Browsing by Author "Kassahun, Fesseha (PhD)"
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Item A Coherently driven Degenarate Three-Level Atom(Addis Ababa University, 2013-06) Terefe, Yosef; Kassahun, Fesseha (PhD)We analyze the squeezing and statistical properties of a degenerate three-level atom coupled to a coherent light and vacuum reservoir. In the other way, employ- ing the Heseinberg and Quantum Langevin equation associated with the normal ordering noise operator, we study the squeezing properties, power spectrum, vari- ance and also calculate the mean photon number of the cavity mode. It turns out that the generated light exhibits squeezing under certain conditionsItem Coherently Driven Three-Level Laser with Parametric Amplifier(Addis Ababa University, 2010-04) Yirgashewa, Tewodros; Kassahun, Fesseha (PhD)The squeezing and statistical properties of the light produced by a coherently driven degenerate as well as nondegenerate three-level laser with a parametric amplifier is studied applying c-number Langevin equations. Employing the solutions of these equations, we have determined the quadrature variance for the cavity and output modes, the squeezing spectrum for the output mode(s), the photon statistics of the cavity mode(s), and the photon number and count statistics of the output mode(s). It so turns out that the parametric amplifier increases the squeezing and the mean photon number significantly. Furthermore, it so happens that the coupling of the top and bottom levels enhances the degree of squeezing particularly when there are nearly equal number of atoms initially in the top and bottom levels. It is also found that one effect of the coupling of the top and bottom levels is to decrease the mean and the normally-ordered variance of the photon number. In addition, our calculation shows that the mean photon number of mode a is greater than that of mode bItem A Degenerate Parametric Oscillator Coupled to a Squeezed Vacuum(Addis Ababa University, 1998-05) Getahun, Misrak; Kassahun, Fesseha (PhD)The intracavity quadrature fluctuations and photon statistics for the signal mode produced by a degenerate parametric oscillator coupled to a squeezed vacuum reservoir are calculated employing the Q-function. The Q-function is obtained by solving the Fokker-Planck equation applying the propagator method developed by Fesseha [lJ. We also calculate the squeezing spectra of the output quadrature operators using the quantum Langevin equationsItem A Degenerate Three-Level Laser Coupled to a Squeezed Vacuum Reservoir(Addis Ababa University, 2005-06) Hiluf, Dawit; Kassahun, Fesseha (PhD)Employing the master equation for a three-level laser driven by coherent light and coupled to a squeezed vacuum reservoir, we obtain stochastic differential equations associated with the normal ordering. Using the solutions of the stochastic differential equations, we calculate the quadrature variance, the squeezing spectrum, the mean photon number, and the variance of the photon number. It turns out that the degree of squeezing increases with the linear gain coefficient or the squeeze parameter. It is also found that the driving coherent light decreases the mean photon numberItem Dynamics of a Coherently Driven Nondegenerate Three-Level Atom(Addis Ababa University, 2013-06) Hailu, Lamrot; Kassahun, Fesseha (PhD)In this thesis we study the statistical and squeezing properties of the light emitted by a nondegenerate three-level atom driven by coherent light and in a cavity coupled to a vacuum reservior via a single-port mirror. We carry out our analysis by putting the noise operators associated with the vacuum reservior in normal order and applying the large-time approximation. It is found that the mean of the two cavity modes are equal. In addition, the photon number statistics is Poissonian for < 0:13 and sub-Poissonian for 0:13. Our result shows that the photon numbers of modes a and b are uncorrelated. We have also calculated the quadrature variance for the separate modes and for the superposition of the two modes. It turns out that mode a is in a chaotic state for arbitrary values of c and but mode b is in chaotic state for c << and in a coherent state for c >> and the superposed cavity modes are in a squeezed state. Furthermore, we have determined the quadrature squeezing of the superposed cavity modes. The maximum quadrature squeezing is found to be 43% below the coherent-state levelItem Dynamics of Coherently Driven Degenerate Three-Level Atom in open Cavity(Addis Ababa University, 2014-04) Melaku, Mulugeta; Kassahun, Fesseha (PhD)In this thesis, we study the quantum properties of the light generated by a coherently driven degenerate three-level atom in an open cavity coupled to a vacuum