Entanglement dynamics of many-body systems: Analytical results

Abstract

We consider a many-body system consisting of a harmonic oscillator linearly coupled to $N$ others and solve the corresponding dynamical problem analytically. Initially, the main oscillator is prepared in a superposition of two coherent states and the $N$ others in the ground states. We divide this system in arbitrary three partitions and the entanglement dynamics between any of these partitions is quantified. We show that the residual entanglement of the tripartite system is always present. Besides, the concurrence of any two partitions depends on the overlap between the two coherent states forming the initial superposition of the main oscillator and the distribution of excitations in the partitions. Finally, we obtain a hierarchy of entanglement between the central oscillator and partitions formed by the other oscillators. For long times the excitations of the main oscillator are completely transferred to the $N$ others and these are found entangled.