Phase engineering, modulational instability, and solitons of Gross-Pitaevskii-type equations in 1+1 dimensions

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	Phase engineering, modulational instability, and solitons of Gross-Pitaevskii-type equations in 1+1 dimensions
	Kengne, E ; Lakhssassi, A ; Liu, WM ; Vaillancourt, R
刊名	PHYSICAL REVIEW E
	2013
卷号	87 期号:2
ISSN号	1539-3755
通讯作者	Kengne, E (reprint author), Chinese Acad Sci, Natl Lab Condensed Matter Phys, Inst Phys, Beijing 100190, Peoples R China.
中文摘要	Motivated by recent proposals of "collisionally inhomogeneous" Bose-Einstein condensates (BECs), which have a spatially modulated scattering length, we introduce a phase imprint into the macroscopic order parameter governing the dynamics of BECs with spatiotemporal varying scattering length described by a cubic Gross-Pitaevskii (GP) equation and then suitably engineer the imprinted phase to generate the modified GP equation, also called the cubic derivative nonlinear Schrodinger (NLS) equation. This equation describes the dynamics of condensates with two-body (attractive and repulsive) interactions in a time-varying quadratic external potential. We then carry out a theoretical analysis which invokes a lens-type transformation that converts the cubic derivative NLS equation into a modified NLS equation with only explicit temporal dependence. Our analysis suggests a particular interest in a specific time-varying potential with the strength of the magnetic trap similar to 1/(t + t)(2). For a time-varying quadratic external potential of this kind, an explicit expression for the growth rate of a purely growing modulational instability is presented and analyzed. We point out the effect of the imprint parameter and the parameter t on the instability growth rate, as well as on the solitary waves of the BECs. DOI: 10.1103/PhysRevE.87.022914
资助信息	Chinese Academy of Sciences Visiting Professorship for Senior International Scientists; NKBRSFC [2011CB921502, 2012CB821305, 2009CB930701, 2010CB922904]; NSFC [10934010, 60978019]; NSFC-RGC [11061160490, 1386-N-HKU748/10]
语种	英语
公开日期	2014-01-16
内容类型	期刊论文
源URL	[http://ir.iphy.ac.cn/handle/311004/57328]
专题	物理研究所_物理所公开发表论文_物理所公开发表论文_期刊论文
推荐引用方式 GB/T 7714	Kengne, E,Lakhssassi, A,Liu, WM,et al. Phase engineering, modulational instability, and solitons of Gross-Pitaevskii-type equations in 1+1 dimensions[J]. PHYSICAL REVIEW E,2013,87(2).
APA	Kengne, E,Lakhssassi, A,Liu, WM,&Vaillancourt, R.(2013).Phase engineering, modulational instability, and solitons of Gross-Pitaevskii-type equations in 1+1 dimensions.PHYSICAL REVIEW E,87(2).
MLA	Kengne, E,et al."Phase engineering, modulational instability, and solitons of Gross-Pitaevskii-type equations in 1+1 dimensions".PHYSICAL REVIEW E 87.2(2013).