Spin-Orbit Coupled Dynamics of Ferromagnetic Spinor Bose-Einstein Condensate

Abstract

In this paper, we investigate the dynamic properties of spin-orbit coupling spin-1 ferromagnetic Bose-Einstein condensates with different trap geometry. Our results are obtained in terms of the threecomponent Gross-Pitaevskii equation of mean-field theory. Two kinds of trap potential are discussed: isotropic and anisotropic. It is shown that the spin-exchange dynamics are greatly influenced by trap geometry. For the latter with weak spin-orbit coupling strength, we find that the three-component oscillation accelerates and some small difference emerges between component m = 1 and m = −1. With the increase in spin-orbit coupling strength, the three components reach almost the same population. In addition, the kinetic energy of the system changes within a small scope for strong spin-orbit coupling, as opposed to a constant value in an isotropic trap. The density distributions display that the stripe phase appears with the increase in spin-orbit coupling strength. The method of generating stripe structure is different from the ground state of ferromagnetic condensate. For isotropic trap, the spatial separation of top and bottom spin-orbit condensates in component m = 1 and m = −1 occurs at weak spin-orbit coupling, and square lattice appears at strong spin-orbit coupling.