reservoir. The three-level atom available in the cavity is driven by coherent light from the bottom to the top level. We perform our analysis by putting the noise operators associated with the vacuum reservoir in normal order. Employing the master equation and the quantum Langevin equation we obtain the di erential equations of the atomic and cavity-mode operators. Using the steady-state solutions of the resulting equations, we determined the photon statistics, quadrature squeezing and the local mean photon number. It is observed that the mean photon number is greater when = 0 than when = 0:1. We nd, like the mean photon number, the variance of the photon number to be greater for = 0 than for = 0:1. Moreover, we have also established that the maximum quadrature squeezing of the light generated by the atom, to be 43.42 % for = 0 and 42.22 % for = 0:1 below the coherent-state level. Thus in the absence of spontaneous emission the mean, the variance and the quadrature squeezing of the cavity light is greater than in the presence of spontaneous emission. Finally, we have found that a large part of the total mean photon number is con ned in a relatively small frequency intervalItem Dynamics of coherently driven Nondegrnerate three-level Atom in open cavity(Addis Ababa University, 2014-05) Yeshiwas, Abinet; Kassahun, Fesseha (PhD)We have investigated the squeezing and statistical properties of the light cavity coupled to a vacuum reservoir via a single-port mirror. We carry out our analysis by considering the vacuum reservoir to be a noiseless physical entity and by applying the large-time approximation scheme to the quantum Langevin equations. We have found that the mean photon numbers of light modes and are the same in the absence of spontaneous emission and the mean photon number of light mode is greater than that of light mode in the presence of spontaneous emission. Our analysis also shows that mode is in general in chaotic state while mode is in a chaotic state under certain conditions. It is also found that the superposed light modes are in squeezed state with a maximum quadrature squeezing of 43% for = 0 and 46.5% for = 0.1 below the coherent vacuum state levelItem Dynamics of Degenerate Three-Level Laser With Spontaneous Emission and Noiseless Vacuum Reservoir(Addis Ababa University, 2018-02-02) Asmelash, Getachew; Kassahun, Fesseha (PhD)In this dissertation we have studied the quantum properties of the cavity light produced by a coherently pumped three-level laser 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 three-level atoms with the vacuum reservoir outside the cavity. Employing the pertinent master equation for a coherently pumped degenerate three-level atom, we have obtained coupled equations of evolution for the expectation values of the atomic operators. Then applying the large-time approximation scheme to the quantum Langevin equations for the cavity mode operators, we have managed to decouple the equations of evolution for the expectation values of the atomic operators. Applying the solutions of the pertinent equations of evolution, we have calculated the local and global mean photon number, the local and global variance of the photon number, and the local and global quadrature squeezing of the degenerate three-level laser. We have established that a large part of the total mean photon number and the total variance of the photon number are confined in relatively small frequency intervals. Moreover, we have observed that the cavity light is in a squeezed state and the squeezing occurs in the minus qudrature. In addition, we have found that the maximum global quadrature squeezing of the cavity light is 43:42% ( and occurs at = 0:1717 for = 0 ). We have also seen that the cavity light produced by the laser operating under the conditions _ c and _ is in a chaotic state. In addition, we have shown that the presence of the spontaneous emission process leads to a decrease in the mean photon number, the variance of the photon number, and the maximum quadrature squeezing. Furthermore, we have established that the iii maximum local quadrature squeezing of the cavity light is 78:48% ( and occurs at _ = 0:0606 for = 0 ). We have also analyzed the squeezing and statistical properties of a pair of superposed degenerate three-level laser light beams. We have found that the global mean photon number of the superposed two-mode laser light beams is the sum of the global mean photon numbers of the constituent two-mode laser light beams. Furthermore, we have noted that unlike the mean photon number, the variance of the photon number for the superposed two-mode laser light beams is not the sum of the photon-number variances of the constituent two-mode laser light beams. However, it turns out