Bose-Einstein Condensate Dark-Soliton And Vortex Soliton In Three-Dimensional Complex Potential

As the fifth kind state of matter except of gas, solid, liquid and plasma, the re-search of Bose-Einstein condensate has important scientific significance and applica-tion value. It provides a total new media for experimental physics. And as a coherent matter wave illumination Bose-Einstein condensate has greatly improved the develop-ment of atomic optical, such as the research of atomic laser. The investigations give us a deeper understanding of the superconducting and superfluid in condensed mat-ter physics and provide a platform for the other quantum phenomena. In aspect of application technology, Bose-Einstein condensate has great development prospect in optical information storage, quantum computer, atomic chip technology, nanotechnol-ogy, precision measurement and so on. All these application need us to have a deep study and understanding of the generation condition of the Bose-Einstein condensate, construction of the soliton solutions, stability and quantum tunneling et al dynamical characteristics. As a very common local wave in nonlinear physics, soliton is a local wave packet with stable structure and has a good particle-like nature. The solitons studied often include bright soliton, dark soliton and vortex soltion. In this paper, we focus on the study of Bose-Einstein condensate dark soliton and vortex soliton. We investigate the stability conditions and realize manipulation in the specific direction. The research results may provide significant theoretical support for relate application such as quantum information storage and control.Bose-Einstein condensate soliton and vortex trapped in external potential has been the research focuses for years. Situations in one-dimensional parabolic and optical lat-tice potential have been widely studied. Due to the instability, it’s not easy to realize Bose-Einstein condensate in high-dimensional space and researches in theory and ex-periment are insufficient. In this paper, we will investigate dynamic characteristics of Bose-Einstein condensate dark soliton and vortex soliton with constructing three-dimensional complex potential consisting of parabolic and other types of potential. The main works include the following two aspects:1. Three-dimensional Bose-Einstein condensate dark solitons in a complex po-tential containing parabolic and gaussian potential. We obtain the initial dark soliton solution through the particle swarm optimization method with the result of energy functional. It is of vital importance to find a reasonable initial solution for finding sta-ble dark soliton solutions. Then we test stabilities of the achieved three-dimensional Bose-Einstein condensate dark soliton solutions by means of the directly numerical simulation method and in the same time analyze the parameters’ influences on the sta-bility. Through a great amount of computations, the value regions of three important parameters to get stable dark solitons are given out, which will provide convenience for the following studies. Finally, we realize manipulation of the stable dark solitons in three-dimensional apace from the initial position to any specified position successfully by slowly moving the potential.2. Three-dimensional vortex solitons in a Bose-Einstein condensate under the confinements of a two-dimensional parabolic trap along the transverse radial direc-tion and a one-dimensional parity-time-symmetric periodic potential along the z axis direction. The stable vortex soliton with three fundamental vortices are obtained vi-a combining energy functional method and the directly numerical simulation of the three-dimensional Gross-Pitaevskii equation. And value ranges of some specific pa-rameters to have stable vortex solitons are analysed. Then stable three-dimensional vortex solitons with three fundamental vortices are depicted with the same and differ-ent atomic numbers, respectively. Moreover, we successfully realize manipulations of the vortex solitons in the z axis direction.