Quench Dynamics Of Bosons In Mott Insulator States

The optical lattice generates a vivid simulation of the solid lattice environment.Cold atoms trapped in optical lattices can be described by the standard Hubbard model.Various kinds of extended Hubbard model are proposed with the successive development of theory and experiment.Especially the trapping and cooling of chromium atoms and hetero-nuclear molecules with large dipole moment have been realized in experiments.It provides an ideal platform for the study of many body systems with dipolar interaction.In this thesis we mainly study the quench dynamical evolution in Mott Insulator of the Boson-Hubbard model with dipole-dipole interaction.We first introduce the development of optical lattice and some related experiments of cold atoms as well as the Boson-Hubbard model.On this basis we analyze the characteristics of the Superfluid state,Mott-Insulator state and phases transition between them.In the Mott Insulator state,the particle-hole pairs are of great importance in the dynamics of quantum correlation.Dynamics problems of two kinds of parameters of the quench in the system of optical lattice are presented through two different analytical methods when the particle-hole pairs appear,i.e.the propagation of density correlations using.Jordan-Wigner transformation and Bogoliubov transformation,and a novel collapse and revival(CR)oscillation and change of visibility for quenched Mott states by means of the strong-coupling expansion and perturbation theory.On this basis,we calculate the dynamical evolution of the quenched Mott-insulator states in one-dimensional Bose Hubbard system with dipolar interaction.Compared with the standard Bose-Hubbard model,the amplitude and period of the evolution of the momentum distribution increase with the dipolar interaction and the phenomenon of collapse and revival appears.The time-dependent visibility exhibits periodic oscillation,the period of which increases linearly with the increase of the dipole interaction.In addition,we also study the influence of the dipole interaction on the Mott-Superfluid phase transition by the parity correlation functions.