Abstract In this thesis we study the quantum statistical properties of noise in several quantum optical systems. In particular we study the quantum statistics of 'added noise' in linear amplifiers, the effect of 'squeezed vacuum' reservoir on the degenerate parametric oscillator and the quantum phase fluctuations in a threelevel laser. Quantum statistics of added noise in a twophoton linear amplifier is presented. The phasesensitivity is introduced by preparing threelevel atoms in a coherent superposition of atomic states. We have shown that, under certain conditions, the additive noise is squeezed whose squeezing parameter depends on the initial atomic variables. The effect of the 'squeezed vacuum' reservoir on the degenerate parametric oscillator is studied. It is shown that when ordinary vacuum is replaced by a 'squeezed vacuum', the maximum 50 percent limit of second order squeezing inside the cavity can be crossed. The photon distribution function for the intracavity field is obtained and it is shown that, under certain conditions, the photon statistics of the intracavity field is identical to an ideal twophoton squeezed state. A study of quantum phase fluctuations in a threelevel laser in the 'squeezed vacuum' environment is presented. It is shown that the anisotropic distribution of the phase fluctuations associated with the 'squeezed vacuum' reservoir leads to the reduction in phase fluctuations created by the spontaneous emission. Under a stable phase locking condition the phase diffusion coefficient is obtained. It is shown that the phase diffusion coefficient depends on squeeze parameter. For larger value of squeeze parameter the phase diffusion coefficient vanishes.
