Superposed Coherently Driven Degenerate Three-Level Laser with Parametric Amplifier in a Vacuum Reservoir

Abstract

In this research, we investigate the squeezing and statistical properties of coherently driven degenerate three-level laser with parametric amplifier for the cavity mode coupled to a single-mode a vacuum reservoir via a single-port mirror. We first derived the master equation in the linear approximation scheme which is used to determine stochastic differential equations. We carry out analysis applying the solutions of c-number Langevin equations associated with the normal ordering, we determined the quadrature squeezing and squeezing spectrum. Using the antinormal order characteristic function, we obtain the Q-function to analyze the squeezing and statistical properties of the generated cavity radiation. Expanding the density operator in the normal order and applying the completeness relation for coherent states, we determined the Q-function of superposed light to analyze the squeezing and statistical properties. We have found that a single light is 47.9% squeezed below the coherent state level at steady state. The effect of parametric amplifier is to increase the intra-cavity squeezing by a maximum of 50%. The maximum intracavity squeezing is found to be 93.2% below coherent state level. The mean photon number of superposed light beam is twice of that of single light beam. The squeezing of the superposed light of single-mode light increases with linear gain coefficients with a squeezing of 95.8% below coherent state level.