to be four times that of a two-mode laser light beam, for the case in which the separate two-mode laser light beams are identical. Finally, we have found that the superposition of the two-mode laser light beams does not affect the local and global quadrature squeezing, but it increases the global (local) mean photon number and the global (local) variance of the photon number. Thus, we note that the superposition of the two-mode laser light beams leads to a more bright squeezed light.Item Dynamics of Three-Level Atom Pumped by Coherent Light and With Spontaneous Emission(Addis Ababa University, 2018-08-02) Fekade, Teshome; Kassahun, Fesseha (PhD)In this research we have studied the squeezing and statistical properties of the cavity light generated by a coherently driven three-level atom with an open cavity coupled to a two-mode vacuum reservoir via a single-port mirror. We carry out our calculation by putting the noise operators associated with the vacuum reservoir in normal order. Employing the master equation and the quantum Langevin equations, we obtained the equations of evolution of the expectation values of the atomic operators. Then applying the resulting solutions, we have calculated the mean photon number, variance of the photon number, and the quadrature variance for the single-modes cavity light as well as the two-mode cavity light. Moreover, we have obtained the quadrature squeezing for the two-mode cavity light. We have noticed that the mean photon number, the variance of the photon number for light mode a, the variance of the photon number for the twomode cavity light, and the quadrature variance of light mode a for = 0 is greater than for = 0.1. The quadrature variance of light mode b in the absence of spontaneous emission ( = 0) is less than in the presence of spontaneous emission ( = 0.1). We have also found that the maximum quadrature squeezing of the two-mode cavity light is 43.42% for both = 0 and = 0.1 below the vacuum-state level.Item Dynamics of Three-Level Atom Pumped by Electron Bombardment and With Spontaneous Emission(Addis Ababa University, 2018-08-02) Sisay, Desalegn; Kassahun, Fesseha (PhD)We have investigated the squeezing and statistical properties of the light generated by a three level atom available in an open cavity and pumped to the top level by electron bombardment. We have determined the quantum Langevin equations and the equation of evolution of the atomic operators by considering the vacuum reservoir to be a noiseless physical entity and by applying the large-time approximation scheme. Moreover, we have obtained the steady state solutions of the equation of evolution of the atomic operators and the quantum Langevin equations . Then applying the resulting solutions, we have calculated the mean photon number, variance of the photon number and quadrature variance of the separate cavity light modes. We have found that the mean photon numbers of light modes a and b are the same in the absence as well as in the presence of spontaneous emission. Light mode a is in a chaotic state when the atom is operating well above threshold, or at threshold, or below threshold. On the other hand light mode b is in coherent state when the atom is operating well above threshold. Finally, applying the same solution we obtained the mean and variance of the two mode cavity light. The mean and variance of the photon number of the two-mode light is greater in the absence than in the presence of spontaneous emission. Moreover, we have determined the quadrature squeezing of the two mode cavity light. It is found that the two-mode light is in squeezed state with a maximum quadrature squeezing of 50% below the coherent state level. The maximum squeezing of the two-mode light occurs when the atom is operating below vacuum state.Item Dynamics of Three-Level Laser Pumped by Electron Bombardment(Addis Ababa University, 2017-11-03) Ayehu, Desalegn; Kassahun, Fesseha (PhD)We have studied the statistical and squeezing properties of the light generated by a three-level laser coupled to a two-mode vacuum reservoir. The three-level atoms available in a closed cavity are pumped from the bottom to the top level by electron bombardment. We have carried out our analysis by taking the noise operators associated with the two-mode vacuum reservoir in arbitrary order. Applying the solutions of the equations of evolution of the cavity mode and atomic operators, we have determined the global mean photon number, the global photon number variance, and the global quadrature squeezing of the one-mode aswell as the two-mode cavity light. In addition, we have calculated the local mean photon number, the local photon number variance, and the local quadrature squeezing of the two-mode cavity light. We have