Spin-orbit Coupled Fermi-hubbard Model Characteristics Of The Fermi Atoms Loaded In Optical Ladder Lattice

The research of condensation of ultra-cold Fermi gas in recent years becomes very popular, so that many physicists are focused in this. The cold atoms to achieve spin-orbit coupling provides another window for a new field, so to explore further and unlock the mystery of this unknown world.In this paper, by using the density-matrix-renormalization-group(DMRG) algorithm in the software of Algorithms and Libraries for Physics Simulations(ALPS) and the most typical Hubbard model we simulate a model that is a strongly correlated system of ultra-cold Fermi gas in double-stranded optical-lattices, in which the state of phase separation has demonstrated.In chapter I, we describe the background knowledge of optical lattice, ultra-cold Fermi gas, Fashbach resonance technology and the progress now, and offer the presence of spin-orbit coupling of degenerate Fermi gas a detailed description.In chapter II, we elaborate the operation of ALPS software, and the installation and the peripheral program of ALPS are included as well. Since proper use of the software is based on a lot of knowledge of the computer, for many pages we describe the specific configuration steps to install the software in an Ubuntu system as well as the use of its peripheral program. Besides, we introduce the DMRG, which is the most efficient algorithm to simulate the one dimensional system. Some detailed development of this algorithm and its scope of application are introduced.In chapter III, in a frame of DMRG algorithm, we numerically calculate respectively the ground state properties of rejection Fermi gas in double-stranded structure optical lattice system, the particle number density, and the energy and polarization rate variation in system that exposed in a Zeeman field and spin-orbit coupling interaction. It is found that the system exhibits the spatial separation of a fully spin-polarized phase from the partially polarized phase for the suitable intensity of Zeeman field without the effect of spin-orbit coupled atoms. The spin-orbit-coupling drives fully spin-polarized phase to partially spin-polarized phase in the whole system. The spin-polarization of weakly and strongly repulsively interacting systems varies differently with spin-orbit interaction strength. The weakly hopping interaction can make the spin-orbit interaction system polarized, while with the hopping interaction becoming strongly the polarization disappeared. Consequently, the polarized spin density wave state appears in the center of Mott insulating region where the hopping strength and spin-orbit strength are skillfully adjusted.In chapter IV, a summarization is arranged and for a guiding purpose we carry on an outlook of the future study in this subject.