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) system with Razavy's hyperbolic potential. With the use of four kinds of initial wavepackets, the correlation function Γ(t) and the concurrence C(t) which is a typical measure of the entanglement in two qubits, are calculated. We obtain the orthogonality time τ which signifies a time interval for an initial state to evolve to its orthogonal state, and the temporal average of Cav(=〈C(t)2〉). The coupling dependence of τ and the concurrence [Cav or C(0)], and the relation between τ and the concurrence are investigated. Our calculations have shown that the evolution speed measured by τ-1 is not necessarily increased with increasing the concurrence in coupled DW systems.