Dynamics of Non-Gaussian Entanglement of Two Magnetically Coupled Modes

Abstract

This paper surveys the quantum entanglement of two coupled harmonic oscillators via angular momentum generating a magnetic coupling ${\omega }_c$. 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 ${\lambda }_k$ with $k\in \left\{0,1,\cdots ,n+m\right\}$, $n$ and $m$ being two quantum numbers associated to the two oscillators. By studying the effect of the anisotropy $R={\omega }_1^2/{\omega }_2^2$, ${\omega }_c$, 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 ${\omega }_c$ depends on $(n,m)$ and $R$. $(iii)-$ The periodic revival of entanglement strongly depends on the physical parameters and quantum numbers.

12 pages, 4 figures