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

本提议的目的是促进对具有额外远程相互作用的玻色-爱因斯坦凝聚体的物理理解，正如在具有偶极-偶极相互作用的铬原子气体中实验实现的那样，并为实验人员提供手头相关物理参数的范围，以便在此类凝聚体中寻找新现象。具体来说，我们将讨论以下主题：1)最近用简单变分方法发现的激发态向混沌动力学的转变能否用精确的数值解来证实？如果是这样，这种动力学的实验特征将是什么？2)对二维偶极凝聚物多层叠层的集体模色散进行了理论分析，揭示了旋转不稳定性的增强。在所有三个空间方向上都有约束的真实实验中，不稳定性开始的特征可以在哪些物理参数中看到？3)能否确定在实际实验中可以观察到的预测在铬凝聚物中出现二维亮孤子的物理参数？4)在偶极凝析液和电磁感应吸引1=r相互作用的凝析液中，嵌入涡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.