found the maximum global quadrature squeezing of the two-mode cavity light to be 37.5% below the vacuum level. This result happens to be less than that obtained by putting the noise operators in normal order. On the other hand, the global photon number variance calculated by taking the noise operators in arbitrary order turns out to be greater than that obtained by putting the noise operators in normal order. In addition, our analysis shows that a large part of the mean and variance of the photon number are confined in a relatively small frequency interval. Furthermore, employing the density operator for the superposition of a pair of two-mode cavity light beams, we have calculated the mean photon number, the photon number variance, and the quadrature squeezing. It so happens that the global (local) mean photon number of the superposed two-mode cavity light beams is the sum of the global (local) mean photon numbers of the component two-mode cavity light beams. On the other hand, the global (local) photon number variance of the superposed two-mode cavity light beams is four times that of the separate two-mode cavity light beams. Moreover, our results show that the global (local) quadrature squeezing of the superposed two-mode cavity light beams is the same as the global (local) quadrature squeezing of the component two-mode cavity light beams.Item Dynamics of Three-Level Laser Pumped by Electron Bombardment(Addis Ababa University, 2017-03) Behailu., Zeleke; Kassahun, Fesseha (PhD)In this project, we discuss the quantum properties of the light generated by a three-level laser with the closed cavity and coupled to a vacuum reservoir. The three-level atoms available in the closed cavity are pumped from the bottom to the top level by means of electron bombardment. Our analysis is carried out by putting the noise operators associated with the vacuum reser- voir in normal order. We have found that the light emitted from the top level is in a chaotic state in any regime of laser operation. On the other hand, the light emitted from the intermediate level is in a coherent state when the laser is operating well above threshold and is chaotic when the laser is operating at threshold. The maximum quadrature squeezing of the superposed light modes is found to be 50 % below the vacuum-state level. We have shown that the maximum local quadrature squeezing is 64.5 %: Moreover the local quadrature squeezing increases with the frequency interval and approaches to the global quadrature squeezing Keywords: Stimulated emission, Photon statistics, Global and Local Quadra- ture squeezingItem Dynamics of three-Level Laser Pumped by Electron Bombardment and With Spontaneous Emission(Addis Ababa University, 2018-09-03) Alemu, Menisha; Kassahun, Fesseha (PhD)In this PhD dissertation we have studied the statistical and squeezing properties of the cavity light generated by a three-level laser. In this quantum optical system, N three-level atoms available in an open cavity, coupled to a two-mode vacuum reservoir, are pumped to the top level by means of electron bombardment at constant rate. We have considered the case in which the three-level atoms and the cavity modes interact with the two-mode vacuum reservoir. We have carried out our analysis by putting the noise operators associated with the vacuum reservoir in arbitrary order. Applying the solutions of the equations of evolution for the expectation values of the atomic operators and the quantum Langevin equations for the cavity mode operators, we have calculated the mean and variance of the photon number as well as the quadrature squeezing for the cavity light. In addition, we have shown that the presence of the spontaneous emission process leads to a decrease in the mean and variance of the photon number. We have seen that the global mean photon numbers of the light modes emitted from the top and intermediate levels are the same both in the presence and absence of spontaneous emission, and are separately in a chaotic state. However, we have observed that the two-mode cavity light is in a squeezed state and the squeezing occurs in the minus quadrature. In addition, we have found that the effect of the vacuum reservoir noise is to increase the photon-number variance and to decrease the quadrature squeezing of the cavity light. However, the vacuum reservoir noise does not have any effect on the mean iii iv photon number. Moreover, the maximum quadrature squeezing of the light generated by the laser, operating far below threshold, is found to be 37:5% below the vacuum-state level. In addition, our result indicates that the quadrature squeezing is greater for = 0 than that for = 0:4 for 0.01 < ra < 0.35 and is smaller for = 0 than that for = 0:4 for 0.35 < ra < 