In this study, our goal is to obtain the entanglement dynamics of trapped three-level ion interaction two laser beams in beyond Lamb-Dicke parameters. Three values of LDP, η=0.09, η=0.2 and η=0.3 are given. We used the concurrence and the negativity to measure the amount of quantum entanglement created in the system. The interacting trapped ion led to the formation of phonons as a result of the coupling. In two quantum systems (ion-phonons), analytical formulas describing both these measurements are constructed. These formulas and probability coefficients include first order terms of final state vector. We report that long survival time of entanglement can be provided with two quantum measures. Negativity and concurrence maximum values are obtained N = 0.553 and for LDP = 0.3. As a similar, the other two values of LDP are determined and taken into account throughout this paper. For a more detailed understanding of entanglement measurement results, “contour plot” was preferred in Mathematica 8.
Quantum correlations and entanglement in identical-particle systems have been a puzzling question which has attracted vast interest and widely different approaches. Witness formalism developed first for entanglement measurement can be adopted to other kind of correlations. An approach is introduced by Kraus \emph{et al.}, [Phys. Rev. A \textbf{79}, 012306 (2009)] based on pairing correlations in fermionic systems and the use of witness formalism to detect pairing. In this contribution, a two-particle-annihilation operator is used for constructing a two-particle observable as a candidate witness for pairing correlations of both fermionic and bosonic systems. The corresponding separability bounds are also obtained. Two different types of separability definition are introduced for bosonic systems and the separability bounds associated with each type are discussed.
The evolution properties of quantum entropy of the field in the Fock state interacting resonantly with a pair of identical two-level entangled atoms in Bell states are studied by utilizing of the complete quantum theory and by the numerical method.The evolution periodicity of quantum field entropy is π/g2(2n+1)～1/2when the two atoms are initially in the first kind of Bell state.The quantum entanglement between the field and the atoms decreases with the increase of the initial field intensity,and the field is completely disentangled from the atoms when the time is a whole-number multiple of the evolution peridicity.The quantum field entropy isn't change with the time and always remains at zero when the two atoms are initially in the second kind of Bell state.The evolution curves of quantum field entropy periodically oscillates with unequal amplitude when the two atoms are initially in the third and the fourth kind of Bell state respectively,and the periodicity of the oscillation of the quantum field entropy increases with the increases of the initial photon number,while the amplitude of the oscillation decreases.The Bell states composed of a pair of identical two-level atoms can be partially distinguished based on the evolution properties of quantum field entropy above.