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理论物理通讯：英文版

Stability of Two-Component Bose-Einstein Condensates in Bessel Optical Lattices

Chen, Haijun, Li, Hao-Cai, Xue, Ju-Kui

Published Jan 1, 2008• 0 citations
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Abstract

二部件的鲍斯·爱因斯坦冷凝物(BEC ) 的扎根的状态的稳定性把对称的 Bessel 装进一个向轴的方向的中央井有吸引人或排斥的原子相互作用的格子(BL ) 潜力用时间依赖者被学习粗野 Pitaevskii 方程(GPE ) 。由使用变化方法，我们发现二部件的 BEC 的稳定的地面状态能在 BL 存在。BL 的深度和 intra 种类原子相互作用在地面状态的稳定性起一个重要作用。在 BL 的二部件的 BEC 的倒塌也被学习，为套住的二部件的 BEC 的一个倒塌条件被获得。二部件的 BEC 展览富人折叠动力学，这被显示出。也就是说，二部件的 BEC 能与 intra-attractive, 在系统崩溃并且内部吸引人，或与 intra 吸引人、内部排斥，或与 intra 排斥、内部吸引人的原子相互作用。而且，在 BL 的二部件的 BEC 的倒塌的控制详细被讨论。在参数空格的扎根的状态的稳定性图被获得。结果证明二部件的 BEC 的倒塌能被原子相互作用的时间的调整控制。

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二部件的鲍斯·爱因斯坦冷凝物(BEC ) 的扎根的状态的稳定性把对称的 Bessel 装进一个向轴的方向的中央井有吸引人或排斥的原子相互作用的格子(BL ) 潜力用时间依赖者被学习粗野 Pitaevskii 方程(GPE ) 。由使用变化方法，我们发现二部件的 BEC 的稳定的地面状态能在 BL 存在。BL 的深度和 intra 种类原子相互作用在地面状态的稳定性起一个重要作用。在 BL 的二部件的 BEC 的倒塌也被学习，为套住的二部件的 BEC 的一个倒塌条件被获得。二部件的 BEC 展览富人折叠动力学，这被显示出。也就是说，二部件的 BEC 能与 intra-attractive, 在系统崩溃并且内部吸引人，或与 intra 吸引人、内部排斥，或与 intra 排斥、内部吸引人的原子相互作用。而且，在 BL 的二部件的 BEC 的倒塌的控制详细被讨论。在参数空格的扎根的状态的稳定性图被获得。结果证明二部件的 BEC 的倒塌能被原子相互作用的时间的调整控制。
我们与另外的限制在一个周期的光潜力为 Bose 爱因斯坦冷凝物(BEC ) 学习静止、繁殖的答案光或磁性的潜力。用有效集体近似，我们以慢慢地变化的信封 modulating 表示冷凝物波浪功能光格子的 Bloch 模式。在弱非线性的限制，我们为不包含格子的快速的摆动的信封功能的繁殖导出一个非线性的 Schrodinger 方程。我们然后在弱、中等、强壮的非线性的相互作用的政体详细考虑扎根的州的答案。我们描述在每政体适当的答案的形式，并且把小心的限制放在答案的每种类型的有效性上。最后，我们扩大学习到旋量的宣传动力学在一个光格子和一些有趣的现象的原子 BEC 被揭示。
黑暗 solitons 在一个光格子套住的二联合 Bose 爱因斯坦冷凝物(BEC ) 的静电干扰特征与变化途径被调查。在有相反的阶段坡度的鈥榢i nk 鈥 ? 和鈥榓n ti 纽结鈥 ? 之间的相互作用是有效地排斥的，这被发现，并且光格子能 controllably 被用来生产一双静态的 BEC 黑暗 solitons。它的效果取决于 BEC 黑暗 solitons，格子振幅和波浪数字的起始的地点。CLC 数字 O469 文件代码 A 不在资助下面由湖北省的教育部门的科技程序支持了。在资助号码 2004ABA112 下面的湖北省的自然科学的 B20052202，和资金。
The stability of the ground state of two-component Bose–Einstein condensates (BECs) loaded into the central well of an axially symmetric Bessel lattices (BLs) potential with attractive or repulsive atoms interactions is studied using the time-dependent Gross–Pitaevskii equation (GPE). By using the variational method, we find that stable ground state of two-component BECs can exist in BLs. The BLs's depth and the intra-species atom interaction play an important role in the stability of ground state. The collapse of two-component BECs in BLs is also studied and a collapse condition for trapped two-component BECs is obtained. It is shown that the two-component BECs exhibit rich collapse dynamics. That is, the two-component BECs can collapse in the system with both intra- and inter-attractive, or with intra-attractive and inter-repulsive, or with intra-repulsive and inter-attractive atom interactions. Furthermore, the control of the collapse of the two-component BECs in BLs is discussed in detail. The stability diagram of the ground state in parameter space is obtained. The results show that the collapse of two-component BECs can be controlled by temporal modulation of the atom interaction.
The ground state solutions of two-component Bose-Einstein condensates (BECs) in Bessel optical lattices (BLs) are studied by means of the balance condition between BLs strength and inter-atomic interactions. We consider a quasi-two-dimensional (2D) BECs system，strongly confined in longitudinal direction and weakly trapped in the radial direction in the transverse plane，which obeys 2D Gross-Pitaevskii equation (GPE) derived from its 3D counterpart. Analytically we obtained the atom number distribution，atom number and energy of ground state and give the parameter ranges. Compared to single-component BEC，two-component BECs exhibit a rich variety of ground state structures. These structures depend upon various parameters，in particular the inter-atomic interactions and the BLs strength. Neglecting the inter-component atomic interaction，the corresponding results of single-component situation are given.
在多维的光格子的 Bose 爱因斯坦冷凝物的高顺序的相互作用被讨论经分解并且数字地。健全速度和 Bloch 波浪的稳定性上的高顺序的原子相互作用的效果强烈取决于格子力量，这被表明。面对高顺序的效果，更紧密、高度维的格子被证实是为维持系统的精力充沛的稳定性的二个积极因素，并且 Bloch 的动态不稳定性飘动能与精力充沛的不稳定性同时发生。另外，我们发现高顺序的相互作用展出远程的行为，在一个倾斜的光格子的长寿协调 Bloch 摆动存在。我们的结果提供一个有效方法在光格子探查高顺序的相互作用。
In order to investigate the stability and dynamics properties of a cold atom Bose-Einstein Condensate (BEC) in two-dimensional Bessel optical lattices, the stability condition of the system is analyzed and the corresponding Gross-pitaevskii equation (GPE) is solved in this paper by time-dependent variational method and numerical simulation. Firstly, the Euler-Lagrange equation containing the parameters describing the system stability and the effective potential energy needed by the variational analysis method to analyze the system stability is obtained by using the adjustable exponent Gaussian trial wave function. Secondly, according to the analytical solution of Euler-Lagrange equation and the local minimum value of potential energy, the stability condition of the system is further illuminated. Finally, the influence mechanism of these parameters on the local dynamics is revealed by solving the corresponding GPE with numerical method.