Ground States In A Rotating Two-component Dipolar Bose-einstein Condensate

Since the first experimental realization of Bose-Einstein condensation in ultra-colddilute gases, the properties of this novel state have attracted great interests of thephysicists. During the past two decades, the researchers have made outstandingachievements both in theory and experiment. Especially, as the experimental realization of52Cr Bose-Einstein condensation, the dipole-dipole interaction has drawn the attention ofthe researchers, and is becoming research hotspot of ultra-cold atomic physics. In thepresent work, we investigate the ground-sate properties of three-dimensionaltwo-component dipolar Bose-Einstein condensates. Our main work and findings aresummarized as follows.In Section1, based on the mean-field theory, we derive the Gross-Pitaevskii equationthat describes the Bose-Einstein condensate. By solving the coupled Gross-Pitaevskiiequations with dipole-dipole interaction term, we can investigate the properties of vortices.Generally speaking, there are two kinds of methods for finding vortex solutions. An exactvortex solution can be obtained by analytical calculation, while this method is usually verydifficult. The other method is numerical simulation, which is simple and effective.In Section2, we investigate the vortex states of rotating3D two-component BECs ina isotropic harmonic trap by ignoring the dipole-dipole interactions. We discuss theinfluence of the inter-component interaction and the rotating frequency on theground-state vortex distribution, and obtained a vortex phase diagram spanned by thestrength of the inter-component interaction and the rotating frequency.In Section3, we investigate the influence of the dipole-dipole interaction on theground-state structure of3D BECs. Firstly, we discuss the role of the dipole-dipoleinteraction in the ground-sate structure of a single component BEC. Secondly, we discussthe influence of the dipole-dipole interaction on the ground-sate structure of atwo-component BEC. Thirdly, we investigate the influence of the dipole-dipole interactionon the structure of the ground-state vortex lattices in rotating3D two-component BECs.