Enhancement of squeezing and entanglement in a three-level laser with a parametric amplifier coupled to a two-mode thermal reservoir

This study investigates the quantum properties of cavity light emitted from a coherently driven three-level, non-degenerate laser system integrated with a parametric amplifier and coupled to a two-mode thermal reservoir in an open cavity. The analysis, based on the normal ordering of noise operators associated with the thermal reservoir, indicates that the average photon number is affected by the presence of initially seeded thermal light, with higher thermal light levels leading to a reduced mean photon number. The coupling parameter $\left(\Omega \right)$ and the pump mode amplitude $\left(\varepsilon \right)$ play a significant role in determining the mean photon number, with higher values of these parameters resulting in an increase in the mean photon number. Furthermore, a comprehensive analysis of the quadrature squeezing behavior in two-mode cavity light reveals a maximum squeezing of 64.4% at $\varepsilon$ = 0.03. The coupling parameter $\Omega$ and the spontaneous emission rate $\left(\gamma \right)$ were found to be crucial in determining the degree of squeezing, with higher spontaneous emission rates leading to reduced squeezing. The presence of initially seeded thermal light significantly affected squeezing, with higher thermal light levels resulting in diminished squeezing. However, manipulating $\varepsilon$ provides a powerful means to significantly enhance compression. The behavior of photon entanglement showed a notable improvement with increasing $\varepsilon$. Compared to existing systems, the interplay of $\varepsilon$, $〈n_{th}〉$, and $\gamma$ enabled unprecedented control over entanglement. This could make the system highly advantageous for quantum technologies. Compared to existing systems, the interplay of $\varepsilon$, $〈n_{th}〉$, and $\gamma$ could position this system as a promising candidate for advancing quantum technologies.