  We theoretically investigate the role of different phases of coupling
constants in the dynamics of atoms and two cavity modes, observing
deterministic generation of prototype or hybrid Bell, W, GHZ, and cluster
states. Commonly induced dipole-dipole interactions (far-off resonance) are
inhibited between particular pairs of qubits under suitable choice of those
phases. We evaluate the generation fidelities when imperfections such as
dissipative environments and time precision errors are considered. We show
violation of local realism for the generated cluster state under such
imperfections, even when approaching the weak coupling regime.
