The present work analyses a lossless cavity through which two two-level atoms passed one after another. The first atom interacted with the cavity field via a three-photon process and left the cavity. The second atom entered the cavity and interacted with it when alterations were already present due to the first atom. The two atoms got entangled in the process even though they do not interact directly [1, 2]. The properties of the radiation field encountered by them crucially affect the nature of entanglement. The entanglement of formation of the joint two-atom state as a function of the Rabi angle $\Omega t$ is calculated for the Fock state field, coherent field, and thermal field, respectively, inside the cavity. We present a comparative analysis of atom-atom entanglement corresponding to different field statistics.