Study On The High-order Effective Dynamics And The Induced Correlation For The Interaction Between Atom And Cavity Modes

The method using some approximation to give the effectiveHamiltonian is so normal that it can be applied to most of interactionsystems. As a particular example, Fr hlich transformation has thecharacteristics of clearness and conciseness comparing with otherapproximation, such as the adiabatic approximation. And thistransformation has been generalized to the field of quantum optics andatomic optics. Most of all, the dynamical effects, such as the interference,diffraction and phase transition are analyzed based on the2ndordereffective Hamiltonian. The coupling shows the form oftime-independence or the form of simple dependences on the time.Introduced by the effective dynamics is the quantum correlation, i.e. theinformation entropy. And one can find the condition for the maximallyentangled states by investigating the entanglement.The research of this thesis focuses on the higher order effectivedynamics and the information entropy for some typical interactions. Thecoupling between the atoms with the field is always dependent of time. That is because that the coupling is always connected with the coordinate,of course the coordinate connected with the time. We pay our attentionmainly on three interaction systems: the time-independent interactionbetween a single atom and a single field mode, the time-dependentinteraction between one atom and one field mode, also one atom andtwo-mode field. The entanglement entropies for the systems above areanalyzed. The results show that there are not a few coefficients dependenton the time. Most of the coefficients come from the integral relation ofthe coupling. The evolution and entanglement have the apparentdifference for the cases of time dependence and independence.