Kassahun, Fesseha (PhD)Yihunie, Ayana2021-04-162023-11-092021-04-162023-11-092020-08-23http://10.90.10.223:4000/handle/123456789/26156In this PhD dissertationwe have studied the quantum properties of the cavity mode driven by coherent light and interacting with a three-level atom available in an open cavity and coupled to a vacuum reservoir via a single-port mirror. We have carried out our analysis by putting the noise operators associated with the vacuum reservoir in normal order and by taking into consideration the interaction of the threelevel atom with the vacuum reservoir outside the cavity. With the aid of the quantum Langevin equations, we have determined the equations of evolution for the cavity mode operators. In addition, employing the pertinent master equation, we have obtained the equations of evolution for the expectation values of the atomic operators. Then applying the steady-state solutions of the equations of evolution for the cavity mode operators and the atomic operators, we have calculated the global mean and variance of the photon number for the light modes emitted from the top and the intermediate levels and for the driven cavity mode. We have also determined the local mean photon number for the driven cavity mode and for the two-mode cavity light. We have seen that the cavity modes a1 and a2 (for " _ c + ) are separately in a chaotic state . Moreover, the driven cavity mode exhibits subPoissonian photon statistics. We have also established that the local mean photon number for the driven cavity mode as well as for the two-mode cavity light approaches the global mean photon number in the absence or presence of spontaneous emission. In addition, we have shown that the driven cavity mode is in a squeezed state and the squeezing occurs in both the plus and the minus quadratures with the maximum squeezing for the plus quadrature being 52:08% below the vacuum state level. The maximum squeezing occurs at " = 0:6 (in the presence of spontaneous emission) and at " = 0:37 (in the absence of spontaneous emission). On the other hand, the maximum squeezing for the minus quadrature is 33.32% and occurs for values of " _ 15 in the presence or absence of spontaneous emission. We consider the discovery of squeezing in both the plus and the minus quadratures to be the single most important result of this PhD dissertation. Furthermore, the two-mode cavity light is in a squeezed state and the squeezing occurs in the minus quadrature with the maximum squeezing being 43.42% below the vacuum state level and occurs at " = 0:22 (in the absence of spontaneous emission) and at " = 0:35 (in the presence of spontaneous emission). Moreover, we have found that the maximum local quadrature squeezing for the driven cavity mode is 65.32% (in the absence of spontaneous emission) and 62.11% (in the presence of spontaneous emission). And the two local maxima occur in the frequency interval __ = 0:01. On applying the steady-state solution of the quantum Langevin equation for a pair of superposed driven cavity modes, we have calculated the mean and variance of the photon number as well as the quadrature squeezing. We have found that the mean photon number of the superposed driven cavity modes is twice the mean photon number of one of the constituent driven cavity mode. Finally, our result shows that the amount of squeezing in the plus or the minus quadrature of the superposed driven cavity modes is the average of the squeezing in the plus and the minus quadratures of one of the constituent driven cavity modes.enInteractionCoherentlyDriven Cavity ModeThree-Level AtomThesis