Bose-einstein Condensation Dynamics Research In The Presence Of The Quadratic Zeeman Effect

A view of the physics of spinor Bose-Einstein condensates (BECs) is presented.Mean-field ground states, Bogoliubov spectra, and many-body ground and excited states ofspinor BECs are discussed. Properties of spin-polarized dipolar BECs and those ofspinor-dipolar BECs are reviewed. Some of the particular features of the vortices in spinorBECs，such as fractional vortices and non-Abelian vortices, are all delineated. From thispaper, we can recieve exact one and superposition solution (SPS) solutions for the tripleGross-Pitaevskii (G-P) equations describing spin-1Bose-Einstein condensates by Hirotabilinear method. Moreover, their dynamics properties and images have been made by3Dtechnology. The main contests of this paper are as follow:First of all, we introduce the developing history of BEC and the formation of ideal gasBEC.Furthermore, we introduce the dynamics equation of BEC and provide the solitontheory including bright soliton and dark soliton.At last, present the introduction of the three components of G-P equation from Zeemaneffect of the energy level splitting. The Hirota bilinear method is applied to studying spin-1Bose-Einstein condensates which is describe by triple G-P equations. Finally, simulate thedynamic effect of the soliton solution by software of3D max, and to further analyze thecharacteristics of soliton solution.