Investigations Of Pair Correlation In Quantum Lattice Physics

In recent years there is a great interest in the physics of degenerate quantum gases and low-energy few-body scattering due to the recent experimental advances in manipulation of ultra-cold atoms by light. Especially an almost perfect artificial periodic potentials called optical lattice can be generated. The lattice spacing is determined by the wavelength of the laser field employed and the angle between the pair of laser beams. The gaps between different bands depends on the lattice depth. All these parameters can be adjusted with high precision. This flexibility allow us to explore different regimes from "free-electron" picture in shallow trapping potential to tight-binding regime in deep trapping potential, in particular the single-band approximation widely used in condensate matter physics can be implemented accurately. Furthermore the Feshbach resonance technique can vary the scattering properties between atoms arbitrarily, which enhance this controllability greatly. The works in my thesis were mainly concentrated on the repulsive atomic bound-pair and quantum phases of Bose lattice gas within the extended Bose-Hubbard model with pair-tunneling.First we derived a complete two-particle solution of one-dimensional periodical potential with scattering state and bound state solution included. It was found that energy spectrum of the bound pair is drastically reshaped due to the pair-hopping term. On some conditions there exist two bound-pair solutions for the two-body system. Furthermore the spatial and momentum distributions of relative wave-function of the bound-pair was discussed in detail.Secondly we investigated the strong correlated lattice Bose gases on a lattice with pair tunneling. The excitation spectrum and the depletion of the condensate of lattice Bose gases are investigated using Bogoliubov transformation method and we find there exists pair-condensate as well as single particle condensate. The various possible quantum phases such as Mott-insulator phase, superfluid phase of individual atom, charge density wave phase, supersolid phase, pair-superfluid and pair-supersolid phase are discussed in different parametric regions within our extended Bose-Hubbard model using perturbation theory.