Quantum Phase Transition Of Ultracold Atoms In Inhomogeneous Optical Lattice

Since Bose-Einstein was achieved,ultracold atomic physics has become one of the most popular research fields.It is an important subject in condensed matter physics and atomic physics,as its potential and wide applications in atom interferometers,cold atomic clocks,quantum computer and so on.After the quantum phase transition from superfluid to Mott-insulator of ultracold atoms in an optical lattice was predicted and demonstrated,scientists have made a lot of researches on unknown quantum phases in these systems.Employing the generalized Bose-hubbard model,we study the ground state of ultracold bosons in homogeneous optical lattices,in which the heterogeneity of optical lattices,including an extra harmonic potential and uneven repulsive interactions between atoms on different lattice sites.Based on the mean-field approximation and numerical diagonalization method,we calculate some parameters charactering the ground state properties,such as,the average number of particles and the order parameter.It is turned out that the Mott-insulator phase and the superfluid phase coexist in these inhomogeneous optical lattices.This paper consists of five chapters:Chapter 1 introduces the basic concepts and development of Bose-Einstein condensates.Two major experiment technologies,i.e.,atomic cooling and trapping technology as well as Feshbach resonance technology,are reviewed in detail.Furthermore,we briefly outline the theoretical foundation of Bose-Einstein condensation,i.e.,the mean-field theory and Gross-Pitaevskii equation.Chapter 2 describes the properties and achievement of optical lattice,the concepts about quantum phase transition and Bose-hubbard model.Chapter 3 studies quantum phase transition for cold bosonic atoms in an square optical lattice with an extra harmonic trapping.First of all,the Hamiltonian of the system is derived.Moreover,we get the single lattice Hamiltonian through the mean-field theory.Finally,we obtain the ground state by the numerical diagonalization method and analyze the phase diagram and the average number distribution.We find that the Mott-insulator phase and the superfluid phase simultaneously appear in the inhomogeneous optical lattice.Chapter 4 studies the quantum phase transition of cold bosonic atoms in an square optical lattice with inhomogeneous atomic interactions.The applied method is similar to previous chapter,we get single lattice Hamiltonian by means of mean-field approximation and further solve the Hamiltonian with the numerical diagonalization method to obtain the ground state,and discuss the phase diagram and the average number distribution.We find that the Mott-insulator phase and the superfluid phase simultaneously appear in the optical lattice with inhomogeneous atomic interactions.Chapter 5 concludes the thesis and presents a future outlook.