Dynamics of Non-Gaussian Entanglement of Two Magnetically Coupled Modes

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 $k\in\left\lbrace 0,1,\cdots,n+m\right\rbrace$, $n$ and $m$ being two quantum numbers associated to the two oscillators. By studying the effect of the anisotropy $R=\omega_{1}^{2}/\omega_{2}^{2}$, $\omega_{c}$, 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.