Entanglement degradation of cavity modes due to the dynamical Casimir effect

We study the entanglement dynamics between two cavities when one them is harmonically shaken in the context of relativistic quantum information. We find four different regimes depending on the frequency of the motion and the spectrum of the moving cavity. If the moving cavity is three dimensional only two modes inside get coupled and the entanglement can either degrade asymptotically with time or oscillate depending on the driving. On the other hand, if the cavity has an equidistant spectrum the entanglement can either vanish asymptotically if it is driven with its fundamental frequency or have a sudden death if it is driven with an uneven harmonic frequency.