An Optical Lattice Spin Of Bec Superfluid-mott Insulator Phase Change

With the rapid development of experimental technique, the physical phenomena, Bose-Einstein condensation (BEC), has been realized in laboratories of several countries, which has not only testified Einstein's prophesy, but also has provided us with a new method to study the nature of low temperature dynamics of atoms and to know other low temperature physical phenomena.The fluctuating of a quantum system will cause the transition of it, but when the system is in a low temperature, the thermal fluctuating will no longer exist. However, according to Heisenberg's uncertainty relationship, the quantum fluctuating does exist, and as long as it is high enough, it will cause the transition of the quantum system, and a typical example is Superfiuity-Mott insulator (SF-MI) transition. Put ultracold bosons into optical lattices, and atoms will move among the optical lattices, which is called tunneling, and then superfluity is formed. When mutual action between atoms is smaller than that of tunneling, superfluity will be formed, and by raising the height of potential barrier, larger structure energy will be got, that is, the transition of Superfluity-Mott insulator will be realized.The thesis, mainly, studies Superfluity-Mott insulator (SF-MI) transition of ultracold spin-3 bosons in an optical lattice. Starting from Bose-Hubbard model of the system, we construct many-body symmetry states to describe eigenstates of the system and calculate matrix elements through the theory of second order perturbation, which modifies the ground state energy and gets the conditions of the transition of Superfluity-Mott and its phase diagrams. And therefore we get the boundaries that the system can realize Superfluity-Mott insulator (SF-MI) transition, and we also discover the rules that superfluity separates with different magnetic number of spin. In addition, we summarize the effect of the change of parameter towards superfluity area, which provides a theoretical instruction for detecting superfluity and superfluity component separation experimentally. The thesis is consisted of four parts. The first part is a brief introduction of the basic nature of Bose-Einstein condensation and the new development of its relevant research, including the realization of experiment and so on. The second part is an introduction of some familiar optical lattices and the recent development of Superfluity-Mott transition and Bose-Hubbard mold, including Bose systems of spin-2 and spin-3. The third part is an introduction of Superfluity-Mott transition of ultracold spin-3 bosons in an optical lattice, including the establishment of theory model, eigenstates, and the calculation of energy eigenvalues, as well as phase diagrams gained from perturbation theory. Finally, the phase diagrams are analyzed and the nature and rule are discussed. The last part of the thesis is a brief summary, and also shows the expectation of the future of this field.