The Vortex Structure Of Bose-einstein Condensates In Power-law Traps

The power-law trap is an important model potential whose shape varies with different power law values.The external potential affects the vortex structure in the Bose-Einstein condensates(BECs).In this paper we study the ground state vortex structure of the BEC in the power-law traps.Here is the substance of this paper:In the first chapter,the concept of BEC,its difference from ordinary fluid and its development process are described.BEC can be trapped in an external potential,quantized vortices can be generated in the BEC by laser beam agitation,we also introduce the basic reason of the formation of the quantization vortices.The vortex structure in the BEC is described in detail,including the triangular lattice,the quadrangular lattice,the hexagonal lattice and the giant vortex structure.The research purpose and significance of this paper are also introduced.In the second chapter,we consider trapping the BEC in power-law traps.The Gross-Pitaevskii equation(GP equation)can be obtained by doing a variational for the energy functional of the system,and the GP equation can be treated by two-dimensional reduction and dimensionless.Based on the GP equation,the ground state density distribution and the corresponding phase distribution of the BEC can be obtained by using the virtual time evolution method and the time-splitting Fourier spectrum method.In the third chapter,we investigate the influence of different power law values on the ground state vortex structure and the formation of the vortices in the BEC,and study the variation of the vortex distribution with the interaction between particles increases.The numerical results and analyses are given.We find that when the rotating angular frequency and the interaction between particles is constant,with the increase of the power law value,the ground state vortex distribution of the BEC has the following characteristic: single quantized vortex firstly appear as general triangular lattice,then the BEC center area density decreases to zero,appears a centerhole,and then forms the giant vortex structure.We find that the critical rotation angular frequency of appearing vortices and the giant vortex become smaller with the increase of the power law value.The power-law trap is steeper for a larger power law value,which is more favorable for the formation of the single quantized vortices and the giant vortex.The interaction between particles is the repulsive interaction,when the interaction of particles is increased,the vortex structure gradually changes from the giant vortex to the triangular lattice structure.In the last chapter,we make a conclusion and also introduce the following research work.