The Characters Of Tunneling Dynamics For Bose-Einstein Condensation In A Double Well And Diamond Lattice Chain

In the recent years,the characters for the tunneling dynamics of BoseEinstein condensates in optical lattices has become a hot issue in cold atom field.Owe to quantum tunneling effect,there exists certain possibilities for cold atom to across a potential barrier and they can not always stay at one optical lattice as the progress in time.As required,cold atom can be precisely transported between(among)various optical lattices via altering certain parameters,such as,interaction,tilt of optical lattice and artificial magnetic field.Most previous studies mainly focus on the effect of two-body interactions on the tunneling dynamics,however,three-body interactions can also play significant implications in the many-body system,which can be manipulated by Feshbach resonance technique and optical-assisted tunneling.Furthermore,the tunneling charecter is also closely related to the shape of optical lattice.Consequently,based on BoseHubbard model(tight-binding model),we investigate the tunneling dynamics for Bose-Einstein condensates in a double well potential and diamond lattice chain.The main contents and specific schedules for this paper are as follows:The first chapter introduces the physical background of this paper and summarizes various quantum phenonmena in a double well potential as well as diamond lattice chains,such as,Josephson oscillations,Localization phenomenon,Rabi oscillations,collapses-revivals phenomenon,Bloch oscillations and LandauZener tunneling,further reviews its research status and existing problems.Eventually,we put forward the research content and the significance of this paper.In the second chapter,we investigate the tunneling dynamics of a few bosons with few-body interactions in a double well potential.Uncorrelated Rabi oscillation with the minimum period can happen only when two-and three-body interactions satisfy a critical condition,i.e.,the effective interaction energy is minimized.When the atomic interactions are slightly away from the critical condition in the weak interaction regime,the uncorrelated tunneling exhibits collapse-revival character.When the atomic interactions are strong and far awayfrom the critical condition,correlated Rabi oscillation occurs.The tunneling period(the period of collapse-revival)increases(decreases)when the rate between two-and three-interaction is away from the corresponding critical condition or when the number of bosons increases.In the third chapter,using the tight-binding model,there exists great significance to study the effect of tilt and artificial magnetic field on the dispersion relations for the system and the tunneling dynamics in the diamond lattice chain,which is based on mean field approximation.It reveals that tilt and artificial magnetic field can later the band structure for the system and manipulate the bands gap,so as to make interesting dynamic behavior happen in the diamond lattice chain,inculding Landau-Zener tunneling,Bloch oscillations and Localization phenomenon,whose transitions in the diamond lattice chain is not only closely related to the initial distribution,but also significantly depends on the the tilt of diamond lattice chain and artificial magnetic field.Ultimately,we summarize the main results and give an outlook of the future in this field.