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

TL;DR

This paper investigates the dynamical evolution and entanglement properties of an exactly solvable coupled quantum double-well system, revealing that faster evolution does not always correlate with higher entanglement.

Contribution

It provides a detailed analysis of the relationship between evolution speed and entanglement in a specific quantum system using exact solutions and various initial wavepackets.

Findings

Evolution speed is not necessarily increased with higher entanglement.

Coupling affects orthogonality time and average concurrence.

Exact solutions enable precise analysis of dynamical properties.

Abstract

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 $\Gamma(t)$ 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 $C(t)$, $C_{av}$ $(=\sqrt{\langle C(t)^2 \rangle})$. 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.