Explicit Analysis of Creating Maximally Entangled State in the Mott Insulator State

We clarify the essence of the method proposed by You (Phys. Rev. Lett. 90(2004)030402) to create the maximally entangled atomic N-GHZ state in the Mott insulator state. Based on the time-independent perturbation theory, we find that the validity of the method can be summarized as that the Hamiltonian governing the evolution is approximately equivalent to the type aJ2x+bJx, which is the well known form used to create the maximally entangled state.