Dynamics and stability of Bose-Einstein condensates with long-range interaction

这个建议的目的是推进物理学的玻色-爱因斯坦凝聚体与额外的长程相互作用的理解，实验实现了在气体中的铬原子与偶极-偶极相互作用，并给实验学家的相关物理参数的范围，在那里寻找新的现象，在这样的凝聚。具体来说，我们将解决以下问题：1）最近发现的激发凝聚态的混沌动力学的过渡使用一个简单的变分方法可以通过精确的数值解证实？如果是这样，这种动力学的实验特征是什么？2)对二维偶极凝聚体多层结构中集体模色散的理论分析表明，旋转子不稳定性大大增强。在一个真实的实验中，在所有三个空间方向上都有约束的情况下，什么样的物理参数能使不稳定性开始的特征被观察到？3)在真实的实验中，人们能否确定预测在铬凝聚体中出现的二维亮孤子的物理参数？4)在偶极凝聚体和具有电磁诱导吸引1=r相互作用的凝聚体中，嵌入涡旋可以存在的参数范围是什么？- 求解Gross-Pitaevskii和Bogoliubov方程的数值工具将是基于耦合高斯波包的新型扩展变分技术。

The objective of this proposal is to advance the understanding of the physics of Bose-Einstein condensates with additional long-range interactions, as realized experimentally in a gas of chromium atoms with dipole-dipole interaction, and to give experimentalists the ranges of relevant physical parameters at hand where to look for new phenomena in such condensates. Specifically, we will address the following topics: 1) Can the transition to chaotic dynamics in excited condensate states discovered recently using a simple variational approach be confirmed by accurate numerical solutions? If so, what will be experimental signatures of such dynamics? 2) The theoretical analysis of collective mode dispersion in multi-layer stacks of two-dimensional dipolar condensates has revealed a strong enhancement of the roton instability. What are the physical parameters for which signatures of the onset of the instability can be seen in a real experiment, with confinement in all three space directions? 3) Can one pin down the physical parameters where two-dimensional bright solitons predicted to appear in chromium condensates can be observed in a real experiment? 4) What are the ranges of parameters where embedded vortices can exist in dipolar condensates and condensates with electromagnetically induced attractive 1=r interaction? - The numerical tools for solving the Gross-Pitaevskii and Bogoliubov equations will be novel extended variational techniques based on coupled Gaussian wave packets.