Symbiotic nonlinear excitations in multi-component Bose-Einstein condensates

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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.