We investigate a cavity mode that interacts with a three-level atom in an open cavity that is coupled to a vacuum reservoir and is driven by coherent light. In our analysis, the interaction of the three-level atom with the external vacuum reservoir is taken into account and the noise operators of the vacuum reservoir are placed in normal order. While the spontaneous emission rate fluctuates as \(\gamma =0.0\) , \(\gamma =0.35\) , \(\gamma =0.45\) , and \(\gamma =0.5\) , the cavity damping constant and stimulated emission decay constant, both set to 0.8, govern the system dynamics. Both the plus and negative components of the cavity light display quadrature squeezing. For coherent driving strengths \(\varepsilon =0.59\) and \(\varepsilon =0.85\) at \(\gamma =0.0, 0.35\) , and \(\varepsilon =0.96\) at \(\gamma =0.45, 0.5\) , the plus quadrature exhibits \(52.1\%\) squeezing below the vacuum level, indicating that increasing the coherent drive can compensate for the decoherence introduced by spontaneous emission. Moreover, for \(\varepsilon \ge 16\) , the minus quadrature achieves \(33.3\%\) squeezing. At high driving strengths, the squeezing in both quadratures becomes independent of spontaneous emission. In the absence of spontaneous emission, the mean photon number increases, and the photon number distribution shows a higher probability for even photon numbers than for odd ones, with the overall distribution decreasing as the photon number increases.
