The atomic quantumbehavior in the interaction system of a single-mode light field with the nonlinearJaynes-Cummings model via two-photon processes are studied by means of quantum theory. Thecondition for taking place of the phenomenon of coherent trapping is given.The influencesof the nonlinear correction term and the two-photon frequency detuning on the timeevolution of atomic particle number population inversion and the atomic dipole squeezingare discussed,respectively,when the initial field is on the vacuum state (= 0) and on the thermalchaotic state (≠ 0).