Quantum entanglement of bound particles under free center of mass dispersion

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.