Entanglement of Coupled Harmonic Oscillators without and with Tunneling Effect and Correction Factor

Abstract

Seeing its simplicity of processing, the system of two coupled harmonic oscillators have witnessed a quick growth of research conducted to quantum information. This approach is explicitly investigated in this paper, in particularly entanglement concept is proved to be intimately related to the tunneling effect. We examine analytically entanglement dynamics by introducing the Lewis and Riesenfeld invariant operator in the Heisenberg picture approach to compute the density matrix on the based of an exact treatment. We use Wigner function of the mixed state as an essential tool to move to linear entanglement entropies and we compute the corresponding correction factor. We follow numerically the evolution of entanglement dynamics without and under tunneling through the quantum potential barrier by introducing two particular models between simple and damped coupled harmonic oscillators. Entanglement dynamics is considered to be average without tunneling, it grows upon encountering the potential barrier and remains moderately constant inside barrier. This specificity is extended for both models but with higher values for damped coupled harmonic oscillators consequently the damping effect rapidly increases entanglement. Correction factor is also considered for both models, it show that; low temperature and high potential barriers make the system more disruptive. An increase of the coupling parameter of the system increase correction factor. Damping make the correction factor more important so damping disturbs more the system. Interference effect increase correction factor and it shows an interference between the values of the barrier penetration integral.