Quantum Phase Transition And Correlation Property In Optical Superlattice

Optical lattice generates a vivid simulation of the solid lattice environment, as well as provides a carrier for various models formed by fermions and bosons. The physical behavior of particles in optical lattice can be described by the Boson-Hubbard model, while the study of phase transition of superfluid Mott insulator is critical to the quantum manipulation. In this thesis we calculate the Superfluid-Mott-Insulator phase transition in the Boson-Hubbard model under the single-site and multi-site mean-field theory respectively, showing the priority of the latter. The phase transition in Hubbard model with anyons in the1D lattice depends on the phase angle. We continue with the calculation of the phase boundaries of bosons trapped in1D superlattice, according to the multi-site mean-field theory as well as exact diagonalization and perturbation theory. The phase diagrams exhibit rich structure for various values for the ratio of tunneling coefficients and the offset in the unit cell. Finally we focus on the correlation property of the particle-hole pairs in the Mott-insulator phase in both homogeneous optical lattice and the two-well-period superlattice. The correlated particle-hole pairs can be detected by the in-situ single-site imaging technique.