Dynamics Of Bose–Einstein Condensate In One-dimensional Optical Lattice Chain

In the recent years,the study for the dynamics and localization of Bose-Einstein condensate in optical lattices has attracted considerable attention both theoretically and experimentally.The parameters of the ultracold atomic system can be freely adjusted as needed,such as the atomic interaction can be controlled by adjusting the s-wave scattering length utilizing the Feshbach resonance technique,the depth and the lattice constant of the optical lattice potential can be manipulated by adjusting the strength and wavelength of the coherent laser beam.Thus,the manipulating for the ultracold atoms in optical lattices has become a popular topic.In this paper,we investigate the dynamics and localization of Bose-Einstein condensate in one-dimensional driven tilted optical lattices and two-leg ladder subject to an artificial magnetic field,rich phenomena are revealed.The paper is organized as follows:In the first chapter,the physical background of this paper and the interesting phenomena in optical lattices,including Bloch oscillations,Landau-Zener tunneling,self-trapping and solitons are introduced briefly.In the second chapter,we study the dynamics of Bose-Einstein condensate in driven tilted optical lattices by using variational approximation and numerical simulation.Rich phenomena are revealed,including diffusion,self-trapping,breather and soliton,which strongly depend on the atomic interaction,the amplitude of the modulation,the constant force and the phase difference between the Bloch oscillations and the drive.The critical conditions for the dynamical transition from diffusion to selftrapping and for the formation of the soliton are derived analytically.In addition,the phase diagrams of dynamic transitions are presented in full parameters space.We find that the dynamics of the system can be completely controlled by adjusting the constant force,the amplitude of the modulation and the phase difference between the Bloch oscillations and the drive.The results are confirmed by the direct numerical simulation of the full Gross–Pitaevskii equation.In the third chapter,we investigate the localization of Bose-Einstein condensate trapped in two-leg ladder in the presence of an artificial magnetic field via BoseHubbard model and discuss its abundant localized phenomena using variational approximation and direct numerical simulation.We show that this system displays a range of interesting localized phenomena,including self-trapping,soliton and breather.We find that these phenomena are related to the effects of the coupling of the atomic interaction,artificial magnetic flux,the coupling strength along the rungs,and the initial population difference of atoms between the two legs of the ladder.Furthermore,the critical conditions leading to the localized-delocalized transitions are given analytically by using the variational method,and the effects of these parameters on localization are intuitively demonstrated in the phase diagram.Finally,the results obtained via variational method are confirmed by the numerical simulations of the full discrete nonlinear Schr?dinger equation.Finally,the fourth chapter contains our main conclusions and outlooks for this field.