Some entanglement features of three-atoms Tavis-Cummings model: Cooperative case

Abstract

In this paper we consider a system of identical three 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 either in the uppermost excited state "$|eee>$" or The $\textmd{GHZ}$-state or the $\textmd{W}$-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 the relationship, between entanglement and some other nonclassical effects in the statistical properties, such as collapses and revivals in the atomic inversion where superharmonic effects appear, is discussed. The $Q$-functions for different cases are discussed. Most remarkably it is found that the $\textmd{GHZ}$-state is more robust against energy losses, showing almost coherent trapping and Schr\"odinger-cat states can not be produced from such state. Also the entanglement of $\textmd{GHZ}$-state is more robust than the $\textmd{W}$-state. Another interesting feature found is that the state which has no pairwise entanglement initially will have a much improvement of such pairwise entanglement through the evolution. Sudden death and sudden revival of atoms-pairwise entanglement are produced with the $\textmd{W}$-state.Comment: 14 pages, 7 figure