AI 中文总结
本文研究经典泵浦馈入腔内的简并三光子参量下转换，采用相空间方法与正Wigner函数方法分析其稳定性、压缩特性及非高斯特性，明确系统仅存在单一稳定稳态分支等结论。
AI 中文摘要
非线性多光子转换过程是量子光学及相关领域中具有理论和实验挑战性的系统，这类现象具备显著的量子特性，在量子信息与计算应用中具有基础重要性。基于近期的实验进展及其在广义三光子压缩中的潜在应用，本文研究了经典泵浦馈入腔内产生的简并三光子参量下转换过程，同时考虑该过程受相干驱动模式的激发，并受腔自发发射的耗散作用。本文采用相空间方法与随机微分方程进行分析，得到了系统稳态的稳定性条件；研究发现该系统不具备多稳态特性，仅存在有限参数区域可形成单一稳定稳态分支，其余为多个不稳定分支。聚焦稳定稳态并对其附近的动力学进行线性化处理后，计算了正交变量的谱密度，明确了三光子下转换的压缩特性。此外，由于高阶多光子过程的准概率微分方程存在高阶导数，难以映射为随机微分方程，本文采用正Wigner函数方法计算与三时间关联函数相关的二维谱密度，旨在研究该系统的非高斯特性。
英文摘要
Nonlinear multiphoton conversion processes are theoretically and experimentally challenging systems in quantum optics and related areas. These phenomena bring remarkable quantum properties and can be of fundamental relevance in quantum information and computation applications. Based on recent experimental advances and the possible uses in generalized three-photon squeezing, we investigate degenerate three-photon parametric down-conversion generated inside a cavity fed by a classical pump. In addition, we consider that the process is stimulated by a coherent driving mode and subjected to dissipation by spontaneous emission of the cavity. A treatment using phase-space methods and stochastic differential equations is applied and the stability conditions of its steady states are found. We find that the system does not exhibit multistability, instead it has a limited parameter region leading to a single stable steady branch, alongside multiple unstable branches. Focusing on the stable steady states and linearizing the dynamics around them, we calculate the spectral densities of the quadrature variables. We identify and characterize the squeezing of three-photon down-conversion. Moreover, since the quasi-probability differential equations of the higher-order multiphoton processes have higher-order derivatives, hindering their mapping into stochastic differential equations, we make use of a positive Wigner function approach to calculate two-dimensional spectral densities associated with three-time correlation functions, with the goal of studying non-Gaussian properties of the system.
Comments24 pages, 8 figures. To be submitted for publication
