The influence of the relative phase on the interaction between a single mode cavity field and a four-level N-type atom

We study the interaction of a four-level N - type atom with a single mode cavity field when the initial phases of the cavity field and atomic superposition state are considered. We solve the model when the field and atom are initially prepared in a coherent state and coherent superposition of its excited and ground states, respectively. The collapse-revival, the anti-bunching of photons, the normal squeezing and the coherent phenomena have been discussed. The effects of the relative phase and detuning parameter on these phenomena are examined. We noticed that the presence of the relative phase and detuning parameter have an important effect on the properties of these phenomena.