Laboratory of Advanced Microsystems Engineering, Department of Computer Science and Engineering, University of Quebec at Outaouais, 101 St-Jean-Bosco, Succursale Hull, Gatineau(PQ) J8Y 3G5, Canada.
Laboratory of Condensed Matter Theory and Materials Computation, Institute of Physics, Chinese Academy of Sciences, No. 8 South-Three Street, ZhongGuanCun, Beijing 100190, China.
Phys Rev E. 2018 Jul;98(1-1):012204. doi: 10.1103/PhysRevE.98.012204.
In this paper, we consider a Gross-Pitaevskii (GP) equation with a time-dependent nonlinearity and a spatiotemporal complex linear term which describes the dynamics of matter-wave solitons in Bose-Einstein condensates (BECs) with time-dependent interatomic interactions in a parabolic potential in the presence of feeding or loss of atoms. We establish the integrability conditions under which analytical solutions describing the modulational instability and the propagation of both bright and dark solitary waves on a continuous wave background are obtained. The obtained integrability conditions also appear as the conditions under which the solitary waves of the BECs can be managed by controlling the functional gain or loss parameter. For specific BECs, the dynamics of bright and dark solitons are investigated analytically through the found exact solutions of the GP equation. Our results show that under the integrability conditions, the gain or loss parameter of the GP equation can be used to manage the motion of both bright and dark solitons. We show that for BECs with loss (gain) of atoms, the bright and dark solitons during their propagation have a compression (broadening) in their width. Furthermore, under a safe range of parameters and under the integrability conditions, it is possible to squeeze a bright soliton of BECs with loss of atoms into the assumed peak matter density, which can provide an experimental tool for investigating the range of validity of the 1D GP equation. Our results also reveal that under the conditions of the solitary wave management, neither the injection or the ejection of atoms from the condensate affects the soliton peak during its propagation.
在本文中，我们考虑了一个带有时间相关非线性项和时空复线性项的 Gross-Pitaevskii（GP）方程，该方程描述了在时变原子间相互作用的抛物势中玻色-爱因斯坦凝聚体（BEC）中物质波孤子的动力学，同时考虑了原子的注入或损失。我们建立了可积性条件，通过这些条件可以得到描述调制不稳定性和连续波背景上亮孤子和暗孤子传播的解析解。所得到的可积性条件也出现在通过控制函数增益或损耗参数来管理 BEC 中孤子的条件下。对于特定的 BEC，通过找到 GP 方程的精确解来分析亮孤子和暗孤子的动力学。我们的结果表明，在可积性条件下，GP 方程的增益或损耗参数可用于管理亮孤子和暗孤子的运动。我们表明，对于有原子损耗（增益）的 BEC，亮孤子和暗孤子在传播过程中会在宽度上发生压缩（展宽）。此外，在参数的安全范围内且在可积性条件下，有可能将有原子损耗的 BEC 的亮孤子压缩到假定的物质密度峰值，这可以为研究 1D GP 方程的有效性范围提供实验工具。我们的结果还表明，在孤子管理条件下，原子从凝聚体中注入或射出都不会影响孤子在传播过程中的峰值。
