| GENERAL |
|
|
|
|
Variational Approach to Study $\mathcal{PT}$-Symmetric Solitons in a Bose–Einstein Condensate with Non-locality of Interactions |
| Wei Qi1**, Hai-Feng Li2, Zhao-Xin Liang3 |
1Department of Applied Physics, School of Arts and Sciences, Shaanxi University of Science and Technology, Xi'an 710021
2School of Science, Xi'an Technological University, Xi'an 710032
3Department of Physics, Zhejiang Normal University, Jinhua 321004
|
|
| Cite this article: |
|
Wei Qi, Hai-Feng Li, Zhao-Xin Liang 2019 Chin. Phys. Lett. 36 040501 |
|
|
|
|
Abstract Considering the non-locality of interactions in a Bose–Einstein condensate, the existence and stability of solitons subject to a $\mathcal{PT}$-symmetric potential are discussed. In the framework of the variational approach, we investigate how the non-locality of interactions affects the self-localization and stability of a condensate with attractive two-body interactions. The results reveal that the non-locality of interactions dramatically influences the shape, width, and chemical potential of the condensate. Analytically variational computation also predicts that there exists a critical negative non-local interaction strength ($p_{\rm c} < 0$) with each fixed two-body interaction ($g_{0} < 0$), and there exists no bright soliton solution for $p_{0} < p_{\rm c}$. Furthermore, we study the effect of the non-locality interactions on the stability of the solitons using the Vakhitov–Kolokolov stability criterion. It is shown that for a positive non-local interaction ($p_{0}>0$), there always exist stable bright solitons in some appropriate parameter regimes.
|
|
|
Received: 25 December 2018
Published: 23 March 2019
|
|
| PACS: |
05.45.Yv
|
(Solitons)
|
| |
67.85.Hj
|
(Bose-Einstein condensates in optical potentials)
|
| |
42.65.Tg
|
(Optical solitons; nonlinear guided waves)
|
|
|
| Fund: Supported by the National Natural Science Foundation of China under Grant Nos 11647017, 11805116 and 21703166, and the Science Research Fund of Shaanxi University of Science and Technology under Grant No BJ16-03. |
|
|
|
| [1] | Moiseyev N 2011 Non-Hermitian Quantum Mechanics (Cambridge: Cambridge University Press) | | [2] | Kagan Y, Muryshev A E and Shlyapnikov G V 1998 Phys. Rev. Lett. 81 933 | | [3] | Rapedius K 2013 J. Phys. B 46 125301 | | [4] | Dast D, Haag D, Cartarius H and Wunner G 2014 Phys. Rev. A 90 052120 | | [5] | Bender C M and Boettcher S 1998 Phys. Rev. Lett. 80 5243 | | [6] | Graefe E M, Günther U, Korsch H J and Niederle A E 2008 J. Phys. A 41 255206 | | [7] | Graefe E M 2012 J. Phys. A 45 444015 | | [8] | Haag D, Dast D, Löhle A, Cartarius H, Main J and Wunner G 2014 Phys. Rev. A 89 023601 | | [9] | Schwarz L, Cartarius H, Musslimani Z H, Main J and Wunner G 2017 Phys. Rev. A 95 053613 | | [10] | Liu Y K and Li B 2017 Chin. Phys. Lett. 34 010202 | | [11] | Wei X, Chen B and Wang C F 2016 Chin. Phys. Lett. 33 034205 | | [12] | Pendse A and Bhattacharyay A 2018 J. Phys.: Condens. Matter 30 455602 | | [13] | Papp S B, Pino J M, Wild R J, Ronen S, Wieman C E, Jin D S and Cornell E A 2008 Phys. Rev. Lett. 101 135301 | | [14] | Claussen N R, Donley E A, Thompson S T and Wieman C E 2002 Phys. Rev. Lett. 89 010401 | | [15] | García-Ripol J J, Konotop V V, Malomed B and Pérez-García V M 2003 Math. Comput. Simul. 62 21 | | [16] | Fu H, Wang Y and Gao B 2003 Phys. Rev. A 67 053612 | | [17] | Collin A, Massignan P and Pethick C J 2007 Phys. Rev. A 75 013615 | | [18] | Zinner N T and Thøgersen M 2009 Phys. Rev. A 80 023607 | | [19] | Qi X Y and Xue J K 2012 Phys. Rev. E 86 017601 | | [20] | Qi W, Liang Z and Zhang Z 2013 J. Phys. B 46 175301 | | [21] | Wamba E, Porsezian K, Mohamadou A and Kofané T C 2013 Phys. Lett. A 377 262 | | [22] | Ankiewicz A, Akhmediev N and Devine N 2007 Opt. Fiber Technol. 13 91 | | [23] | Devassy L, Jisha C P, Alberucci A and Kuriakose V C 2015 Phys. Rev. E 92 022914 | | [24] | Jisha C P, Devassy L, Alberucci A and Kuriakose V C 2014 Phys. Rev. A 90 043855 | | [25] | Vakhitov N and Kolokolov A A 1973 Radiophys. Quantum Electron. 16 783 | | [26] | Malomed B A, Kaup D J and Gorder R A V 2012 Phys. Rev. E 85 026604 | | [27] | Chen Z, Liu J, Fu S, Li Y and Malomed B A 2014 Opt. Express 22 29679 | | [28] | Mertens F G, Cooper F, Arévalo E, Khare A, Saxena A and Bishop A R 2016 Phys. Rev. E 94 032213 |
|
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
