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利用变分法和数值计算方法研究了空间调制作用下Bessel型光晶格中玻色-爱因斯坦凝聚体系中孤立子的稳定性, 给出了存在随空间非周期变化的线性Bessel型光晶格和非线性光晶格(原子之间非线性相互作用的空间调制)时, 各种参数组合下涡旋和非涡旋孤立子的稳定性条件. 首先, 利用圆对称的高斯型试探波函数得出描述体系稳定性参数满足的Euler-Lagrange方程和变分法分析体系稳定性所需要的有效作用势能的表达式. 然后, 根据有效作用势能是否具有局域最小值判断体系是否具有稳定状态, 得出体系具有稳定状态时参数所满足的条件. 最后, 利用有限差分法求解Gross-Pitaevskii方程验证变分法结果的正确性, 所得结果和变分法结果一致.
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关键词:
- Bessel型光晶格 /
- 非线性光晶格 /
- 孤立子 /
- 稳定性
Using variational and numerical solutions of the mean field Gross-Pitaevskii equation, we investigate the stabilities of nonrotating and vortex solitons in Bessel optical lattice by spatial modulation of the nonlinearity(nonlinear optical lattice). It is demonstrated that there exist the stable matter-wave solitons in a combination of optical lattices with linear Bessel optical lattices and nonlinear optical lattice. Using the time-dependent variational approach, we derive the odinary differential equations for the time evolutions of the width and phase of solitons. Through an effective potential, we obtain the stable criteria for all kinds of combinations of the system parameters. We perform direct numerical simulations to support our analytical results, and find that they are in goog agreement.-
Keywords:
- Bessel optical lattice /
- nonlinear optical lattices /
- solitons /
- stability
[1] Morsh O, Oberthaler M 2006 Rev. Mod. Phys. 78 179
[2] Brazhnyi V A, Konotop V V 2004 Mod. Phys. Lett. B 18 627
[3] Yang H S, Xu Z J, Cheng C, Wu Q, Xiong H W 2004 Acta Phys. Sin. 53 2835 (in Chinese) [杨欢耸, 徐志君, 程成, 武强, 熊宏伟 2004 物理学报 53 2835]
[4] 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 物理学报 59 3720]
[5] Vogels J M, Freeland R S, Tsai C C, Verhaar B J, Heinzen D J 2000 Phys. Rev. A 61 043407
[6] Modugno G, Modugno M, Riboli F, Roati G, Inguscio M 2002 Phys. Rev. Lett. 89 190404
[7] da Luz H L F, Abdullaev F K, Gammal A, Sarlerno M, Tomio L 2010 Phys. Rev. A 82 043618
[8] Ji S T, Yan P G, Liu X S 2014 Chin. Phys. B 23 030311
[9] Li Z J, Hai W H, Deng Y 2013 Chin. Phys. B 22 090505
[10] Wang X M, Li Q Y, Li Z D 2013 Chin. Phys. B 22 050311
[11] Baizakov B B, Malomed B A, Salerno M 2006 Phys. Rev. E 74 066615
[12] Baizakov B B, Malomed B A, Salerno M 2003 Europhys. Lett. 63 642
[13] Trombettoni A, Smerzi A 2001 Phys. Rev. Lett. 86 2353
[14] Abdullaev F K H, Baizakov B B, Darmanyan S A, Konotop V V, Salerno M 2001 Phys. Rev. A 64 043606
[15] Sakaguchi H, Malomed B A 2005 Phys. Rev. E 72 046610
[16] Abdullaev F K H, Garnier J 2005 Phys. Rev. A 72 061605
[17] Abdullaev F, Abdumalikov A, Galimzyanov R 2007 Phys. Lett. A 367 149
[18] Chen H J, Li X F 2013 Acta Phys. Sin. 62 070302 (in Chinese) [陈海军, 李向富 2013 物理学报 62 070302]
[19] Dong L W, Wang J D, Wang H, Yin G Y 2009 Phys. Rev. A 79 013807
[20] Kartashov Y V, Dholakia K, Egorov A E, Vysloukh V A, Torner L 2009 Phys. Rev. E 70 065602
[21] Kartashov Y V, Vysloukh V A, Torner L 2004 Phys. Rev. Lett. 93 093904
[22] Kartashov Y V, Vysloukh V A, Torner L 2009 Phys. Rev. E 71 036621
[23] Adhikaria S K 2004 Phys. Rev. E 65 016703
[24] Adhikaria S K 2004 Phys. Rev. A 69 3613-1
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[1] Morsh O, Oberthaler M 2006 Rev. Mod. Phys. 78 179
[2] Brazhnyi V A, Konotop V V 2004 Mod. Phys. Lett. B 18 627
[3] Yang H S, Xu Z J, Cheng C, Wu Q, Xiong H W 2004 Acta Phys. Sin. 53 2835 (in Chinese) [杨欢耸, 徐志君, 程成, 武强, 熊宏伟 2004 物理学报 53 2835]
[4] 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 物理学报 59 3720]
[5] Vogels J M, Freeland R S, Tsai C C, Verhaar B J, Heinzen D J 2000 Phys. Rev. A 61 043407
[6] Modugno G, Modugno M, Riboli F, Roati G, Inguscio M 2002 Phys. Rev. Lett. 89 190404
[7] da Luz H L F, Abdullaev F K, Gammal A, Sarlerno M, Tomio L 2010 Phys. Rev. A 82 043618
[8] Ji S T, Yan P G, Liu X S 2014 Chin. Phys. B 23 030311
[9] Li Z J, Hai W H, Deng Y 2013 Chin. Phys. B 22 090505
[10] Wang X M, Li Q Y, Li Z D 2013 Chin. Phys. B 22 050311
[11] Baizakov B B, Malomed B A, Salerno M 2006 Phys. Rev. E 74 066615
[12] Baizakov B B, Malomed B A, Salerno M 2003 Europhys. Lett. 63 642
[13] Trombettoni A, Smerzi A 2001 Phys. Rev. Lett. 86 2353
[14] Abdullaev F K H, Baizakov B B, Darmanyan S A, Konotop V V, Salerno M 2001 Phys. Rev. A 64 043606
[15] Sakaguchi H, Malomed B A 2005 Phys. Rev. E 72 046610
[16] Abdullaev F K H, Garnier J 2005 Phys. Rev. A 72 061605
[17] Abdullaev F, Abdumalikov A, Galimzyanov R 2007 Phys. Lett. A 367 149
[18] Chen H J, Li X F 2013 Acta Phys. Sin. 62 070302 (in Chinese) [陈海军, 李向富 2013 物理学报 62 070302]
[19] Dong L W, Wang J D, Wang H, Yin G Y 2009 Phys. Rev. A 79 013807
[20] Kartashov Y V, Dholakia K, Egorov A E, Vysloukh V A, Torner L 2009 Phys. Rev. E 70 065602
[21] Kartashov Y V, Vysloukh V A, Torner L 2004 Phys. Rev. Lett. 93 093904
[22] Kartashov Y V, Vysloukh V A, Torner L 2009 Phys. Rev. E 71 036621
[23] Adhikaria S K 2004 Phys. Rev. E 65 016703
[24] Adhikaria S K 2004 Phys. Rev. A 69 3613-1
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