Cluster-type entangled coherent states generation

We present a generation scheme for the cluster-type entangled coherent state (CTECS) among four spatially separated cavities. CTECS is a continuous variable extension, proposed by Munhoz et al [1], of the qubits-based cluster state, which is known to be the basis of one-way quantum computing model. In this work we show how such generation could be achieved in a simple way. We consider two types of interaction between atoms and the quantized cavity field; the first one using a three-level atom, described by the degenerate Raman coupled model and the second one using the dispersive two-level Jaynes-Cummings model. Besides the flying atom, which interacts with the four cavities, the scheme also uses one or two Ramsey Zones (depending on the type of atom), where a classical field transforms the atom's internal energy levels in an appropriate way. After crossing the cavities, the atom has to be measured, and CTECS are generated irrespective of the atomic detection result. In addition to the generation scheme, we also study the effect of energy dissipation on the CTECS. Explicit equations for the time dependent density operator and the purity are given.