1. We have also noted that the local quadrature squeezing approaches the global quadrature squeezing as the frequency interval increases. Furthermore, applying the density operator for a pair of superposed two- mode laser light beams, we have calculated the mean and variance of the photon number as well as the quadrature squeezing. We have found that both the mean photon number and the quadrature variance for the superposed two-mode laser light beams is the sum of the mean photon numbers and the quadrature variances of the constituent two-mode light beams. However, the variance of the photon number of the superposed two-mode laser light beams is not the sum of the variances of the photon numbers of the constituent two-mode light beams. Finally, our result shows that the quadrature squeezing of the superposed two-mode laser light beams is equal to the quadrature squeezing of one of the superposed the two-mode light beams. This implies that the superposition of the two-mode laser light beams does not affect the quadrature squeezing, but it increases the global mean photon number and the global variance of the photon number. Thus we note that the superposition of the two-mode laser light beams leads to a more bright squeezed light.Item Interaction of Coherently Driven Cavity Mode with Three-level Atom(Addis Ababa University, 2020-08-23) Yihunie, Ayana; Kassahun, Fesseha (PhD)In 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.Item Interaction of Subharmonic Light Modes with Three-Level Atom(Addis Ababa University, 2021-01-09) Tufa, Merid; Kassahun, Fesseha (PhD)In this dissertation we have studied the photon statistical and the quadrature squeezing properties of the two-mode cavity light available following the interaction of subharmonic light modes, emerging from a nonlinear crystal pumped by coherent light, with a single three-level atom in a closed cavity. The cavity is coupled to a vacuum reservoir via a single port mirror. We have considered the case in which the top and bottom levels of the three-level atom are not coupled by the coherent light emerging from the nonlinear crystal. Employing the pertinent Hamiltonian and master equations, we have obtained the equations of evolution of the expectation values for the cavity mode and atomic operators. Applying the steady-state solutions of the equations of evolution of the expectation values for the cavity mode and atomic operators, we have calculated the global mean photon number for the two-mode cavity light. The global mean photon number of the two-mode cavity light is found to be the sum of the mean photon number due to the subharmonic generation and the mean photon number emitted and absorbed by the atom. We have observed that the effect of the interaction of the subharmonic light modes with the three-level atom is to decrease the global mean photon number of the two-mode cavity light. This is due to the fact that the mean number of photons absorbed is greater than the mean number of photons emitted. Moreover, applying the time dependent solutions of the equations of evolution of the expectation values for the cavity mode and atomic operators, we have also obtained the local mean photon number for the two-mode cavity light. Our analysis shows that the local mean photon number of the two-mode cavity light increases with frequency and eventually approaches to the global mean photon number within a relatively small frequency interval. In addition, we have calculated the global photon-number variance for the twomode cavity light. We have noticed that the photon statistics of the two-mode cavity light is supper poissonian. Our analysis indicates that the global photon-number variance in the presence of the interaction is less than that in the absence of the interaction. This implies that the effect of the interaction is to decrease the global photon-number variance. Furthermore, we have determined the global quadrature squeezing for the twomode cavity light with arbitrary ordering of the two-mode vacuum reservoir noise operators. We have established that the two-mode cavity light is in squeezed state and the squeezing occurs in the plus quadrature. We have also found that the global quadrature squeezing in the presence of the interaction (43:5%) is less than the global quadrature squeezing (50%) in the absence of the interaction. In addition, We have seen that the maximum local quadrature squeezing for the two-mode cavity light is 60:8% at _ = 0:17 and eventually approaches to the global quadrature squeezing as the frequency increases. Finally, applying the steady-state solutions of the equations of evolution of the expectation values for the cavity mode operators, we have determined the global quadrature squeezing for the two-mode