Symbiotic nonlinear excitations in multi-component Bose-Einstein condensates

本项目包括对两组分玻色-爱因斯坦凝聚体：暗-亮孤子和涡旋-亮孤子的局域非线性激发，即所谓的共生激发的全面分析和基本认识的发展。我们的目标是预测具有不同数量共生激发的系统的新的稳定结构，并揭示它们有趣的动力学，以便控制它们的性质和行为。这些研究将在平均场水平和超越平均场理论下进行，采用新发展的多层多组态含时Hartree玻色子方法(ML-MCTDHB)，该方法恰好考虑了系统的所有关联。除了Gross-Pitaevskii方程的模拟和ML-MCTDHB方法的应用外，我们还将开发一个有效的粒子图，使我们能够详细地描述和分析共生激发的相互作用和动力学。这样，就有可能探索这些天体的大型星团甚至有限大小的晶体。这些团簇的多模动力学将为研究它们的动力学稳定性和结合性质提供新的见解。弹性和非弹性碰撞，以及不同陷阱几何形状的共生激发的子成分之间的隧穿过程，有望为我们提供非常丰富的动力学，以及人们在单成分凝聚中不会遇到的大量非线性效应和现象。详细的建模、分析和渐近方法的应用以及大规模计算研究，特别是探索平均场理论以外的关联效应，是本项目的主要方面。调查将与华盛顿州立大学和马萨诸塞大学的实验小组密切合作进行。我们的目的是对实验观测和理论模拟进行详细的比较。

This project contains a comprehensive analysis and the development of a fundamental understanding for localized nonlinear excitations, so-called symbiotic excitations, for two-component Bose-Einstein condensates: dark-bright solitons and vortex-bright solitons. Our aim is to predict novel stable structures of systems with different numbers of symbiotic excitations and to reveal their intriguing dynamics in order to control their properties and behaviour. The investigations will be performed on the mean-field level and beyond mean-field theory by employing the newly developed Multi-Layer Multi-Configuration Time-Dependent Hartree method for bosons (ML-MCTDHB) which exactly takes into account all the correlations of the system. Besides the simulations of the Gross-Pitaevskii equations and the application of the ML-MCTDHB approach we will develop an effective particle picture which allows us to describe and analyze in detail the interactions and dynamics of symbiotic excitations. This way it will be possible to explore large clusters or even finite-sized crystals of these objects. The many-mode dynamics of these clusters will provide new insights into their dynamical stability and binding properties. Elastic and inelastic collisions as well as tunneling processes among the subcomponents of the symbiotic excitations for different trap geometries hold the promise of providing us with a very rich dynamics with a plethora of nonlinear effects and phenomena which one does not encounter in single component condensates. A detailed modelling, the application of analytical and asymptotic methods as well as large scale computational studies to in particular explore the correlations effects beyond mean-field theory represent major aspects of the present project. The investigations will be performed in close collaboration with experimental groups at the Washington State University and the University of Massachusetts. We aim at a detailed comparison of experimental observations and theoretical simulations.