Simulation of entanglement dynamics for a scattering between a free and a bound carrier in a quantum wire

We present a numerical analysis of the creation of entanglement between an electron freely propagating along a quantum wire and a charged particle bound to a specific site by a harmonic potential. The latter can be considered as a simplified model of an ionized impurity with an internal structure or of a localized phonon mode. Its dynamics is coupled to that of the free electron through a screened Coulomb potential. The time-dependent Schrodinger equation is solved numerically for the two-particle wave function thus describing the coherent evolution of the bipartite system. The two particle are considered distinguishable. As initial condition the product of a minimum uncertainty wave packet and the ground state of the harmonic oscillator are considered.