Solitons In Spin-orbit-coupled Bose-einstein Condensates

In recent years,the spin-orbit coupling effect of cold-atom system has attracted wide interest and widespread concern.Spin-orbit coupling,which closely linked two intrinsic properties of particles known as spin and orbital motion,has caused many important macroscopic and microscopic physical effect in condensed matter physics and atom molecule physics.Especially,the spin-orbit coupled Bose-Einstein condensate(BEC)in the cold-atom system was found in the experiment.Therefore,it is very important to study the soliton properties in this system to understand the basic properties of spin-orbit coupled BEC.This paper was divided into two parts to study the solitons of spin-orbit coupled BECs.In the first part,we investigated gap solitons in spin-orbit coupled BECs in bichromatic optical lattices and mainly focued the effect on the gap solitons by changing the depth of the secondary periodic potential trap.The gap solitons and linear Bloch waves were obtained by solving coupled Gross-Pitaevskii equation(GP equation)in bichromatic optical lattice.Linear stability analysis method has been employed to investigate the stability of gap solitons located in the first and second band gaps.The results proved that the periodic secondary potential trap depths had important effects on the stability of gap solitons.In the second part,the moving bright solitons of spin-orbit coupled BECs with weak attraction was studied when there was no external potential trap.By solving the coupled nonlinear Schr?dinger equation with the variational method and the imaginary time evolution method,two kinds of solitons(plane wave soliton and stripe solitons)were found in different parameter regions.Meanwhile,the influence of soliton speed on the structure of soliton and the effect of detuning between Raman beam and energy states of the atoms on spin polarization strength of the system were studied.Last,the soliton dynamics was also studied for various moving speed.