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 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 kinleftlbrace 0,1,cdots,n+mrightrbrace, n and m being two quantum numbers associated to the two oscillators. By studying the effect of the anisotropy R=ω₁²/ω₂², 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.