The Dynamics Of Spinor Bose-Einstein Condensates In An Optical Lattice

With the realization of Bose-Einstein condensates(BECs) and the maturation of laser cooling technology,it becomes easier to investigate the macroscopic quantum phenomena of BECs in artificial crystals(optical lattices).On the one hand,we can mimic the dynamics of electrons in the crystal lattices on macroscopic level by BECs in optical lattices.On the other hand,we can research the effects of nonlinearity of atom optics and other nonlinear physics by BECs because of its intrinsic nonlinearity. When the spin of atoms is considered,the atomic BECs in optical lattices will show more interesting phenomena.The dynamics of scalar BECs in optical lattices can be governed by effective-mass equation,which is similar to the electron in solid crystal lattices.When the sign of effective-mass is changed,the dynamics of scalar BECs in optical lattices is different from that of scalar BECs' without optical lattices.For these reasons,this thesis investigates the dynamics of spinor BECs in an optical lattice.We get the effective-mass equation of spinor BECs in the optical lattice by applying the effective-mass or multiple scales methods and then numerically analyze it.First of all,we investigate the dynamics of spinor BECs.It is found that the evolution of different components of BECs is decided by the pair interaction coefficients and sign of effective-mass.When the sign of effective-mass is different, the wave packets of spinor components may be unstable and subject to collapse or expand.Next,we study the levitation of spinor BECs in present of gravity field.The result implies that the spinor components of BECs in the optical lattice would levitate for the negative effective-mass,which is similar to scalar case.The numerical results show that the levitation of different components in spinor BECs are similar.Moreover, the changing of the pair interaction coefficients don't affect the levitation of spinor BECs. In the thesis,the concept of effective-mass is applied in the motion of spinor Bose-Einstein condensates.Ferromagnetism and aitiferromagnetism of spinor Bose-Einstein condensates bear new characters in the picture of effective-mass.