非马尔科夫环境中各向异性海森堡自旋链的量子失协

doi:10.19596/j.cnki.1001-246x.8393

摘要/Abstract

摘要：

利用量子失协方法研究在非马尔科夫环境中具有时变磁场的两比特各向异性海森堡XYZ模型量子失协的动力学演化。海森堡XYZ系统的初始态为最大纠缠态 $\left|\psi_{A B}\right\rangle=(1 / \sqrt{2})(|11\rangle+|00\rangle)$ , 利用非马尔科夫量子态扩散方法解析求解非马尔科夫主方程, 得出系统的约化密度矩阵; 然后代入量子失协公式得出系统量子失协的演化动力学。讨论自旋耦合强度、环境关联系数γ和余弦磁场强度B对量子失协动力学的影响。研究发现: 当环境关联系数γ较小时, 系统的量子失协明显呈现上升趋势, 因此可以表明非马尔科夫环境具有增加系统量子失协的作用。同时较大的自旋耦合系数J和J_Z以及余弦磁场强度B也具有增加系统量子失协的作用。

关键词: 非马尔科夫量子态扩散方法, 量子失协

Abstract:

We study dynamical evolution of quantum discord of a two-bit anisotropic Heisenberg XYZ model in a cosine magnetic field using a quantum discord method. With the maximum entangled state $\left|\psi_{A B}\right\rangle=(1 / \sqrt{2})(|11\rangle+|00\rangle)$ as the initial state of the Heisenberg XYZ spin chain, the non-Markovian master equation is solved analytically with the non-Markovian quantum state diffusion method and the reduced density matrix of anisotropic Heisenberg XYZ is obtained; Then we bring it into the quantum discord formula to derive evolution dynamics of quantum discord of the system. It is found that as the environmental correlation coefficient γ is small, quantum discord of the system obviously shows an upward trend. It shows that the non-Markovian environment has a positive effect on the quantum discord of the system. Greater spin coupling coefficient J, J_Z and cosine magnetic field intensity increase the quantum discord as well.

Key words: non-Markovian quantum state diffusion method, quantum discord

唐诗生, 艾合买提·阿不力孜. 非马尔科夫环境中各向异性海森堡自旋链的量子失协[J]. 计算物理, 2022, 39(2): 165-172.

Shisheng TANG, AHMAT Abliz. Quantum Discord of Heisenberg XYZ Spin Chain in Non-Markovian Environment[J]. Chinese Journal of Computational Physics, 2022, 39(2): 165-172.

图/表 5

图1 不同环境关联系数γ下，量子失协的时间演化(其他参数J=4, JZ=0.1, β=0, B=0.1, ω=0.6。)

Fig.1 Time evolution of quantum discord with different environmental correlation coefficient γ (Other parameters are J=4, JZ=0.1, β=0, B=0.1, ω=0.6.)

图2 不同自旋耦合系数J下，量子失协的时间演化(其他参数JZ=0.1, β=0, B=0.1, ω=0.6, γ=0.1。)

Fig.2 Time evolution of quantum discord with different spin coupling coefficient J (Other parameters are JZ=0.1, β=0, B=0.1, ω=0.6, γ=0.1.)

图3 不同自旋耦合系数JZ下, 量子失协的时间演化(其他参数J=2，β=0，B=0.1，ω=0.6，γ=0.1。)

Fig.3 Time evolution of quantum discord with different spin coupling coefficient JZ (Other parameters are J=2, β=0, B=0.1, ω=0.6, γ=0.1.)

图4 不同XY面上, 各向异性参数β作用下, 量子失协的时间演化(其他参数J=4, JZ=0.1, B=0.1, ω=0.6, γ=0.1。)

Fig.4 Time evolution of quantum discord with different anisotropic parameters β on the XY surface (Other parameters are J=4, JZ=0.1, B=0.1, ω=0.6, γ=0.1.)

图5 不同时变磁场强度B下, 量子失协的时间演化(其他参数J=2, JZ=0.1, β=0，ω=0.6, γ=0.1。)

Fig.5 Time evolution of quantum discord with different time-varying magnetic field intensity B (Other parameters are J=2, JZ=0.1, β=0, ω=0.6, γ=0.1.)

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