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 spatial dimension bound by harmonic forces and having its free center of mass initially localized in space in a minimum uncertainty wavepacket. The existence of such initial states in which the bound particles are not entangled is discussed. Galilean invariance of the system ensures that the dynamics of entanglement between the two particles is independent of the wavepacket mean momentum. In fact, as shown, it is driven by the dispersive center of mass free dynamics, and evolves in a time scale that depends on the interparticle interaction in an essential way.