We consider the interaction of a qubit system with a two-mode field in the presence of multi-photon transition and phase damping effect. We use the master equation to obtain the density operator when the qubit is initially prepared in its excited state and the field is in a finite-dimensional pair coherent state. The properties of the considered system, such as the population inversion, amount of the mixedness, parameter estimation, and squeezing, are explored for one- and two-photon transitions. The effects of photon addition to the field and phase damping on the evaluation of these quantumness measures are also investigated.
