Dynamics Of Bose-Einstein Condensate Solitons And Vortices Under The Disordered Complex Potential

In recent years a large number of research groups across the world have generated Bose-Einstein condensates (BECs) by bringing various dilute gases to extremely low temperatures via laser and evaporative cooling methods. This provided the new proof for the fluctuation characteristic of the atoms, and offered the important tool for the research and the use of the macroscopic quantum system. Bose-Einstein condensate as a new state of matter, in the field of cold atoms arouse a research campaign, a lot of theoretical and experimental works has been emerged.In this paper,we mainly studied the dynamics characteristics of solitons and vortices under the complex potential consisted of a parabolic magnetic and lattice potential. The main work embodies as following:1. We consider bright matter-wave solitons in the presence of a parabolic magnetic potential and a time-space periodic optical lattice. The dynamics of condensates is shown to be well approximated by four coupled nonlinear differ-ential equations. A noteworthy feature is that the extended variation approach gives a critical strength ratio to support multiple stable lattice sites for the con-densate. We further examine the existence of the solitons and their stabilities at the multiple stable lattice sites. We then successfully manipulate matter-wave solitons without collapse, which are dragged from an initial stationary to a prescribed position by a moving periodic optical lattice.2. We study the dynamical behavior of2D matter-wave solitons confined by both a symmetric parabolic magnetic potential and a bichromatic lattice. We developed an extended variation approach to give a critical strength ratio of the two potentials in a suitable range necessary to support multiple stable lattice wells for the condensate. Then we demonstrate the stabilities of the localized state by considering its time evolution in the form of a stable breathing oscillation in different stable lattice wells. We then compare spatiotemporal evolution of solitons in a bichromatic optical lattice and an ordinary optical lattices in the presence of a parabolic trap, respectively. It is shown that the localization of condensate is more obvious in an bichromatic lattice than that in an optical lattice. We also examined the existence and the stabilities of the solitons by means of analysing the disordered parameters. We finally discuss the dynamics of dragging manipulation of matter wave solitons, and find a stable region to make sure successful manipulating.3. We study the dynamics behaviors of Bose-Einstein condensate under the complex potential which contained3D parabolic trap and ID bichromatic optical lattice alone the Z axis. We have obtained a trial wave function of the ground and vortex states based on the mean field energy functional and variational method. Then we get the optimization wave function through the particle swarm opti-mization algorithm for obtaining a stable ground state and vortex states. We find that the third vortex state is also stable. What’s more, we have obtained the transition between the superfluid and insulation by means of adjusting the strength of the lattice potential. At the same time, we can use the control func-tion successfully drag the condensate from stable lattice potential to arbitrary destination.