We have investigated the squeezing an entanglement properties of light generated by a three-level laser coupled to a two-mode squeezed vacuum reservoir. By applying the master equation, we derived the time evolution of the cavity mode and atomic operators. From the steady-state solutions of these evolution equations, we determined the average and variance of the photon number, quadrature variance of radiation, entanglement, normalized second-order correlation of the cavity radiation in two-mode cavities, the linear correlation coefficient between the two modes, and fluctuations in the intensity difference. Our findings reveal that the spontaneous emission rate ( \(\gamma\) ) and the squeezed parameter significantly affect the average photon number, with higher values of the squeezed parameter increasing the photon count, while the spontaneous emission rate decreases it. The study also elucidates the quadrature squeezing behavior, showing that increased spontaneous emission rates reduce squeezing and that optimal squeezing depends on specific values of the coupling parameter ( \(\Omega\) ) and the spontaneous emission rate. Additionally, higher squeezed parameters lead to lower minus quadrature and photon entanglement. Specifically, the maximum quadrature squeezing observed is \(59.2\%\) below the vacuum state, demonstrating that entanglement is present in the system whenever there is squeezing in the two-mode light. These insights have significant implications for advancing quantum technologies, such as quantum communication, where controlled squeezing and entanglement improve secure communication channels and signal-to-noise ratios, quantum computing, and quantum sensing, where they increase sensitivity for more precise measurements of physical quantities.
