Dynamical and energetic instabilities of F=2 spinor Bose-Einstein condensates in an optical lattice

The dynamical and energetic instabilities of the F=2 spinor Bose-Einstein condensates in an optical lattice are investigated theoretically and numerically. By analyzing the dynamical response of different carrier waves to an additional linear perturbation, we obtain the instability criteria for the ferromagnetic, uniaxial nematic, biaxial nematic and cyclic states, respectively. When an external magnetic field is taken into account, we find that the linear or quadratic Zeeman effects obviously affect the dynamical instability properties of uniaxial nematic, biaxial nematic and cyclic states, but not for the ferromagnetic one. In particular, it is found that the faster moving F=2 spinor BEC has a larger energetic instability region than lower one in all the four states. In addition, it is seen that for most states there probably exists a critical value kc>0, for which k>kc causes the energetic instability to arise under appreciative parameters.