Evolution of the Two-Mode Entangled States With An Atomic Coupler

We develop a model to investigate the behavior of atomic coupler consistsof two waveguides,each of which includes a localized or a trappedatom with a two-mode pair coherent state source. the waveguides areplaced close enough to each other to allow energy exchange betweenthem. the two atoms,in the different waveguides,are located adjacentto each other. in each waveguide,one mode propagates along and interactswith the atom inside in a standard way as the jaynes- cummingsmodel (jcm). the atom-mode system,in each waveguide,interacts withthe other one via the evanescent wave. pair coherent states (pcs) areone of the most important states in quantum information theory sinceit includes sufficient entanglement causing the violation of the bell inequality. moreover,the pcs possesses prominent nonclassical propertiessuch as sub-poissonian statistics,correlation in the number fluctuations,squeezing and violations of the cauchy schwartz inequalities.