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International Journal of Theoretical Physics

Quantum Entropy of a Four-Level Atom with Arbitrary Nonlinearities

A. A. Eied, Sadek Ahmed Hanoura, A.‐S. F. Obada

Published Apr 18, 2012• 16 citations
Publisher
DOI
10.1007/s10773-012-1160-4

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In this paper, we use the quantum field entropy to measure the degree of entanglement in the time development of a three-level atom interacting with two-mode fields including all acceptable kinds of nonlinearities of the two-mode fields. This model describes a very general situation in which the system admits two detuning parameters and includes an arbitrary form of the nonlinearity of the two modes. It is shown that when the individual modes of the field are detuned far from the intermediate atomic level, the dynamic Stark shift is induced by the nonlinear medium. The results show that the non-linearity effect yields the superstructure of atomic Rabi oscillations and changes the quasiperiod of the field entropy evolution and entanglement between the atom and the field. The general conclusions reached are illustrated by numerical results.
Abstract In this interferometry the geometrical phase, von-Neumann entropy, and non-classical features of a field interacting with a four-level moving atom in the presence of a Kerr medium were investigated. We highlight the influence of intensity-dependent coupling and energy dissipation to examine the temporal behavior of the geometrical phase, the statistical properties of the field as well as the von-Neumann entropy. The results show that the evolution of system dynamics, atomic von-Neumann entropy, and geometrical phase are strongly influenced by the Kerr medium, field mode structure, and atomic motion. Using empirically available parameters, we test this result, and many new items are discovered.
The interaction between a ♢\diamondsuit♢-type four-level atom and a single-mode field in the presence of Kerr medium with intensity-dependent coupling involving multi-photon processes has been studied. Using the generalized (nonlinear) Jaynes-Cummings model, the exact analytical solution of the wave function for the considered system under particular condition, has been obtained when the atom is initially excited to the topmost level and the field is in a coherent state. Some physical properties of the atom-field entangled state such as linear entropy showing the entanglement degree, Mandel parameter, mean photon number and normal squeezing of the resultant state have been calculated. The effects of Kerr medium, detuning and the intensity-dependent coupling on the temporal behavior of the latter mentioned nonclassical properties have been investigated. It is shown that by appropriately choosing the evolved parameters in the interaction process, each of the above nonclassicality features, which are of special interest in quantum optics as well as quantum information processing, can be revealed.