Fusion of entangled coherent W and GHZ states in cavity QED

Efficient preparation of W and GHZ states encoded in various degrees of freedom of quantum particles is vital in quantum information science. So far, most of the studies have focused on polarization encoded photonic W and GHZ states. In this paper, we focus on W- and GHZ-class entangled coherent states, and propose schemes to fuse small W- and GHZ-entangled coherent states into larger ones. Based on successive detuned interactions between optical modes and an ancilla atom, an (N+M−2)-mode entangled coherent W state can be probabilistically prepared from an N-mode and an M-mode entangled coherent W states. This fusion scheme applies to entangled coherent GHZ states too, and it can succeed in a deterministic way. The ancilla atom only interacts with a single optical mode, which avoids the problem of synchronizing many atoms in the previous cavity QED based fusion schemes. The detuning property of the interaction makes the current fusion scheme more feasible that the ones based on resonant atom-light interactions. In addition, the two levels of the ancilla atom for encoding quantum information are two degenerate ground states, and the excited state is adiabatically eliminated during the fusion process, so the atomic decay from excited states does not affect the quality of the fusion process.