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arXiv 2108.04129quant-ph
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两个磁耦合模的非高斯纠缠动力学

Dynamics of Non-Gaussian Entanglement of Two Magnetically Coupled Modes

Radouan Hab-arrih, Ahmed Jellal, Abdeldjalil Merdaci

摘要:

研究了两个耦合谐振子通过角动量产生磁耦合$ω_{c}$的量子纠缠。利用三种正则变换对相应的哈密顿量进行对角化,得到了相应的驻波函数。基于Schmidt分解,我们明确地确定了Schmidt模$λ_{k}$,其中$k\in\left\lbrace 0,1,\cdots,n+m\right\rbrace$,$n$和$m$是与两个振子相关的两个量子数.通过研究各向异性$ R=ω_{1}^{2}/ω_{2}^{2} $、$ω_{c}$、非对称性$ |n-m| $和动力学对纠缠的影响,我们得到如下结果。随着$ (i)- $的增加,纠缠变得很大。$ (ii)- $对$ω_c$的敏感性取决于$ (n,m) $和$R$。$ (iii)- $纠缠的周期性恢复强烈地依赖于物理参数和量子数。

英文摘要:

This paper surveys the quantum entanglement of two coupled harmonic oscillators via angular momentum generating a magnetic coupling $ω_{c}$. The corresponding Hamiltonian is diagonalized by using three canonical transformations and then the stationary wave function is obtained. Based on the Schmidt decomposition, we explicitly determine the Schmidt modes $λ_{k}$ with $k\in\left\lbrace 0,1,\cdots,n+m\right\rbrace$, $n$ and $m$ being two quantum numbers associated to the two oscillators. By studying the effect of the anisotropy $ R=ω_{1}^{2}/ω_{2}^{2} $, $ω_{c}$, asymmetry $ |n-m| $ and dynamics on the entanglement, we summarize our results as follows. $ (i)- $ The entanglement becomes very large with the increase of $ (n,m) $. $ (ii)- $ The sensistivity to $ω_c$ depends on $ (n,m) $ and $R$. $ (iii)- $ The periodic revival of entanglement strongly depends on the physical parameters and quantum numbers.

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