Spin Dynamics Of Spinor Bose-einstein Condensates

Recently, a geometric Hall effect was observed in a spinor Bose-Einstein condensate in a time and space-dependent magnetic field. In the experiment, a pancake-shaped 23 Na condensate is prepared in a spacedependent magnetic field. The motion of the condensate in one direction driving by the translational oscillations of the magnetic field in this direction followed by the motion in its perpendicular direction due to the coupling arising from the non-homogenous magnetic field. For the resonance driving frequency, a circular motion of the center-of-mass with almost zero ellipticity was developed for certain driving time. In addition, they observed over 100 quantized vortices when the condensate circulated.The variational approach has been shown to be an efficient method to describe the dynamics of Bose-Einstein condensate. It has been used to study the breather mode and scissor mode [8] of the spinless condensate. Very recently, the dipole mode of a spin-orbital coupling condensate is investigated with this approach. We numerically simulate the dynamics of 23 Na condensate in a time and space-dependent magnetic field with a variational approach. It is shown to be an efficient method to describe the complex dynamics of the system. Our results agree with the experimental observations of Choi et al.. We reproduce quantitatively the geometric Hall effect. We also find that the condensate demonstrates a scissor-mode-like motion, which may play the shearing force to deform the condensate and consequently lead to the dynamical nucleation of quantized vortices.