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In this paper we investigate the quantum phase properties for the coherentsuperposition states (Schr\"odinger-cat states) for two-mode multiphotonJaynes-Cummings model in the framework of the Pegg-Barnett formalism. We alsodemonstrate the behavior of the Wigner ($W$) function at the phase spaceorigin. We obtain many interesting results such as there is a clearrelationship between the revival-collapse phenomenon occurring in the atomicinversion (as well as in the evolution of the $W$ function) and the behavior ofthe phase distribution of both the single-mode and two-mode cases. Furthermore,we find that the phase variances of the single-mode case can exhibitrevival-collapse phenomenon about the long-time behavior. We show that suchbehavior occurs for interaction time several times smaller than that of thesingle-mode Jaynes-Cummings model.

Quantum phase properties of two-mode Jaynes-Cummings model for Schr\"odinger-cat states: interference and entanglement