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Acta Physica Sinica

The entanglement character of two entangled atoms in Tavis-Cummings model

Shan Chuan-Jia, Yun‐Jie Xia, 曲阜师范大学物理工程学院，曲阜 273165

Published Jan 1, 2006• 43 citations
Publisher

Abstract

We investigate the entanglement time evolution of two entangled two-level atoms that interact resonantly with a single-mode field in the Fock state. The results show that the two-atom entanglement state appears with periodicity. The influence of the two-atom initial state, the dipole-dipole coupling intensity between two atoms, and the field in the Fock state on the entanglement degree of two atoms are revealed. Meanwhile the two-atom quantum state will forever stay in the maximum entangled state when the initial state is proper.

DOI
10.7498/aps.55.1585

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We investigate the entanglement time evolution of two entangled two-level atoms that interact resonantly with a single-mode field in the Fock state. The results show that the two-atom entanglement state appears with periodicity. The influence of the two-atom initial state, the dipole-dipole coupling intensity between two atoms, and the field in the Fock state on the entanglement degree of two atoms are revealed. Meanwhile the two-atom quantum state will forever stay in the maximum entangled state when the initial state is proper.
We investigated the entanglement time evolution of two entangled two-level atoms. The two atoms can undergo multiphoton transition when they interact resonantly with a single-mode field in the coherent state. The results show that the two-atom entangled state evolves periodicity. The influence of the two-atom initial state，the dipole-dipole coupling intensity between two atoms，the parameter of the coherent state and the number of the transitional photons on the entanglement degree of two atoms are revealed. When the initial state is a maximum entangled state，the state of the two entangled atoms will forever stay in this maximum entangled state. So this kind of entanglement state can be used for quantum information storage.
Considering the dipole–dipole coupling intensity between two atoms and the field in the Fock state, the entanglement dynamics between two atoms that are initially entangled in the Tavis–Cummings model with intrinsic decoherence have been investigated. The two-atom entanglement appears with periodicity without considering intrinsic decoherence. However, the intrinsic decoherence causes the decay of entanglement between two atoms, with the decrease of the intrinsic decoherence coefficient, the entanglement will quickly become a constant value, which is affected by the two-atom initial state, the dipole–dipole coupling intensity and the field in the Fock state. Meanwhile, the two-atom quantum state will stay forever in the maximal entangled state when the initial state is proper, even in the presence of intrinsic decoherence. Furthermore, the two atoms can generate maximal entangled state even if they are initially separated by adjusting the dipole–dipole interaction, the strong coupling can improve the value of entanglement.
Based on the entanglement degree of two subsystem which can be measured by the negative eigenvalues of the partial transposition matrix,time evolution of entanglement degree of two atoms in the Tavis-Cummings model,which is interacted with a field in the Fock state,is investigated by numerical methods.When these two atoms are initially prepared in mixed states,the results show that the field in the Fock state,the initial state of two-atom and the coupling constant between the field and the two-atoms have a dramatic influence on the time evolution character of entanglement degree of two atoms.
Considering the dipole-dipole coupling intensity between two atoms and the field in the Fock state, the entanglement dynamics between two atoms that are initially entangled in the system of two two-level atoms coupled to a single mode cavity in the presence of phase decoherence has been investigated. The two-atom entanglement appears with periodicity without considering phase decoherence, however, the phase decoherence causes the decay of entanglement between two atoms, with the increasing of the phase decoherence coefficient, the entanglement will quickly become a constant value, which is affected by the two-atom initial state. Meanwhile the two-atom quantum state will forever stay in the maximal entangled state when the initial state is proper even in the presence of phase decoherence. On the other hand, the Bell violation and the entanglement do not satisfy the monotonous relation, a large Bell violation implies the presence of a large amount of entanglement under certain conditions, while a large Bell violation corresponds to a little amount of entanglement in certain situations. However, the violation of Bell-CHSH inequality can reach the maximal value if two atoms are in the maximal entangled state, or vice versa.
The entanglement character between a two-level atom and a two-mode field as well as two-level atoms in the non-degenerate two photons Tavis-Cummings model in the resonance and non-resonance cases have been investigated, and the analytical expression about entanglement is obtained. Based on two kinds of initial states, the effects of field frequency, atomic frequency and dipole-dipole coupling between atoms on the entanglement are shown in detail. The cases of resonance and non-resonance are compared.
We investigate the Raman coupled model of two entangled Λ-type three-level atoms interacting with a two-mode quantized cavity field.With the negative eignevalues of the partial transposition matrix,we obtain the time evolution of entanglement between the two atoms.The results show that the entanglement of the two atoms displays periodicity;the evolution regular of entanglement is influenced by the initial state of two atoms and initial photon number of the cavity.For special initial state,the two-atom quantum state will stay in the maximum entangled state forever and have no relation with the initial photon number.Compared with Tavis-Commings model,the entanglement of the two atoms can live for much longer time in the proposed model.