变分法研究二维光晶格中玻色-爱因斯坦凝聚的调制不稳定性

陈海军

doi:10.7498/aps.64.054702

摘要

利用含时变分法研究了二维光晶格中准二维玻色-爱因斯坦凝聚中的调制不稳定性. 在平均场近似下, 由准二维Gross-Pitaevskii方程出发, 利用变分法给出了调制波振幅和相位所满足的时间演化方程, 通过求解时间演化方程和能量分析法给出了发生调制不稳定性的条件, 决定于平面波振幅, 晶格强度, 调制波的波矢量和原子之间的两体相互作用.

关键词:

We investigate the modulational instability of a two-dimensional Bose-Einstein condensate in a two-dimensional optical lattice using a time-dependent variational approach. Within this framework, we derive the ordinary differential equations for time evolution of the amplitude and phase of modulational perturbations. Analyzing these equations and the Hamiltonian of the system, we obtain the modulational instability criterion.

Keywords:

作者及机构信息

陈海军

1.
陇东学院电气工程学院, 庆阳 745000

Authors and contacts

Chen Hai-Jun

1.
Electrical Engineering College, Longdong University, Qingyang 745000, China

参考文献

[1]	Sulem C, Sulem P L 1999 The Nonlinear Schrödinger Equation (Spinger-Verlag,New York)
[2]	Gross M C, Hohenberg P C 1993 Rev. Mod. Phys. 65 851
[3]	Yang X X, Wu Y 2002 Chin. Phys. Lett. 19 1413
[4]	Wu L, Zhang J F 2007 Chin. Phys. Lett. 24 1471
[5]	Li S C, Duan W S 2009 Chin. Phys. B 18 4177
[6]	Baizakov B B, Bouketir A, Messikh A 2009 Phys. Rev. E 79 046605
[7]	Li L, Li Z D, Malomed B A, Mihalache D, Liu W M 2005 Phys. Rev. A 72 033611
[8]	Zhao X D, Xie Z W, Zhang W P 2007 Phys. Rev. B 76 214408
[9]	2012 Phys Rev. E 86 017601
[10]	Yu D S, Chen J B 2008 Chin. Phys. Lett. 25 1792
[11]	2014 Phys Rev. E 89 052917
[12]	Rapti Z, Kevrekidis P G, Smerzi A, Bishop A R 2004 Phys. Rev. E 69 017601
[13]	2008 77 046216 (in Chinese) [Wamba E, Mohamadou A, Kofané T C, 2008 Phys Rev. E 77 046216]
[14]	Jia L L, Sun S L, Li J H 2012 Acta Sinica Quantum Optica 18 65 (in Chinese) [贾磊磊, 孙山林, 李精华 2012 量子光学学报 18 65]
[15]	Zhang H, Duan W S 2013 Acta Phys. Sin. 62 044703 (in Chinese) [张恒, 段文山 2013 物理学报 62 044703]
[16]	Huang J S, Chen H F, Xie Z W 2008 Acta Phys. Sin. 57 3435 (in Chinese) [黄劲松, 陈海峰, 谢征微 2008 物理学报 57 3435]
[17]	Teng F, Xie Z W 2013 Acta Phys. Sin. 62 026701 (in Chinese) [藤斐, 谢征微 2013 物理学报 62 026701]

施引文献

[1]	Sulem C, Sulem P L 1999 The Nonlinear Schrödinger Equation (Spinger-Verlag,New York)
[2]	Gross M C, Hohenberg P C 1993 Rev. Mod. Phys. 65 851
[3]	Yang X X, Wu Y 2002 Chin. Phys. Lett. 19 1413
[4]	Wu L, Zhang J F 2007 Chin. Phys. Lett. 24 1471
[5]	Li S C, Duan W S 2009 Chin. Phys. B 18 4177
[6]	Baizakov B B, Bouketir A, Messikh A 2009 Phys. Rev. E 79 046605
[7]	Li L, Li Z D, Malomed B A, Mihalache D, Liu W M 2005 Phys. Rev. A 72 033611
[8]	Zhao X D, Xie Z W, Zhang W P 2007 Phys. Rev. B 76 214408
[9]	2012 Phys Rev. E 86 017601
[10]	Yu D S, Chen J B 2008 Chin. Phys. Lett. 25 1792
[11]	2014 Phys Rev. E 89 052917
[12]	Rapti Z, Kevrekidis P G, Smerzi A, Bishop A R 2004 Phys. Rev. E 69 017601
[13]	2008 77 046216 (in Chinese) [Wamba E, Mohamadou A, Kofané T C, 2008 Phys Rev. E 77 046216]
[14]	Jia L L, Sun S L, Li J H 2012 Acta Sinica Quantum Optica 18 65 (in Chinese) [贾磊磊, 孙山林, 李精华 2012 量子光学学报 18 65]
[15]	Zhang H, Duan W S 2013 Acta Phys. Sin. 62 044703 (in Chinese) [张恒, 段文山 2013 物理学报 62 044703]
[16]	Huang J S, Chen H F, Xie Z W 2008 Acta Phys. Sin. 57 3435 (in Chinese) [黄劲松, 陈海峰, 谢征微 2008 物理学报 57 3435]
[17]	Teng F, Xie Z W 2013 Acta Phys. Sin. 62 026701 (in Chinese) [藤斐, 谢征微 2013 物理学报 62 026701]

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