Abstract
Generalized trio coherent states are made by superposing a number of trio coherent states. They possess inherent nonclassical properties such as sub-Poissonian distribution and violation of Cauchy-Schwarz inequalities. Their phase distribution in the framework of the Pegg and Barnett theory is discussed. We study the interaction of the radiation field prepared in a generalized trio coherent state with an atom in a superposition coherent state in the rotating wave approximation. We investigate the time dependence of the sub-Poissonian distribution and the violation of Cauchy-Schwarz inequalities for such a system. General conclusions reached are illustrated by numerical results.