Dynamical properties of an exactly solvable coupled quantum double-well system: The evolution speed and entanglement

We have studied dynamical properties of an exactly solvable quantum coupled double-well (DW) systems with Razavy’s hyperbolic potential. With the use of four kinds of initial wavepackets, the correlation function $\mathrm{\Gamma }(t)$ and the concurrence $C(t)$ which is a typical measure of the entanglement in two qubits, are calculated. We obtain the orthogonality time $\tau$ which signifies a time interval for an initial state to evolve to its orthogonal state, and the temporal average of $C(t)$, $C_{av}$ $(=\sqrt{⟨C(t{)}^2⟩})$. The coupling dependence of $\tau$ and the concurrence [$C_{av}$ or $C(0)$], and the relation between $\tau$ and the concurrence are investigated. Our calculations have shown that the evolution speed measured by ${\tau }^{-1}$ is not necessarily increased with increasing the concurrence in coupled DW systems.