Temporal behavior of an atom-cavity system in two distinct regimes

The time-dependent treatment of a three-level atom in the V configuration confined in an optical cavity as well as the dynamics of the cavity field in two different regimes, in the presence and absence of the nonlinear mirror, has been discussed. The time-dependent infinite coupled differential equations of motion are solved by the matrix continued fraction method. In deriving the numerical inverse Laplace transform, the quotient difference algorithm and the fast Fourier transform have been applied. The nonlinear effects of the system over the time evolution of the population inversion, the mean photon number and the second-order correlation function for some dimensionless parameters are delineated. Ultimately the reduction of the three-level atom to an effective two-level one under specific conditions and in a weak-driving limit has been performed.