Dynamics of ring dark solitons in Bose-Einstein condensates

Guo Hui; Wang Ya-Jun; Wang Lin-Xue; Zhang Xiao-Fei

doi:10.7498/aps.69.20191424

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:

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)

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References

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Cited By

图 1 形变扰动下环状暗孤子的稳定性相图^[51]

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

DownLoad: Full-Size Img PowerPoint

图 2 单分量BEC中形变扰动下环状暗孤子的衰变行为^[51]

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

DownLoad: Full-Size Img PowerPoint

图 3 两分量BEC中相同深度环状暗孤子的衰变行为^[86]

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

DownLoad: Full-Size Img PowerPoint

图 4 四组涡旋极子在两分量BEC中的动力学演化^[86]

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

DownLoad: Full-Size Img PowerPoint

图 5 两分量BEC中不同深度环状暗孤子的衰变行为^[86]

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

DownLoad: Full-Size Img PowerPoint

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]

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

DownLoad: Full-Size Img PowerPoint

图 7 斑图在周期调制相互作用系统中的演化^[94]

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

DownLoad: Full-Size Img PowerPoint

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$\cos{\phi(0)} = 0.76$.

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[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
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[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
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[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
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[24]	Frantzeskakis D J 2010 J. Phys. A: Math. Theor. 43 213001 Google Scholar
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[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
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[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
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[84]	Yang T, Hu Z Q, Zou S, Liu W M 2016 Sci. Rep. 6 29066 Google Scholar
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