Dynamics Of Wave Packet In Bose-einstein Condensates With Engineered Dispersion

In recent years,ultracold atoms have been recognized as an important platform for studying macroscopic quantum states and quantum effects of matter,with the development of experimental technologies.Ultracold atoms have characteristics of high purity,high tunability,and long coherence time,which have important applications in quantum simulation,quantum metrology,and quantum information science.Dynamical phenomena are research hotspots in ultracold atomic physics all the time.Various dynamical phenomena have been revealed in Bose-Einstein condensates,such as Bloch oscillation,Landau-Zener tunneling,Josephson effect,atomic squeezed state,the transition from superfluid state to Mott insulator state,and matter-wave solitons.The research on dynamics in quantum gases requires quantum control technologies.Optical lattice and synthetic spin-orbit coupling are two widely used methods.On the one hand,atoms can be trapped in periodically optical fields,so that periodic lattice environments in solids can be simulated.Compared with crystal lattices,optical lattices have large periodicity and parameter adjustment ranges,which provides a convenient route to simulating solid materials and studying transport dynamics in lattices.On the other hand,the realization of the synthetic spin-orbit coupling in cold atoms makes it possible to simulate the behaviors of charged particles in electromagnetic fields.This provides a new route to study and understand electron motions in materials and properties of topological insulators.In both two systems,the dispersion can be engineered,which serves as a powerful tool for the study of dynamics in the evolution of wave packets.In this thesis,we study some interesting and even counterintuitive macroscopic quantum phenomena in wave packet dynamics of cold atoms,such as self-interference of wave packet,self-trapping phenomenon in repulsive nonlinear systems,and a new method for generating gap solitons in spin-1 spin-orbit coupled Bose-Einstein condensates.Firstly,we theoretically analyze self-interference phenomena in the free evolution of wave packet in both optical lattices and spin-orbit coupled Bose-Einstein condensates,in which the interactions between particles are absent.Positive and negative effective mass regions exist in the linear dispersion spectra of both the two systems,which play a key role in wave packet evolution.We find that self-interfering wave packet can be observed when the initial wave packet occupies both the negative-and positive-mass regions.Furthermore,different initial states have a significant impact on the interference pattern in the evolution of wave packet.Secondly,dynamics in an interacting boson gas loaded in an optical lattice are studied.In such a system,the wave packet can stop expanding after a period of evolution,while most particles are arrested in the region around the initial location of the wave packet where stable boundaries are formed on both sides.This phenomenon is the so-called self-trapping.At present,the research on this phenomenon is mainly in the periodic optical lattice system.We believe that this phenomenon is related to the existence of nonlinearity and negative effective mass region.There are also positive and negative effective mass regions in the linear spectrum of the multi-well structure of spin-orbit coupled Bose-Einstein condensates,and it is aperiodic,which is different from the optical lattice system.By comparing the evolution of wave packets in the two systems,we find a similar self-trapping phenomenon in the spin-orbit coupled Bose-Einstein condensates system,only with a different lifetime.On the one hand,the duration of the self-trapping phenomena increases when the number of components increases in spin-orbit coupled systems,on the other hand,a larger positive nonlinearity will repel more particles out of the self-trapping region and eventually leads to the collapse of self-trapping.We think that the periodic structure of optical lattice is not the influencing factor of self-trapping and this phenomenon is closely related to the existence of nonlinear and negative effective mass regions.Finally,we find a new method to generate gap solitons in spin-1 spin-orbit coupled Bose-Einstein condensates.Gap structure exists in the dispersion of a spin-orbit coupled Bose-Einstein condensate.During the expansion of atoms,some atoms are pushed into the band gap by the repulsive interaction.The balance between the nonlinearity and dispersion can produce a moving gap soliton.Abundant soliton dynamics can be observed by tuning system parameters such as nonlinear interactions and the detuning between Raman lasers.