8]	曲春雷, 赵清. 周期驱动玻色-爱因斯坦凝聚系统的棘齿效应. 物理学报, 2009, 58(7): 4390-4395. doi: 10.7498/aps.58.4390
[9]	严冬, 宋立军, 陈殿伟. 两分量玻色-爱因斯坦凝聚系统的自旋压缩. 物理学报, 2009, 58(6): 3679-3684. doi: 10.7498/aps.58.3679
[10]	宗丰德, 杨阳, 张解放. 外势场作用下的玻色-爱因斯坦凝聚啁啾孤子的演化与操控. 物理学报, 2009, 58(6): 3670-3678. doi: 10.7498/aps.58.3670
[11]	张蔚曦, 王登龙, 丁建文. 准二维凝聚体中暗孤子环的动力学演化. 物理学报, 2008, 57(11): 6786-6791. doi: 10.7498/aps.57.6786
[12]	王志霞, 张喜和, 沈柯. 玻色-爱因斯坦凝聚中的混沌反控制. 物理学报, 2008, 57(12): 7586-7590. doi: 10.7498/aps.57.7586
[13]	王海雷, 杨世平. 三势阱中玻色-爱因斯坦凝聚的开关特性. 物理学报, 2008, 57(8): 4700-4705. doi: 10.7498/aps.57.4700
[14]	李菊萍, 谭磊, 臧小飞, 杨科. 偶极旋量玻色-爱因斯坦凝聚体在外场中的自旋混合动力学. 物理学报, 2008, 57(12): 7467-7476. doi: 10.7498/aps.57.7467
[15]	宗丰德, 张解放. 装载于外势场中的玻色-爱因斯坦凝聚N-孤子间的相互作用. 物理学报, 2008, 57(5): 2658-2668. doi: 10.7498/aps.57.2658
[16]	刘泽专, 杨志安. 噪声对双势阱玻色-爱因斯坦凝聚体系自俘获现象的影响. 物理学报, 2007, 56(3): 1245-1252. doi: 10.7498/aps.56.1245
[17]	何章明, 王登龙. 凝聚体中亮孤子和暗孤子的交替演化. 物理学报, 2007, 56(6): 3088-3091. doi: 10.7498/aps.56.3088
[18]	臧小飞, 李菊萍, 谭磊. 偶极-偶极相互作用下双势阱中旋量玻色-爱因斯坦凝聚磁化率的非线性动力学性质. 物理学报, 2007, 56(8): 4348-4352. doi: 10.7498/aps.56.4348
[19]	王冠芳, 傅立斌, 赵鸿, 刘杰. 双势阱玻色-爱因斯坦凝聚体系的自俘获现象及其周期调制效应. 物理学报, 2005, 54(11): 5003-5013. doi: 10.7498/aps.54.5003
[20]	徐　岩, 贾多杰, 李希国, 左　维, 李发伸. 大N近似下玻色-爱因斯坦凝聚体中单个涡旋态的解. 物理学报, 2004, 53(9): 2831-2834. doi: 10.7498/aps.53.2831

计量

文章访问数: 11640
PDF下载量: 298
被引次数: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

搜索

留言板