In this paper, the detailed inseparability criteria of entanglement quantification of correlated two-mode light generated by a three-level laser with a coherently driven parametric amplifier and coupled to a two-mode vacuum reservoir is thoroughly analyzed. Using the master equation, we obtain the stochastic differential equation and the correlation properties of the noise forces associated with the normal ordering. Next, we study the squeezing and the photon entanglement by considering different inseparability criteria. The various criteria of entanglement used in this paper show that the light generated by the quantum optical system is entangled and the amount of entanglement is amplified by introducing the parametric amplifier into the laser cavity and manipulating the linear gain coefficient.

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In this paper, the quantum properties of a two-level atom interaction with squeezed vacuum reservoir is throughly analyzed. With the aid of the interaction Hamiltonian and the master equation, we obtain the time evolution of the expectation values of the atomic operators. Employing the steady-state solution of these equations, we calculate the power spectrum and the second-order correlation function for the interaction of two-level atom with squeezed vacuum reservoir. It is found that the half width of the power spectrum of the light increases with the squeeze parameter, r . Furthermore, in the absence of decay constant and interaction time, it enhances the probability for the atom to be in the upper level.

In this paper, we report the effect of classical and quantum superposition of atomic states on quantum correlations. Coupled photon pairs generated in a ladder quantum beat laser using coherent-induced classical field and atomic state coherent superposition are considered. Once the quantum coherence get sufficient time, it can generate quantum correlations that include quantum discord, quantum entanglement, and quantum steering, which quickly increase with time until they get their maximum strength. Their strength can be improved further by increasing the number of superposed atoms per unit time, selecting an appropriate amplitude of the classical fields, and managing the amount of temperatures and phase fluctuations. In particular, two-way quantum steering, which is a guarantee for the existence of quantum discord and quantum entanglement, can be achieved by increasing the rate of atomic injection from 2 kHz to 25 kHz even if the mean temperature of the heat bath is considered. The maximum achievable strength of quantum correlations is enhanced by increasing the rate of atomic injection and choosing an appropriate parameters of the coherent-induced classical field in the open quantum system which is treated by using the density operator approach.

The detailed analysis of the two-mode quadrature squeezing and statistical properties of light generated by a nondegenerate three-level laser which has a parametric amplifier and coupled with a thermal reservoir is executed. The combination of the master equation and the stochastic differential equation is presented to study the nonclassical features of the light generated by the quantum system. Moreover, with the aid the resulting solutions together with the correlation properties of noise operators, we calculated the quadrature squeezing, entanglement, and mean number of photon pairs of the cavity light. It is found that the external small-amplitude driving radiation induces a strong correlation between the top and bottom states of three-level atoms to produce a high degree of squeezing. Moreover, the presence of a parametric amplifier is found to enhance the degree of squeezing of the cavity light. We have also established that an increase in the mean thermal photon number appears to degrade the squeezing, but enhances the mean number of photon pairs of the cavity light.