The Study Of Entanglement In Two-component Bosons System

At present,，there is currently an enormous effort underway to understand therich dynamics of interacting Bose systems.Among various problems are the propertiesof Bose-Einstein condensate in external ifelds,the Bose coherent effects of excitonsand polaritons in semiconductor microcavities,and the production of scatteredradiation due to interaction of the incident laser beam with vibrational modes of amedium.the generic ferture of interacting Bose systems is the formation ofBose-ifeld collective states with nonclassical statistical and lfuctuationproperties.Another prominent feature is an entanglement produced by the interactionbetween different system constituents,which is one of the most subtle and intriguingphenomena in nature.Nowadays,there is explosive activity in the study of theentanglement due to its potential usefulness in quantum teleportation,quantumcrypotgraphy,and,in general,in quantum information theory.This thesis mainly studies the two mode boson system Berry phase andentanglement. First, the bogoliubov transformation make:（H|^）=h（ω₁|-）c₁|^)⁺（c₁|^）+h（ω₂|-）（c₂|^）⁺（c₂|^）+hg₁（（c₁|^）⁺（c₂|^）⁺+（c₁|^）（c₂|^））+hg₂[（（c₂|^）⁺（c₂|^）⁺+（c₂|^）（c₂|^））-（（c₁|^）⁺（c₁|^）⁺+（c₁|^）（c₁|^））]Diagonalization, and pray for the approximate instantaneous eigen state and level, andthen ask the density matrix to evaluate the characteristics of the system, with thewigner function instead of density matrix, using the gaussian features introducedentangled state, discusses the choice with different initial state and coupling constantto control the Entanglement dynamics.（H|^）=h（ω₁|-）c₁|^)⁺（c₁|^）+h（ω₂|-）（c₂|^）⁺（c₂|^）+hg₃（（c₁|^）⁺（c₂|^）+（c₂|^）⁺（c₁|^））+hg₄[（（c₂|^）⁺（c₂|^）⁺+（c₂|^）（c₂|^））-（（c₁|^）⁺（c₁|^）⁺+（c₁|^）（c₁|^））]For the intrinsic state and level, and entanglement.