The nonlinear effects over time evolution of a three-level atom confined in a single mode optical cavity

A single atom is trapped in an optical cavity in the presence and absence of a nonlinear mirror corresponding to the nonlinear and linear regimes, respectively. The time evolutions of both systems are derived. The resultant equations are numerically solved by a fourth-order RungeKutta method. The effect of the nonlinear mirror over time evolution of the population inversion, the mean photon number and the second-order coherence function is investigated. It is shown that in the presence of the nonlinear effects, the time average of the population inversion is increased. As the time evolution proceeds, the mean photon number is decreased as well as the light exhibiting sub-Poissonian photon distributions. Under specific conditions and in a weak-driving limit, these systems can be well approximated by an effective two-level atom. The result of the calculations confirms the predictions of the two-level model.