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Acta Physica Sinica

Entanglement evolution and Bell inequality violation of two atoms in Tavis-Cummings model with intrinsic decoherence

Guo De-Jun, Shan Chuan-Jia, Yun‐Jie Xia, (1)湖北师范学院物理系,黄石 435002; (2)曲阜师范大学物理工程学院,曲阜 273165

Published Jan 1, 2007• 4 citations
Publisher

Abstract

Considering the interaction between two two-level atoms and a single-model field, we find an exact solution of the Milburn equation for the system. We investigate the time evolution of the entanglement between the two atoms and the maximal violation of Bell-CHSH inequality. The influence of dipole-dipole interaction and detuning between the caving and the atom on the entanglement and Bell violation is discussed. The effect of dipole-dipole interaction between two atoms on the entanglement and Bell inequality violation is obvious; with the detuning increasing, the entanglement between two atoms and Bell inequality violation becomes larger and we find that the stationary value of the entanglement between two atoms only depends on the difference between the dipole-dipole coupling intensity and the detuning. The Bell inequality violation and the entanglement does not satisfy the monotonic relation, a large Bell inequality violation may correspond to a small amount of entanglement.

DOI
10.7498/aps.56.2139

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Acta Physica Sinica•Jan 1, 2006•43 citations
Considering the interaction between two two-level atoms and a single-model field, we find an exact solution of the Milburn equation for the system. We investigate the time evolution of the entanglement between the two atoms and the maximal violation of Bell-CHSH inequality. The influence of dipole-dipole interaction and detuning between the caving and the atom on the entanglement and Bell violation is discussed. The effect of dipole-dipole interaction between two atoms on the entanglement and Bell inequality violation is obvious; with the detuning increasing, the entanglement between two atoms and Bell inequality violation becomes larger and we find that the stationary value of the entanglement between two atoms only depends on the difference between the dipole-dipole coupling intensity and the detuning. The Bell inequality violation and the entanglement does not satisfy the monotonic relation, a large Bell inequality violation may correspond to a small amount of entanglement.
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.
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.
Considering the interaction between two-mode SU(1,1) coherence states and a two-level atom, we find an exact solution of the Milburn equation for the system. We investigate the time evolution of the entanglement of field-atom and one of two modes of field using the quantum-reduced entropy and quantum relative entropy, respectively. The influences of intrinsic decoherence and two-mode photon number difference on the evolution of the entanglement of field-atom and one of two modes of field are discussed. It is shown that the entanglement of field-atom reduces to a stationary value with time evolution and the entanglement between two modes increases to another stationary value with intrinsic decoherence, and the values only depend on the two-mode photon number and mean photon number.
The simple system of two atoms couple to single mode optical cavity with the phase decoherence is studied for investigating the entanglement and Bell violation between atoms and cavity or between two atoms. We show that in the resonance case (i) atom-field entanglement rapidly decays with phase decoherence and disappears in the stationary state, (ii) atom-atom entanglement is more robust against phase decoherence and survives in the stationary state. In the nonresonance case, the pairwise atom-atom and atom-field entanglement is sensitive to the detuning parameter and is not completely destroyed during evolution. On the other hand, violation of Bell-CHSH inequality is very fragile against the phase decoherence and finally disappears in the stationary state. The phenomenon that the more Bell violation, the less entanglement, or vice versa in such a realistic physical system, is revealed. This phenomenon maybe is the consequence of the choice of concurrence as the entanglement measure and the observables to build the Bell-CHSH inequality. The genuine three-partite entanglement is also analyzed by making use of the state preparation fidelity. It is shown that the genuine three-partite entanglement can appear in the evolution of the system even in the presence of the phase decoherence.
How the mean photon number,the probability of excited state and intrinsic decoherence coefficient influence the time evolution of entanglement is unknown,when a single-mode quantized optic field and a two-level atom coupling system is governed by Milburn equation.The Jaynes-Cummings model is considered.A lower bound of concurrence is proposed to calculate the entanglement.Simulation results indicate that the entanglement of system increases following the increasing of intrinsic decoherence coefficient or the decreasing of the mean photon number.Besides that,the entanglement of the system decreases,while the probability of the exited state increases from 0 to 0.1,and increases,while the probability of the exited state increases from 0.1 to 1.
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.