Some entanglement features of a three-atom Tavis-Cummings model: a cooperative case

In this paper we consider a system of three identical two-level atoms interacting at resonance with a single mode of the quantized field in a lossless cavity. The initial cavity field is prepared in the coherent state while the atoms are taken initially to be in either the uppermost excited state '|eeerang', the GHZ-state or the W-state. For this system we investigate different kinds of atomic inversion and entanglement, which arise between the different parts of the system due to the interaction. Also, we discuss the relationship between the entanglement and some other nonclassical effects in the statistical properties, such as collapses and revivals in the atomic inversion where superharmonic effects appear. The Q-functions for different cases are discussed. Most remarkably it is found that the GHZ-state is more robust against energy losses, showing almost coherent trapping, and Schrödinger cat states cannot be produced from such a state. Also the entanglement of the GHZ-state is more robust than that of the W-state. Another interesting feature is that a state which has no pairwise entanglement initially will have considerable improvement of such pairwise entanglement through the evolution. Sudden death and sudden revival of atoms' pairwise entanglement are produced with the W-state.