The Magnetic Property Of Ultra Cold Alkali Metal Atom

First of all, we mainly elaborate two methods, namely, quantum many-bodymethod and mean field method. These two kinds of methods play an importantrole in solving some ground state problem of Bose gas that interactions amongthem are weaker. And we introduce the methods about how to apply angularmomentum representation and particle number representation respectively toresearch the quantum properties of the ground state of F1spinor BEC. Thespinor BEC mixture formed by87Rb atoms and23Na atoms is spin11system.We extend representation transformation into this system. Then we use algebraicmethod to solve population distribution and fluctuation distribution of the wholesystem. We apply exact diagonalization to test the results we have get. We alsostudy the situation of system in external magnetic field.Second, we study the spin dynamics behavior of spinor BEC. Spindynamics is that spin exchange interaction is smaller than density interactionand we could only think about the distribution and evolution of inner spin part,spatial wave function is approximately impregnable. That is to say three kinds ofatoms could mix and share one and the same spatial wave function.If we add uneven magnetic filed to BEC system, the spin magnetic momentwill be obviously affected by magnetic filed gradient. We make use of gaugetransformation to study the effect of magnetic filed gradient. And we can get theoscillation behavior of the magnetization dynamics and how will the oscillationof the magnetization affect population distribution of the0component of theZeeman energy levels.