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利用变分法和数值计算方法研究了二维线性和非线性光晶格中二维玻色-爱因斯坦凝聚体系中物质波孤立子的存在及其稳定性. 利用定态变分原理及Vakhitov-Kolokolov判据总结了线性和非线性结合光晶格中几种参数组合下定态定域解的稳定性. 结果表明, 当存在二维非线性光晶格时, 在吸引和排斥相互作用的原子体系中均可以存在稳定的物质波孤立子. 另外, 利用含时变分法研究了线性和非线性光晶格中物质波孤立子随时间的传播特性, 使波包参数对时间的一阶导数等于零, 可以给出稳定状态对应的参数, 结论和定态变分法给出的结果一致. 最后用数值计算方法研究变分结果的正确性, 把变分结果作为初始条件代入Gross-Pitaevskii方程研究其随时间传播特征, 得到了稳定的传播过程, 所得到的结果和变分分析结果一致.By means of variational solution and direct numerical simulation of the Gross-Pitaevskii equation (GPE), we have studied the stability of matter-wave solitons in two-dimensional (2D) Bose-Einstein condensations (BECs), with 2D linear and nonlinear optical lattices (OLs). Using the static variational approach and Vakhitov-Kolokolov criterion necessary for stability, we obtain the stability condition for solitons in different combinations of OL's parameters. We show that the 2D linear and nonlinear optical lattices allow us to stabilize 2D solitons for both attractive and repulsive interactions. We also study the time-evolution problems of 2D BECs, using the time-dependent variational approach and numerical solution of GPE for 2D linear and nonlinear OLs. Very good agreement between the results corresponding to both treatments is observed.
[1] Wang D S, Hu X H, Liu W M 2010 Phys. Rev. A 82 023612
[2] Zhao W L, Dou F Q, Wang J Z 2012 Acta Phys. Sin. 61 220503 (in Chinese) [赵文垒, 豆福全, 王建忠 2012 61 220503]
[3] Xi Y D, Wang D L, She Y C, Wang F J, Ding J W 2010 Acta Phys. Sin. 59 3720 (in Chinese) [奚玉东, 王登龙, 佘彦超, 王凤姣, 丁建文 2010 59 3720]
[4] Chen H F, Huang J S, Xie Z W 2008 Acta Phys. Sin. 57 3435 (in Chinese) [陈海峰, 黄劲松, 谢征微 2008 57 3435]
[5] Salerno M, Konotop V V, Bludov Y V 2008 Phys. Rev. Lett. 101 030405
[6] Wimberger S, Mannella R, Morsch O, Arimondo E, Kolovsky A R, Buchleitner A 2005 Phys. Rev. A 72 063610
[7] Anderson B P, Kasevich M A 1998 Science 282 1686
[8] Xie Y D 2012 Acta Phys. Sin. 61 210305 (in Chinese) [谢元栋 2012 61 210305]
[9] Baizakov B B, Malomed B A, Salerno M 2003 Europhys. Lett. 63 642
[10] Baizakov B B, Malomed B A, Salerno M 2004 Phys. Rev. A 70 053613
[11] Mihalache D, Mazilu D, Lederer F, Kartashov Y V, Crasovan L C, Torner L 2004 Phys. Rev. E 70 0556039(R)
[12] Yang L Y, Fang Y C, Yang Z A 2008 Acta Phys. Sin. 57 661 (in Chinese) [杨丽云, 房永翠, 杨志安 2008 57 661]
[13] Abdullaev F K, Kamchatnov A M, Konotop V V, Brazhnyi V A 2003 Phys. Rev. Lett. 90 230402
[14] Belmonte-Beitia J, Perez-Garcia V M, Vekslerchik V, Torres P J 2007 Phys. Rev. Lett. 98 064102
[15] Belmonte-Beitia J, Perez-Garcia V M, Vekslerchik V, Konotop V V 2008 Phys. Rev. Lett. 100 164102
[16] da Luz H L F, Abdullaev F K, Gammal A, Salerno M, Tomio L 2010 Phys. Rev. A 82 043618
[17] Sakaguchi H, Malomed B A 2005 Phys. Rev. E 72 046610
[18] Sakaguchi H, Malomed B A 2010 Phys. Rev. A 81 013624
[19] Vakhitov N G, Kolokolov A A 1973 Izv. Vyssh. Uchebn. Zaved. Radiofiz. 16 1020
[20] Cheng Y S, Adhikari S K 2011 Phys. Rev. A 83 023620
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[1] Wang D S, Hu X H, Liu W M 2010 Phys. Rev. A 82 023612
[2] Zhao W L, Dou F Q, Wang J Z 2012 Acta Phys. Sin. 61 220503 (in Chinese) [赵文垒, 豆福全, 王建忠 2012 61 220503]
[3] Xi Y D, Wang D L, She Y C, Wang F J, Ding J W 2010 Acta Phys. Sin. 59 3720 (in Chinese) [奚玉东, 王登龙, 佘彦超, 王凤姣, 丁建文 2010 59 3720]
[4] Chen H F, Huang J S, Xie Z W 2008 Acta Phys. Sin. 57 3435 (in Chinese) [陈海峰, 黄劲松, 谢征微 2008 57 3435]
[5] Salerno M, Konotop V V, Bludov Y V 2008 Phys. Rev. Lett. 101 030405
[6] Wimberger S, Mannella R, Morsch O, Arimondo E, Kolovsky A R, Buchleitner A 2005 Phys. Rev. A 72 063610
[7] Anderson B P, Kasevich M A 1998 Science 282 1686
[8] Xie Y D 2012 Acta Phys. Sin. 61 210305 (in Chinese) [谢元栋 2012 61 210305]
[9] Baizakov B B, Malomed B A, Salerno M 2003 Europhys. Lett. 63 642
[10] Baizakov B B, Malomed B A, Salerno M 2004 Phys. Rev. A 70 053613
[11] Mihalache D, Mazilu D, Lederer F, Kartashov Y V, Crasovan L C, Torner L 2004 Phys. Rev. E 70 0556039(R)
[12] Yang L Y, Fang Y C, Yang Z A 2008 Acta Phys. Sin. 57 661 (in Chinese) [杨丽云, 房永翠, 杨志安 2008 57 661]
[13] Abdullaev F K, Kamchatnov A M, Konotop V V, Brazhnyi V A 2003 Phys. Rev. Lett. 90 230402
[14] Belmonte-Beitia J, Perez-Garcia V M, Vekslerchik V, Torres P J 2007 Phys. Rev. Lett. 98 064102
[15] Belmonte-Beitia J, Perez-Garcia V M, Vekslerchik V, Konotop V V 2008 Phys. Rev. Lett. 100 164102
[16] da Luz H L F, Abdullaev F K, Gammal A, Salerno M, Tomio L 2010 Phys. Rev. A 82 043618
[17] Sakaguchi H, Malomed B A 2005 Phys. Rev. E 72 046610
[18] Sakaguchi H, Malomed B A 2010 Phys. Rev. A 81 013624
[19] Vakhitov N G, Kolokolov A A 1973 Izv. Vyssh. Uchebn. Zaved. Radiofiz. 16 1020
[20] Cheng Y S, Adhikari S K 2011 Phys. Rev. A 83 023620
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