%0 Journal Article %T The Pancharatnam Phase of a Three-Level Atom Coupled to Two Systems of N-Two Level Atoms %A D. A. M. Abo-Kahla %J Journal of Quantum Information Science %P 44-55 %@ 2162-576X %D 2016 %I Scientific Research Publishing %R 10.4236/jqis.2016.61006 %X In this paper, we present the analytical solution for the model that describes the interaction between a three-level atom and two systems of N-two level atoms. The effects of the quantum numbers and the coupling parameters between spins on the Pancharatnam phase and the atomic inversion, for some special cases of the initial states, are investigated. The comparison between the two effects shows that the analytic results are well consistent. %K Pancharatnam Phase %K Atomic Inversion %K Systems of N-Two Level Atoms %U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=65198