Entanglement evolution in an anisotropic two-qubit Heisenberg XYZ model with Dzyaloshinskii－Moriya interaction

doi:10.1088/1674-1056/19/5/050302

中国物理B ›› 2010, Vol. 19 ›› Issue (5): 50302-050302.doi: 10.1088/1674-1056/19/5/050302

Entanglement evolution in an anisotropic two-qubit Heisenberg XYZ model with Dzyaloshinskii－Moriya interaction

陈涛, 黄燕霞, 单传家, 李金星, 刘继兵, 刘堂昆

College of Physics and Electronic Science, Hubei Normal University, Huangshi 435002, China

收稿日期:2009-08-03 修回日期:2009-10-13 出版日期:2010-05-15 发布日期:2010-05-15
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No.~10904033), Educational Commission of Hubei Province (Grant No.~D20092204) and Natural Science Foundation of Hubei Normal University (Grant No.~2007D21).

Entanglement evolution in an anisotropic two-qubit Heisenberg XYZ model with Dzyaloshinskii－Moriya interaction

Chen Tao(陈涛), Huang Yan-Xia(黄燕霞), Shan Chuan-Jia(单传家), Li Jin-Xing(李金星), Liu Ji-Bing(刘继兵), and Liu Tang-Kun(刘堂昆)^†

College of Physics and Electronic Science, Hubei Normal University, Huangshi 435002, China

Received:2009-08-03 Revised:2009-10-13 Online:2010-05-15 Published:2010-05-15
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No.~10904033), Educational Commission of Hubei Province (Grant No.~D20092204) and Natural Science Foundation of Hubei Normal University (Grant No.~2007D21).

摘要/Abstract

摘要： This paper investigates the entanglement evolution of a two-qubit anisotropic Heisenberg XYZ chain in the presence of Dzyaloshinskii--Moriya interaction. The time evolution of the concurrence is studied for the initial pure entangled states $\cos \theta \left\vert 00\right\rangle +\sin \theta \left\vert 11\right\rangle $ and $\cos \phi \left\vert 01\right\rangle +\sin \phi \left\vert 10\right\rangle $ at zero temperature. The influences of Dzyaloshinskii--Moriya interaction $D$, anisotropic parameter $\varDelta$ and environment coupling strength $\gamma$ on entanglement evolution are analysed in detail. It is found that the effect of noisy environment obviously suppresses the entanglement evolution, and the Dzyaloshinskii--Moriya interaction $D$ acts on the time evolution of entanglement only when the initial state is $\cos \phi \left\vert 01\right\rangle +\sin \phi \left\vert 10\right\rangle $. Finally, a formula of steady state concurrence is obtained, and it is shown that the stable concurrence, which is independent of different initial states and Dzyaloshinskii--Moriya interaction $D$, depends on the anisotropic parameter $\varDelta$ and the environment coupling strength $\gamma$.

Abstract: This paper investigates the entanglement evolution of a two-qubit anisotropic Heisenberg XYZ chain in the presence of Dzyaloshinskii--Moriya interaction. The time evolution of the concurrence is studied for the initial pure entangled states $\cos \theta \left\vert 00\right\rangle +\sin \theta \left\vert 11\right\rangle $ and $\cos \phi \left\vert 01\right\rangle +\sin \phi \left\vert 10\right\rangle $ at zero temperature. The influences of Dzyaloshinskii--Moriya interaction $D$, anisotropic parameter $\varDelta$ and environment coupling strength $\gamma$ on entanglement evolution are analysed in detail. It is found that the effect of noisy environment obviously suppresses the entanglement evolution, and the Dzyaloshinskii--Moriya interaction $D$ acts on the time evolution of entanglement only when the initial state is $\cos \phi \left\vert 01\right\rangle +\sin \phi \left\vert 10\right\rangle $. Finally, a formula of steady state concurrence is obtained, and it is shown that the stable concurrence, which is independent of different initial states and Dzyaloshinskii--Moriya interaction $D$, depends on the anisotropic parameter $\varDelta$ and the environment coupling strength $\gamma$.

Key words: Heisenberg model, entanglement evolution, decoherence, Dzyaloshinskii--Moriya interaction

中图分类号: (Quantized spin models, including quantum spin frustration)

75.10.Jm

75.30.Gw (Magnetic anisotropy) 75.30.Et (Exchange and superexchange interactions) 03.65.Ud (Entanglement and quantum nonlocality)

陈涛, 黄燕霞, 单传家, 李金星, 刘继兵, 刘堂昆. Entanglement evolution in an anisotropic two-qubit Heisenberg XYZ model with Dzyaloshinskii－Moriya interaction[J]. 中国物理B, 2010, 19(5): 50302-050302.

Chen Tao(陈涛), Huang Yan-Xia(黄燕霞), Shan Chuan-Jia(单传家), Li Jin-Xing(李金星), Liu Ji-Bing(刘继兵), and Liu Tang-Kun(刘堂昆). Entanglement evolution in an anisotropic two-qubit Heisenberg XYZ model with Dzyaloshinskii－Moriya interaction[J]. Chin. Phys. B, 2010, 19(5): 50302-050302.

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Entanglement evolution in an anisotropic two-qubit Heisenberg XYZ model with Dzyaloshinskii－Moriya interaction

Entanglement evolution in an anisotropic two-qubit Heisenberg XYZ model with Dzyaloshinskii－Moriya interaction

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