Effect Of Periodic Modulation On Nature Of Bose-Einstein Condensates

In 1995, seventy years after Einstein theory, Bose-Einstein condensate (BEC) of alkali metals'atoms was made in experiment for the first time in the world with physicists'effort, 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. There is science meaning and application value of the realization of BEC. BEC connects with basic theory of physics, and also connects with physical technique. BEC not only has something important with basic research, and also has widely application outlook in chip technique, accurate measurement, and nanotechnology, so BEC become the hotspot of theory and experiment research.In this article, we exploit two-mode model to investigate dynamical phase transition of Bose-Einstein Condensates with external periodic modulation. Particularly, phase transition to chaos is studied, and entanglement entropy denotation of chaos. And then chaos tunneling is studied. Our main work is:1,Dynamical phase transition of Bose-Einstein Condensates in double-well trap with external periodic modulation on interaction is investigated in this paper. Particularly, phase transition to chaos and entanglement entropy is studied. It is found that, when interaction is minor, it is periodic orbits in phase space; self-trapping is merged with increase of interaction; when resonance between external periodic frequency and natural frequency happens, this system can turn to instability (chaos). In chaotic region, distribution of particles is random, and average of population difference fluctuates around zero. Self-trapping is recur with increase of interaction. Especially, chaos can be denoted by entanglement entropy. In the chaotic zone, both of two average entanglement entropies approach to their maxima. Phase transition course can be well denoted by this two entanglement entropies.2,Further more, chaos tunneling is studied. Phase transition to chaos of Bose-Einstein Condensates in double-well trap with external periodic modulation is investigated. Particularly, chaos tunneling is studied. Using the evolution of Husimi function with time in the corresponding quantum condition, we identify the effect of tunneling by chaos, and variation of tunneling with interaction. It is found that, when chaos emerges, chaos region and chaos tunneling is various with interaction.