In this paper, we give an overview of nonclassical effects, such as squeezing and sub-Poissonian states, of an optical field in coherent anti-Stokes Raman scattering and coherent anti-Stokes hyper-Raman scattering under the short time scale. We establish the coupled Heisenberg equations of motion of quadrature operators in terms of real and imaginary parts. We investigate the photon statistics of the pump mode in these processes and find that they are sub-Poissonian in nature. We demonstrate that squeezing and sub-Poissonian photon statistics are greater in coherent anti-Stokes hyper-Raman scattering (CAHRS) than in coherent anti-Stokes Raman scattering (CARS). The effect of the sub- Poissonian nature of an optical field in terms of total noise is also incorporated. We show that the depth of nonclassicality directly depends on the amount of total noise present in the system. This suggests that the more squeezed the state, the greater its total noise in the system.

中文翻译：

---

直至一阶哈密顿相互作用的相干反斯托克斯拉曼和超拉曼散射中光和总噪声的非经典效应的实现

在本文中，我们概述了短时标下相干反斯托克斯拉曼散射和相干反斯托克斯超拉曼散射的光场的非经典效应，例如压缩和亚泊松状态。我们根据实部和虚部建立了正交算子运动的耦合海森堡运动方程。我们研究了这些过程中泵浦模式的光子统计，发现它们本质上是亚泊松分布的。我们证明，相干反斯托克斯超拉曼散射（CAHRS）中的压缩和亚泊松光子统计量大于相干反斯托克斯拉曼散射（CARS）中的压缩和亚泊松光子统计量。就总噪声而言，还包含了光场的亚泊松性质的影响。我们表明，非经典性的深度直接取决于系统中存在的总噪声量。这表明状态压缩得越多，其在系统中的总噪声就越大。