Symbiotic nonlinear excitations in multi-component Bose-Einstein condensates

该项目包含了对玻色-爱因斯坦双组分凝聚体的局部非线性激发，即所谓的共生激发的全面分析和基本理解的发展：暗亮孤子和涡亮孤子。我们的目标是预测具有不同数量共生激励的系统的新型稳定结构，并揭示其有趣的动力学，以便控制其性质和行为。研究将在平均场水平和超越平均场理论的水平上进行，采用新开发的多层多配置时间相关的玻色子Hartree方法（ML-MCTDHB），该方法精确地考虑了系统的所有相关性。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，使我们能够详细描述和分析共生激发的相互作用和动力学。通过这种方式，将有可能探索这些物体的大集群甚至是有限大小的晶体。这些簇的多模动力学将为它们的动力学稳定性和结合特性提供新的见解。弹性和非弹性碰撞以及不同圈闭几何形状的共生激发子组分之间的隧道过程有望为我们提供一个非常丰富的动力学，其中包含大量的非线性效应和现象，这是在单组分凝析物中没有遇到的。详细的建模，分析和渐近方法的应用，以及大规模的计算研究，特别是探索超越平均场理论的相关性影响，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察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.