The Bloch Oscillations Of Bose-Einstein Condensate In Optical Lattices And Degenerate Fermi Gases

In this thesis, we mainly discuss the Bloch oscillations of two-component Bose-Einstein condensates in spin-dependent optical lattices and degenerate Fermi gases.Firstly, starting from the optical Bloch equations of quantum optics, we deduce the optical potentials of the Multi-level atom, i.e. the optical lattices, in the standing wave by eliminating the excited states adiabatically. Based on this, the atomic forces and Sysphus cooling are introduced. For designing atomic potentials, we give an experimental advance about spin-dependent optical lattices, which further provide an important theoretical evidence for studying the Bloch oscillations of two-component Bose-Einstein condensates.After doing this work, we discuss the Bloch oscillations of two-component Bose-Einstein condensates in spin-dependent optical lattices in detail. For the atoms moving in the tilted potentials given by the sum of the gravitational potential and the laser field, utilizing the collective-parameter method and introducing a Gaussian wave function including four parameters, we obtain the equations of motion for the variational parameters through ignoring the nonlinear Landau-Zener tunnelling. By discussing the influence of the intercomponent atom interaction on the system, we draw the following conclusion: accelerated breakdown of the Bloch oscillations and revival phenomena are found respectively for the repulsive and attractive case;for both cases, the system will finally be set in a quantum self-trapping state due to dynamical instability.Feshbach resonance and optical lattice provide a well background for studying degenerate Fermi gases. In the third part, above all, the essential principle about Feshbach resonance is introduced. Moreover, we briefly show how to change the reciprocity among the atoms by adjusting the magnetic field. The experimental and theoretical researches are at drawn. Due to the different statistic properties between the fermionic and bosonic atoms, there exhibits many novel physical effects. For the repulsive case, the fermionic atoms will form molecules, while for the attractive case, the two atoms will compose a Cooper pair, which can be researched using the BCS theory. Based on it, we study the energy gap and the collective excited modes of the degenerate Fermi gases. Finally, the effective Hamiltonian, which describes the degenerate Fermi gases inthe optical lattices, is studied briefly. Studying the experiment of the Esslinger's group, the multi-band Fermi-Bose-Hubbard Hamiltonian is introduced. It can be reduced to a Hamiltonian of XXZ model for strongly confining limit.