Preparation of the Cluster States in a Linear Trap Systems

A scheme for the preparation of four-ion entangled cluster states has been proposed. Two two-level ions are confined in a linear trap and are simultaneously driven with a laser beam. In the Lamb-Dicke regime, we can get the effective Hamiltonian in the interaction picture.The effective Hamiltonian may be used to describe a realistic physical system. The scheme is insensitive to both the initial vibrational state and heating.