Magnetic field induced dynamical instabilities in an anti-ferromagnetic spin-1 Bose-Einstein condensate

We theoretically investigate four types of dynamical instability, in particular the periodic and oscillatory type $I_O$, in an anti-ferromagnetic spin-1 Bose-Einstein condensate in a nonzero magnetic field, by employing the coupled-mode theory and numerical method. This is in sharp contrast to the dynamical stability of the same system in zero field. Remarkably, a pattern transition from a periodic dynamical instability $I_O$ to a uniform one $II{I}_O$ occurs at a critical magnetic field. All the four types of dynamical instability and the pattern transition are ready to be detected in ${}^{23}$Na condensates within the availability of the current experimental techniques.