We have analyzed the squeezing and statistical properties of the cavity light beam produced by a coherently driven degenerate three-level laser with a degenerate parametric amplifier (DPA) in an open cavity and coupled to a vacuum reservoir via a single-port mirror. We have carried out our analysis by putting the noise operators associated with the vacuum reservoir in normal order. Applying the solutions of the equations of evolution for the expectation values of the atomic operators and the quantum Langevin equation for the cavity mode operator, the mean photon number and the quadrature squeezing of the cavity light are calculated. And a large part of the mean photon number is confined in a relatively small frequency interval. Furthermore, we also obtain the antinormally ordered characteristic function defined in the Heisenberg picture. With the aid of the resulting characteristic function, we determine the function which is then used to calculate the photon number distribution.

中文翻译：

---

参数放大器对简并三能级原子的相干驱动数

我们已经分析了相干驱动的简并三能级激光器与简并参量放大器（DPA）在开放腔中并通过单端口镜耦合到真空容器时产生的腔光束的压缩和统计特性。我们通过将与真空容器相关的噪声算子按正常顺序进行了分析。运用演化方程的解作为原子算子的期望值，并应用量子朗格文方程为腔模的算子，计算了腔光的平均光子数和正交压缩。并且平均光子数的很大一部分被限制在相对较小的频率间隔中。此外，我们还获得了海森堡图像中定义的反正态有序特征函数。 然后用于计算光子数分布的函数。