Quantum entanglement of bound particles under free center of mass dispersion

TL;DR

This paper analytically studies how quantum entanglement evolves over time in a bipartite system of two harmonically bound particles with a localized center of mass, revealing conditions for initial unentanglement and monotonic entanglement growth.

Contribution

It provides a full analytical solution for the unitary dynamics of a bound two-particle quantum system, highlighting entanglement behavior under free center of mass dispersion.

Findings

Entanglement increases monotonically over time.

Initial unentangled states exist with localized center of mass.

Entanglement evolution is independent of mean momentum.

Abstract

On the basis of the full analytical solution of the overall unitary dynamics, the time evolution of entanglement is studied in a simple bipartite model system evolving unitarily from a pure initial state. The system consists of two particles in one spacial dimension bound by harmonic forces and having its free center of mass initially localized in space in a minimum uncertainty wave packet. The existence of such initial states in which the bound particles are not entangled is pointed out. The entanglement of the two particles is shown to be independent of the wavepacket mean momentum, and to increase monotonically in a time scale distinct from that of the spreading of the center of mass wavepacket.