Entanglement of three atoms induced by a coherent field

We calculate the concurrence and spin squeezing parameter of three atoms induced by a coherent field. It shows that when the mean numbers of photon of the field is very small, concurrence exhibits a certain kind of approximative periodic vibration. With the increase of the mean numbers of photon, its periodicity will be interrupted. As for the relationship between the concurrence and spin squeezing, numeric result shows that under Dick model, spin squeezing serves as a sufficient but not necessary condition for concurrence.