Classical Instability Effects on Photon Excitations and Entanglement

The Schr\"{o}dinger dynamics of photon excitation numbers together with entanglement in two non-resonant time-dependent coupled oscillators is investigated. By considering $ \pi-$periodically pumped parameters and using suitable transformations, we obtain the coupled Meissner oscillators. Consequently, our analytical study shows two interesting results, which can be summarized as follows. (i): Classical instability of classical analog of quantum oscillators and photon excitation {averages $\left\langle N_{j}\right\rangle $} are strongly correlated. (ii): Photon excitation's and entanglement are connected to each other. These results can be used to shed light on the link between quantum systems and their classical counterparts. Also it allow to control entanglement by engineering only classical systems where the experiments are less expensive.