cavity light when the two-mode vacuum reservoir noise operators are in normal order. We have found that the global quadrature squeezing for the two-mode cavity light is 100% for c = 16 15 _ 1:067 and is 88:3% for c = 1:25 with the vacuum noise operators in normal order.Item Interaction of Two-Level Atoms with a Squeezed Vacuum(Addis Ababa University, 1997-06) Tesfa, Sintayehu; Kassahun, Fesseha (PhD)The squeezing and the statistical properties as well as the spectrum of the radiation resulting from the interaction of two-level atoms with a sqneezed vacuum is analyzed. We have considered the case in which the two-level atoms, all initially in the upper level, are placed in a squeezed vacuum. We have also considered the case in which the atoms, initially with nearly equal number in each level, are confined in a cavity coupled to a squeezed vacuum. The quadrature fluctuations, the photon number distribution and the spectrum of the the radiation are calculated using the Q-function formalism. The Q-function is determined applying the method of evaluating the propagator developed by Fesseha [19,20]. The radiation is found out to be in a squeezed state for certain period of time in the first case and for all times in the second case. It is also shown that one effect of the squeezed vacuum is to increase the height of the spectrum of the radiationItem Interactions of Two-Level Atoms with a Cavity Mode(Addis Ababa University, 1999-06) Woldmichael, Berhanu; Kassahun, Fesseha (PhD)Applyillg the solutions of the qualltulIl Langevin equations, we calculate the variances of the quadrature operators for the cavity mode, the squeezing spectrulI/, spectrulll of intensity fluctuatiolls alld the power spectrum of the output mode produced by two-level atoll/s interacting with a single cavity mode, driven by a coherent light and coupled to a squeezed vacuum reservoir. Employing the same solutions, we obtain the antillorll/ally ordered characteristic jilllctioll defined ill the Heisellberg picture. With the aid of the resultillg characteristic jill/ctioll, we determille the Q jill/ctioll which is thell used to calculate the lIleall alld variallce of the photollllulllber as well as the photolllllllllber distributioll of the output modeItem Laser dynamics with a squeezed Vacuum(Addis Ababa University, 1999-01) Kebede, Tesfaye; Kassahun, Fesseha (PhD)We present a detailed derivation ofthe c-number Langevin equations for a laser coupled to a squeezed vacuum reselVoir fi'om the conesponding operator Langevin equations. Employing these equations we investigate the effects of the squeezed vacmUll on the photon statistics, the spectnllll of intensity fluctuations, squeezing spectrum and the power spectnllll for a laser operating below tln·eshold. The same set of equations are also used to study the effects of the squeezed vacuum on the photon statistics, the power spectrum, and spectmm of intensity fluctuations for a laser operating above threshold. We find that the intensity fluctuations and laser linewidth depend on the relative phase between the squeezed vacuum and the laserItem The Nondegenerate Parametric Oscillator Coupled to Squeezed vacuum reservoirs(Addis Ababa University, 1998-05) Mebrahtu, Alem; Kassahun, Fesseha (PhD)Employing the pertinent quantum Hamiltonian describing the interaction of a tw;mode light with two uncorrelated squeezed vacuum reservoirs, we derive the equation governing the time evolution of the reduced density operator. With the help of the resulting equation, we obtain the master equation for the signal-idler modes produced by a nondegenerate parametric oscillator coupled to two uncorrelated squeezed vacuum reservoirs. The corresponding Fokker-Planck equation for the Q-function' is then solved employing the method of evaluating the propagator developed by Fesseha [1}. Finally, applying this Q-function, we calculate the quadrature fluctuations and the photon number distributions for the signal mode as well as the signal-idler modesItem A Nondegenerate Three- Level Laser with the Cavity modes driven by Coherent Light(Addis Ababa University, 2007-07) Mekonen, Wubshet; Kassahun, Fesseha (PhD)In this thesis we study the squeezing and statistical properties of the light produced by a nondegenerate three-level laser, with the cavity modes driven by coherent light. With the aid of the master equation, we obtain stochastic differential equations. Applying the solutions of the resulting differential equations, we calculate the quadrature variance, the squeezing spectrum , the mean and variance of the photon number sum and difference. For a linear gain coefficient of 75 and for a cavity damping constant of 0.8, the maximum intracavity squeezing is found at steady state and at threshold to be 64%