Effects Of Atomic Interactions On Coherent Tunneling

Recently, controlling transportation of ultracold atoms has attracted some attentions in modern physics. Because of quantum tunnelling, atoms located in one well potential can pass through a barrier and not be trapped in the one of the double-well for a long time. But if the double-well potential is driven by an external periodic force, the quantum tunnelling can be suppressed, and atoms can be tapped in one well, it is known as the coherent destruction of tunnelling (CDT). However, the researches of CDT are limited in the system only with two-body interaction. However, the tunnelling of BECs is a many-atoms system where three-body interactions between atoms plays an important role. Techniques have allowed to create and exploit three-body interactions via the Feshbach resonance techniques or with photon-assisted tunnelling. The spin-orbit (SO) coupling of atoms has been realized by the artificial gauge field, which is significant for controlling tunnelling of different spin bosons. In this paper, we discuss the tunnelling dynamics of ultracold atoms with three-body interactions and with SO coupling in a periodically driving double-well potential. The specific contents and conclusions of this paper are as follows:In the first chapter, the physical background and the related physical knowledge are briefly introduced, including CDT, spin-orbit coupling Bose gas, three-body interactions of atoms.In the second chapter, the selective CDT of ultracold Bose gas with three-body in-teractions in a modulated double-well potential is discussed. It is shown that the effects of two- and three-body interactions on the dynamics of the selective CDT are strongly coupled and the three-body interactions significantly modify the selective CDT. For weak three-body interactions, an upper bound of the boson number for realizing the selective CDT exists and the region of boson number for realizing the selective CDT is enlarged (reduced) with repulsive (attractive) three-body interactions. For strong three-body in-teractions, the boson number in the system for realizing the selective CDT not only has an upper bound, but also has a lower bound. The results are confirmed by numerical simulationsIn the third chapter, the tunnelling dynamics of dilute boson gases with three-body interactions in a periodically driven double wells are investigated both theoretically and numerically. In our findings, when the system is with only repulsive two-body interactions or only three-body interactions, the tunnelling will be suppressed; while in the case of the coupling between two- and three-body interactions, the tunnelling can be either sup-pressed or enhanced. Particularly, when attractive three-body interactions is twice large as repulsive two-body interactions, CDT occurs at isolated points of driving force, which is similar to the linear case. Considering different interaction, the system can experience different transformation from coherent tunnelling (CT) to CDT. The quasi-energy of the system as the function of the periodically driving force shows a triangular structure, which provides a deep insight into the tunnelling dynamics of the system.In the fourth chapter, the tunnelling dynamics of two-species SO coupled Bose-Einstein condensates in a periodically driven double-well potential are investigated both theoretically and numerically. We find that, the atomic interactions, the SO coupling, and the Zeeman field have coupled effects on the tunnelling dynamics of the system. When the SO coupling is absent, the atomic interactions suppress the tunnelling, but the Zeeman field does not influence the tunnelling. When the SO coupling is present, the coupling of the Zeeman-field intensity and the atomic interactions can either enhance or suppress the tunnelling. The system undergoes rich transformations from the CT to the CDT when the SO coupling or the atomic interactions or the Zeeman-field intensity changes. In high-frequency region, the triangular structure and the circle structure are revealed in quasi-energy bands of the system, which provides an insight into CDT. And the SO coupling modifies traditional degenerate modes of quasi-energy bands. The results provide a possible way to control the usual tunnelling and the spin-flipping tunnelling in double-well potential.Finally, we summarize the main results and give an outlook of the future in this field.