Entanglement in a generalized Jaynes--Cummings model

We investigate the pairwise entanglement and global entanglement in a generalized Jaynes--Cummings model, which can be used to realize Greenberger--Horne--Zeilinger (GHZ) entangled state (Zheng S B 2001 Phys. Rev. Lett. 87 230404). Our results show that the W-type entangled states cannot be generated based on the model. The dependences of entanglement on Rabi frequency \lambda and dipole--dipole coupling strength \it \Omega are given. It is found that there exists the quantum phase transition when \lambda=\it \Omega. For typical experimental data, the critical temperature for pairwise entanglement is on the order of 10^-6 K. Based on these results, two strategies that overcome decoherence are proposed.