Regular And Chaotic Motions Of Bose-Einstein Condensate In A Double-well Potential

Since the experimental realization of Bose-Einstein condensates, the dynamics of Bose-Einstein condensates in a double-well potential has attracted extensive attention, and the atomic tunneling and self-trapping have been researched considerably. By using an external driving field or adjusting the atomic interaction by Feshbach resonance, we investigate the tunneling, and the regular and chaotic motions of atomic wave-packet within the mean-field theory. We propose a scheme to control the distribution of atoms in the double-well, and to control the entrance or suppression of chaos. Some meaningful results are obtained in our research. This paper is organized as the following six chapters:In the first chapter, we introduce the experimental realization of Bose-Einstein condensates and related fundamental concepts, the mean-field theory and the Gross-Pitaevskii equation. With the mean-field approximation and the two-mode approximation, we analyze the dynamics of Bose-Einstein condensates in a double-well, especially, the Josephson oscillation, self-trapping and the effects of periodic modu-lation have been emphasized. Moreover, the chaos of Bose-Einstein condensates and the effect of chaos assisting tunneling have also been introduced.In chapter 2, we study the effects of chaotic dynamics on atomic tunneling between two weakly coupled Bose-Einstein condensates driv-en by a double-frequency periodic field. Under the Melnikov's chaos criterion, we divide the parameter space into three parts of different types:regular region, low-and high-chaoticity regions, and give the accurate boundaries between the different regions. It is found that the atomic tunneling can be enhanced in the presence of chaos. Particu-larly, in the high-chaoticity regions, the chaos-induced inversion of the population imbalance is observed numerically.In chapter 3, we investigate the dynamics of Bose-Einstein con-densates in a double-well driven by a quasi-square-wave shaped field. The chaotic regions of systemic parameters have been obtained by perturbation analysis and the time evolutions of atomic distribution difference between the two wells have been exhibit numerically. In the case of strong driving, we numerically study the effects of the quasi-square-wave driving on atomic Josephson oscillation and self-trapping.In chapter 4, we investigate the dynamics of a quasi-one-dimensional Bose-Einstein condensate confined in a double-well potential with s-patiotemporally modulated interaction. A variety of phenomena is i-dentified in different frequency regimes, including the self-compression, splitting, breathing and near-fidelity of the matter wavepacket, which are associated with different routes for the onset of spatiotemporal chaos. The results suggest an experimental scheme for controlling reg-ular and chaotic motions of the atomic wavepacket.In chapter 5, we investigate the dynamics of a quasi one di-mensional Bose-Einstein condensate with spatiotemporally modulated nonlinearity in an asymmetrical double-well potential. The directional movement and oscillation behavior of atomic wave-packet have been observed numerically and the method of entering or suppressing chaos has been proposed. It is found that the atomic wave-packet enters into chaos through the three different routes, namely the directional movement, oscillation and quasi-stationary state.In the last chapter, we give a simple summary and discussion to the above-mentioned works, and discuss the prospects of applicants concerning the Bose-Einstein condensate systems. Our main works are involved from the second to the fifth chapters.