Influence Of Noise On Self-trapping Of Bose-Einstein Condensates In Double-well Trap

Physicists have always been interested in microscopic particles, and so have most of the philosophers. The formation of Bose-Einstein condensate is a quite common phenomenon in microscopic world, and studying it is of great value for us to know the microscopic world and take the advantage of the laws of it. As early as in 1924 Einstein predicted the matter what we now call Bose-Einstein condensates. In 1995, Bose-Einstein condensate of alkali metals'atoms was made for the first time in the word, which made atoms equal to laser in some extent. Because of this new kind of matter we can use atoms to observe the nonlinear effects instead of using photons, and much attention was drawn to it. Lots of scientific work was done towards this aspect and the results were encouraging. Because it is very difficult to make Bose-Einstein condensates in experiment, and the condensates cannot exist long, being quite sensitive to the environment around them, and we take the social conditions in consideration, this law is always followed: theory first, experimental results second.Noise is common in nature and in experiment. Because Bose-Einstein condensates are quite sensitive to the environment around them, noise can have great influence on the formation, existence and evolution of them. In this thesis, we numerically studied the influence of noise on self-trapping of Bose-Einstein condensates in double-well trap mainly based on phase space analysis. We generate a series of numbers as expected, put them into the dynamic equations of Bose-Einstein condensates which evolve in double-well trap, then get the solutions of the equations and analyze them considering the real physical facts. In this article our main work is: we study self-trapping of Bose-Einstein condensates in a symmetric double-well potential with uniform noise or Gaussian noise existing respectively. We find that both uniform noise and Gaussian noise destroy the critical behavior of self-trapping with the interaction increasing and create a transition zone between Josephson oscillation and self-trapping, between which exists a critical point originally. Furthermore, the stronger the noise becomes, the wider the transition zone is. Meanwhile, we find that phase space thoroughly falls into confusion when we increase noise intensity to certain extent with interaction fixed and the trajectories reappear after we increase interaction without increasing noise intensity. In full-quantum situation, we study the system in the same way and find that in this case there is no critical value between Josephson oscillation and self-trapping, but a transition zone,and the stronger the noise becomes, the wider the transition zone is. What is different in this kind of conditions is that for a system which is in self-trapping noise can strengthen the self-trapping.Considering the recent experimental observations of self-trapping of Bose-Einstein condensates in double-well trap we give some modest deductions. We hope that our theoretical results can give explanation to some experimental phenomena and stimulate the developing of experiment.