Transportation Properties Of Ultracold Atoms In A Double-well Potential

In recent years, transportation properties of cold atoms in a double-well potential has become a hot topic in modern physics. Especially in the bosonic system with spin orbit coupling, energy band structure and Josephson dynamics produce to expected behaviors. And the coherence of bosonic gas in a disordered double-well potential has attracted many attentions. Due to the realization of artificial gauge field, making it possible to spin-orbit coupling of neutral atoms and make investigation on the system with spin-orbit coupling become a hot issue. Because of the existence of spin-orbit coupling, energy band structure and the tunneling dynamics of the system exhibit new and interesting phenomenon. In addition, people's research are mainly limited to in pure lattice and has two-body interactions. But in the reality system, optical or random and small defect in the crystal lattice impurities is impossible to completely avoid, muti-atoms interactions conforms to the actual situation. Hence the introduction of disorder and three-body interactions enrich the coherence study of bosonic gas. In this paper, the specific contents and conclusions are as follows:In the first chapter, the physical background and the related physical knowledge are briefly introduced, including spin-orbit-coupled Bose-Einstein condensates, quantum bosonic gas in disordered potential, and the effect of effective two-and three-body inter-actions on tunnelling dynamics.In the second chapter, We theoretically investigate the energy band structure and Josephson dynamics of an spin-orbit coupled Bose-Einstein condensate in a double-well potential. We study the energy band structure and the corresponding tunneling dynam-ics of the system by properly adjusting the SO coupling, Raman coupling, Zeeman field and atomic interactions. The coupled effects of SO coupling, Raman coupling, Zeeman field and atomic interactions lead to the appearance of complex energy band structure including the loop structure. Particularly, the emergence of the loop structure in energy band also depends on SO coupling, Raman coupling, Zeeman field and atomic interac-tions. Correspondingly, the Josephson dynamics of the system strongly related to the energy band structure. Especially, the emergence of the loop structure results in complex tunneling dynamics, including suppression-revival transitions and self-trapping of atoms transfer between two spin states and two wells. This engineering provides a possible means for studying energy level and corresponding dynamics of two-species SO coupled BECs.In the third chapter, We investigate the coherence of disordered bosonic gas with ef-fective both two- and three-bodv interactions within a two-site Bose-Hubbard model both theoretically and numerically. By properly adjusting the two-and three-body interactions and the disorder, the coherence of the system exhibits new and interesting phenomenon, including the resonance character of coherence against the disorder in purely two-or three-body interactions system. More interestingly, the disorder and three-body interac-tions together can suppress the coherence of the purely three-body interactions system, which is different from the case where the disorder and two-body interaction together can enhance the coherence in certain values of two-body interaction. Furthermore, when two-or three-body interactions is attractive or repulsive, the phase coherence exhibits com-pletely different phenomenon. Especially, if two-or three-body interactions is attractive, the coherence of the system can be significantly enhanced in certain regions. Correspond-ingly, the phase coherence of the system are strongly related to the effective interaction energy. The results provide a possible means for studying the coherence of bosonic gas with multi-atoms interactions in the presence of the disorder.Finally, we summarize the main results and give an outlook of the future in this field.