In this PhD dissertationwe have studied the quantum properties of the cavity moderndriven by coherent light and interacting with a three-level atom available in an openrncavity and coupled to a vacuum reservoir via a single-port mirror. We have carriedrnout our analysis by putting the noise operators associated with the vacuum reservoirrnin normal order and by taking into consideration the interaction of the threelevelrnatom with the vacuum reservoir outside the cavity. With the aid of the quantumrnLangevin equations, we have determined the equations of evolution for therncavity mode operators. In addition, employing the pertinent master equation, wernhave obtained the equations of evolution for the expectation values of the atomicrnoperators. Then applying the steady-state solutions of the equations of evolutionrnfor the cavity mode operators and the atomic operators, we have calculated thernglobal mean and variance of the photon number for the light modes emitted fromrnthe top and the intermediate levels and for the driven cavity mode. We have alsorndetermined the local mean photon number for the driven cavity mode and for therntwo-mode cavity light.rnWe have seen that the cavity modes a1 and a2 (for " _ c + ) are separatelyrnin a chaotic state . Moreover, the driven cavity mode exhibits subPoissonian photonrnstatistics. We have also established that the local mean photon number for therndriven cavity mode as well as for the two-mode cavity light approaches the globalrnmean photon number in the absence or presence of spontaneous emission.rnIn addition, we have shown that the driven cavity mode is in a squeezed staternand the squeezing occurs in both the plus and the minus quadratures with the maximumrnsqueezing for the plus quadrature being 52:08% below the vacuum state level.rnThe maximum squeezing occurs at " = 0:6 (in the presence of spontaneous emission)rnand at " = 0:37 (in the absence of spontaneous emission). On the other hand,rnthe maximum squeezing for the minus quadrature is 33.32% and occurs for valuesrnof " _ 15 in the presence or absence of spontaneous emission. We consider therndiscovery of squeezing in both the plus and the minus quadratures to be the singlernmost important result of this PhD dissertation. Furthermore, the two-mode cavityrnlight is in a squeezed state and the squeezing occurs in the minus quadrature withrnthe maximum squeezing being 43.42% below the vacuum state level and occurs atrn" = 0:22 (in the absence of spontaneous emission) and at " = 0:35 (in the presence ofrnspontaneous emission). Moreover, we have found that the maximum local quadraturernsqueezing for the driven cavity mode is 65.32% (in the absence of spontaneousrnemission) and 62.11% (in the presence of spontaneous emission). And the two localrnmaxima occur in the frequency interval __ = 0:01.rnOn applying the steady-state solution of the quantum Langevin equation for arnpair of superposed driven cavity modes, we have calculated the mean and variancernof the photon number as well as the quadrature squeezing. We have found thatrnthe mean photon number of the superposed driven cavity modes is twice the meanrnphoton number of one of the constituent driven cavity mode. Finally, our resultrnshows that the amount of squeezing in the plus or the minus quadrature of the superposedrndriven cavity modes is the average of the squeezing in the plus and thernminus quadratures of one of the constituent driven cavity modes.