Abstract: New dynamics properties of the field and the atom with an intensity-dependent couplingLi Chun-Xian Directed by Fang Mao-FaIn the quantum optics field, the study of the quantum properties of the system of the field interacting with the atom has been always devoted to considerable attention. It is one of the most important contents for the quantum optics to study on the dynamics and non-classical properties of the interaction between the field and the atom in the Jaynes-Cummings model with an intensity-dependent coupling. In this paper, the new dynamics behaviors, of the atomic quantum information entropy squeezing and of the linear entropy and the phase of the field, are studied, and a series of significant results are obtained.In chapter 1, a simple history overview is presented of the interaction system with an intensity-dependent coupling between the field and the atom. With the Hamilto-nian of the interaction between the field and the atom with an intensity-dependent coupling, the evolution operator and the reduced density operators of the field and the atom are derived without taking the influence of the environment into account, then the basic work model without dissipation is established. The model has been generalized to the condition with dissipation, which is an effective work of mine, and the evolution equation of the density operator is present. The theories of the atomic quantum information entropy squeezing, the linear entropy and the Pegg-Barnett phase of the field are absorbed in the last of this chapter, which form the theoretical basic of the work in the following chapters.In chapter 2, the dynamics behaviors of quantum information entropy squeezingof the atomic dipoles are investigated without considering the dissipation from the environment. The influences of the atomic coherence and the intensity of the field on the quantum information entropy squeezing of the atomic dipoles are investigated in detail. The comparing the numerical results obtained from the uncertainty relation of Heisenberg (HUR) to those from the uncertainty relation of the quantum information entropy (EUR) proves the triviality of HUR with exact examples. The results show that the number of the squeezed atomic dipoles is decided by the coherence of the atom, the direction of the quantum information entropy squeezing is decided by the phases of the field and the atom, and the quantum information entropy squeezing is a precision tool for the squeezing of the atom, especially when the atom is in the eigenstates of the dipole operators.In chapter 3, the dynamics properties of the linear entropy of the field with the dissipation approximation are studied. The influences of the intensity of the field, the atomic distribution angle and the dissipation constant on the linear entropy of the field are investigated. With the dissipation approximation, the results show that if the dissipation constant is considerably small, the influence of the environment on the coherence of the field can be ignored; the larger the field's intensity is, the weaker the entanglement between the field and the atom, and the larger the degree of the mixture for the field; the more the atomic distribution angle tends to Tr/2, the larger the mixture degree of the field is, while the stronger the entanglement between the field and the atom.In chapter 4, With the dissipation approximation, the dynamics behaviors of the phase of the field are studied in terms of phase theory presented by Pegg and Barnett. The probability distribution of the phase and the phase fluctuation are discussed during the single photon process. The results show that, the stronger the field is, the more the probability of the phase centralized, and the larger the values of the peaks are; and because of the dissipation, the probability of the phase becomes equal everywhere and the fluctuation shrinks with time…

Key words: The Jaynes-Cummings model with an intensity-dependent coupling; Interaction between the field and the atom; The phase dynamics; The linear entropy dynamics; The squeezing effect; Entanglement and decoherence.

# New Dynamics Properties of the Field and the Atom with an Intensity-dependent Coupling

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