Topological Excitations Of Spinor Bose-Einstein Condensates

Motivated by the recent experiments realized in a flat-bottomed optical trap by two groups in 2015, we study the ground state of polar-core spin vortex of quasi-2D ferromagnetic spin-1 condensate in a homogeneous trap with a variational method. The exact spatial distribution of local spin is obtained in the ground state of polar-core spin vortex. Unlike the fully-magnetized planar spin texture with a zero-spin core,which was schematically demonstrated in previous studies, the spatial distributions of spin magnitude of the polar-core spin vortex we obtained emerge some platforms for the larger effective spin-dependent interaction. More importantly, the spin magnitudes of the platforms have an asymptotic value with the increase of the interaction, which is about 0.86 in our simulation, but not 1 as expected in the fully-magnetized spin texture. The effective spin-dependent interaction is proportional to the bare spin-dependent 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. If additional external magnetic field is applied, the asymptotic value of the platforms can be controlled by the quadratic Zeeman energy q, which decreases with the increase of q.In 2014,the Dirac monopole was observed experimentally by Ray et al in America with a ferromagnetic 3D spin-1 87Rb condensate driving by a space- and time-dependent magnetic field. A variational method is developed to investigate the dynamics of collective-mode excitations in spinor condensate driven by an inhomogeneous magnetic field. Specifically, for the spin-1 87Rb condensate in a space and time-dependent magnetic field, our results agree well with the most experimental observations,and predict certain probably interesting phenomena; such as the vortex line of the -1 atom-cloud is shot when the zero point of magnetic field adiabatically approaches the center of the condensate, and the center-of-mass of the condensate does not follow the zero point of magnetic field. Hopefully, our method can be extended to the similar dynamics for the other spinor condensates.