Spin Squeeing In Dicke Model In Thermodynamic Limit

Dicke model is an important model for studying the quantum phase transition.It is thought to have important applications in quantum information and quantum measurement in future.In this thesis,we studied the Dicke model,and the main research contents are as follows:the influence of the photon-photon interaction term on the quantum phase transition in the Dicke model is considered.In thermodynamic limit,we analysis the change of the eigen energy of the upper and lower polaritons in Dicke model as the coupling intensity with light and atom.We found the eigen energy of the lower polariton becomes zero at the critical coupling strength,which is thought to be one of the important signs of quantum phase transition.In thermodynamic limit,the atom spin squeezing coefficient is calculated analytically,and the spin squeezing coefficient can be used as an identical point to the superradiant phase transition.The phase transition point increases as the increase of the intensity of photon-photon acting intensity.We found that the degree of squeezing increases with the increase of photon-photon acting intensity.We discuss atom spin squeezing properties in Dicke model.Different from the thermal fluctuation of classical phase transitions,quantum phase transitions are normally identified by the critical behavior of quantities.We study the process of superradiation quantum phase transition and the squeezing spin states as the increase of the coupling strength between bosons and atoms.The structure of this paper is as follows:in chapter one,we review the various quantum states of Bose-defined field,such as vacuum state,Fock state,coherent state,squeezed state.In chapter two,we briefly introduce the definition of atomic squeezing spin state which is the basis of quantum measurement.In chapter three,we give the numerical solution of the Dicke Hamiltonian(DH).For finite but enough large number of atoms,parity of DH is conservative,the ground state of DH is non degenerate,and since light field coherent states of particles consistent with a Poisson distribution,the maximum of the number of particles in coherent state can take a finite one and It can be used for two dimensional lattice basic vector space representation of Hilbert.In the vicinity of the critical coupling region,the fluctuations(variance)decrease,and the transition of non classical squeezed quantum states.As the increase of coupling strength,states of light and atoms evolve into two subsystems mixed states.become highly mixture.Chapter IV as the core of this paper,we first review the superradiation quantum phase transition,analytic method of Dicke model to deal with the thermodynamic limit is given,and analyzed the photon intensity D from different values,influence on the spin squeezing,the D value is greater,the spin squeezing is more obvious.