Dynamics of Non-Gaussian Entanglement of Two Magnetically Coupled Modes

TL;DR

This paper investigates how the quantum entanglement between two coupled harmonic oscillators varies dynamically with system parameters, revealing conditions for large entanglement and periodic revivals.

Contribution

It provides an explicit analysis of non-Gaussian entanglement dynamics in magnetically coupled oscillators using canonical transformations and Schmidt decomposition.

Findings

Entanglement increases with higher quantum numbers (n,m).

Sensitivity to magnetic coupling depends on quantum numbers and anisotropy.

Entanglement revival periods are influenced by physical parameters and quantum states.

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 $k\in\left\lbrace 0,1,\cdots,n+m\right\rbrace$, $n$ 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.