Spontaneous Dynamics Of Spin Textures In Spinor Condensates

Spin dynamics of spinor condensate is a hot topic in the field of Bose-Einstein condensation.Recently,many nontrivial spin textures,i.e.,the local spins are inhomogeneous in space,have been imprinted on spinor condensates by spatially tailored magnetic fields.What is the fate of the created nontrivial spin texture and how to investigate theoretically the spontaneous evolution without any external driving? The spontaneous dynamics of spin textures in spin-1 condensates is investigated in this thesis.A spin texture corresponds to a certain spin wave function,which satisfies the GrossPitaevskii equation.The dynamics of a spin texture can be investigated by the corresponding spin wave function.Any initial pure spin state would be inevitably mixed with the other two components during the spontaneous evolution for a nontrivial initial spin texture.We first proved that a nontrivial spin texture should be described by the general spin wave function including all the three pure spin states by the means of short-time analysis and find that the source driving the evolution is just the nontrivial initial spin textures themselves.The complete hydrodynamic equations are then obtained analytically by the left projection of the spin-1 Gross-Pitaevskii equations with the three pure spin states,respectively.In addition,motivated by the recent experiments realized in a flat-bottomed optical trap,we studied the ground state of polar-core spin vortex of quasi-2D spin-2 condensate in a finitesized homogeneous trap plus a weak magnetic field.The exact spatial distribution of local spin is obtained.The effective spin-spin interaction is proportional to both the bare spin-spin interaction and the radius of the homogeneous trap,simultaneously.Thus the polar-core spin vortex we obtained can be easily controlled by the radius of the trap.