In this dissertation we have studied the photon statistical and the quadraturernsqueezing properties of the two-mode cavity light available following the interactionrnof subharmonic light modes, emerging from a nonlinear crystal pumped byrncoherent light, with a single three-level atom in a closed cavity. The cavity is coupledrnto a vacuum reservoir via a single port mirror. We have considered the case inrnwhich the top and bottom levels of the three-level atom are not coupled by the coherentrnlight emerging from the nonlinear crystal. Employing the pertinent Hamiltonianrnand master equations, we have obtained the equations of evolution of thernexpectation values for the cavity mode and atomic operators.rnApplying the steady-state solutions of the equations of evolution of the expectationrnvalues for the cavity mode and atomic operators, we have calculated the globalrnmean photon number for the two-mode cavity light. The global mean photon numberrnof the two-mode cavity light is found to be the sum of the mean photon numberrndue to the subharmonic generation and the mean photon number emitted andrnabsorbed by the atom. We have observed that the effect of the interaction of thernsubharmonic light modes with the three-level atom is to decrease the global meanrnphoton number of the two-mode cavity light. This is due to the fact that the meanrnnumber of photons absorbed is greater than the mean number of photons emitted.rnMoreover, applying the time dependent solutions of the equations of evolutionrnof the expectation values for the cavity mode and atomic operators, we have alsornobtained the local mean photon number for the two-mode cavity light. Our analysisrnshows that the local mean photon number of the two-mode cavity light increasesrnwith frequency and eventually approaches to the global mean photon numberrnwithin a relatively small frequency interval.rnIn addition, we have calculated the global photon-number variance for the twomoderncavity light. We have noticed that the photon statistics of the two-mode cavityrnlight is supper poissonian. Our analysis indicates that the global photon-numberrnvariance in the presence of the interaction is less than that in the absence of the interaction.rnThis implies that the effect of the interaction is to decrease the globalrnphoton-number variance.rnFurthermore, we have determined the global quadrature squeezing for the twomoderncavity light with arbitrary ordering of the two-mode vacuum reservoir noisernoperators. We have established that the two-mode cavity light is in squeezed staternand the squeezing occurs in the plus quadrature. We have also found that the globalrnquadrature squeezing in the presence of the interaction (43:5%) is less than thernglobal quadrature squeezing (50%) in the absence of the interaction. In addition,rnWe have seen that the maximum local quadrature squeezing for the two-mode cavityrnlight is 60:8% at _ = 0:17 and eventually approaches to the global quadraturernsqueezing as the frequency increases.rnFinally, applying the steady-state solutions of the equations of evolution of thernexpectation values for the cavity mode operators, we have determined the globalrnquadrature squeezing for the two-mode cavity light when the two-mode vacuumrnreservoir noise operators are in normal order. We have found that the globalrnquadrature squeezing for the two-mode cavity light is 100% for c = 16rn15 _ 1:067rnand is 88:3% for c = 1:25 with the vacuum noise operators in normal order.