Analytic Study To Two-component Bose-Einstein Condensate

Bose-Einstein condensates have been an attractive subject in recent decades.They not only offer the perfect macroscopic quantum systems to investigate many foundmental problems in quantum mechanics but also have extensively application foregrounds such as in atom laser and quantum computation.In the framework of mean-field theory the Bose-Einstein condensate is governed by the Gross-Pitaevskii equation.Based on the Gross-Pitaevskii equation,we perform analytic study on two-component Bose-Einstein condensate.Our main study exist in two aspects.The one is the exact nonstationary solutions for a two-component Bose-Einstein condensate which compose of two species have different atomic masses,the other is about the interaction between two dark matter solitons in a two-component Bose-Einstein condensate.This paper consists of four chapters.In the first chapter,we chiefly concern the following aspects:the first one is about the fundamental conception of Bose-Einstein condensate;the second one is the experimental principle to realize BEC;the third one is a introduction to two-component Bose-Einstein condensate;the fourth one a simple deduction to the mean-field theory;the last one is a concise summary of our work.In the second chapter,we mainly researched two aspects.The one is that we discovered a series of exact nonstationary solutions for a two-component Bose-Einstein condensate which compose of two species have different atomic masses.The other is that we use the exact nonstationary solutions discussed the interesting behaviour of the atomic velocity and the flow density.We find that if adjust the lasers under some conditions, when one componet's atomic velocity is always periodic and finite,the other component's velocity may be infinite.We also find that the motion of the two components can be controlled by the experimental parameters.In the third chapter,we studied the interaction between two dark matter solitons in a two-component Bose-Einstein condensate.First,we find an exact dark soliton solution for a two-component Bose-Einstein condensate when it is at equilibrium state.Then,based on the exact dark soliton solution,we give an reasonable ansatz for the solions affected by some perturbation,and gain a set of differential equations governing the parameter functions by the least-action principle.At last,we discussed the interaction between the two dark solions by an effective potential.We find that when g12＞0,the two solitons repulse each other;while when g12＜0,the force between the two solitons is a short range force which causes the two solitons oscillate about and pass through each other.Moreover, for the case of g12＜0,the relative motion of the two solitons and the oscillating angular frequency are also studied.In the last part of this paper,we give a simple summary and discussion to the abovementioned works.