Dynamics of an atom cavity field system in interacting Fock space

In this paper, we investigate one-time passing of a $V$-type three-level atom through a single-mode interacting field in a cavity. We extend the idea of elementary Jaynes-Cummings model by assuming that the field vector belongs to interacting Fock space. In the process, we arrive at a state vector which will be analyzed to study the nonclassicality of the evolved state of the system.