三能级∧原子与两个准单色场发生共振相互作用时，原子并不被激发，而只在两个基态之间进行双光子共振（暗共振），进入基态相干叠加态（暗态），光场吸收和色散均消失。轻微调谐光场引入相干微扰，可诱导许多高阶非线性作用，导致光场和自旋压缩。由于暗共振和相干微扰交织在一起，传统理论是求解12个海森堡-朗之万方程，很难分辨哪些高阶非线性对压缩态起作用。另一方面，光场压缩态可由玻戈留波夫变换从真空态产生，本质是物质不被激发时发生的参量双光子过程。我们面临的问题是：原子保持在暗态时相干微扰是否能建立类似的参量过程与玻戈留波夫变换？本项目拟对此进行研究，分四个方面。一、暗共振和相干微扰的分离与腔内光场相对模的参量双光子过程；二、暗态原子自旋的参量过程；三、暗共振窗的相干调控与多模光场相互作用；四、暗共振窗内不同自旋之间的非线性作用。项目意义是揭示近暗态系统中隐藏的参量过程，为利用暗态制备量子态提供理论依据。

When three-level ∧ atoms interact with two quasimonochromatic fields, the atoms are not excited, but jump between the two ground states (dark resonance),and enter a coherent superposition state of the ground states (dark state). Both absorption and dispersion of the light fields vanish. Tuning the light fields slightly introduces coherent perturbation of the dark state, induces higher-order nonlinearities, and leads to squeezing of the light fields and the atomic spins. Since the dark resonance and the coherent perpurbation are interweaved together, the ordinary theory is to solve 12 Heisenberg- Langevin equations. Clearly it is difficult to realize which nonlinearities have their effects on the squeezed states. On the other hand, the squeezed states of light can be obtained from the vacuum state via Bogoliubov transformation. The essence is the parametric two-photon processes when the coupled matter remains unexcited. The problem we are faced with is: do similar parametric processes and Bogoliubov transformations appear due to the coherent perturbation of the dark state when the atoms remain unexcited in the dark state? This project will be focusing on this problem in four aspects as follows. Firstly, we separate the dark-resonance from coherent perturbation and explore the parametric two-photon process for the relative mode of the two cavity fields. Secondly, we explore the parametric processes for the atomic spins. Thirdly, we manipulate the dark resonance window in a coherent way and study the multimode light interactions. Fourthly, we study the interactions between different spins within the dark-resonance window. The significance of the project is to reveal the parametric processes that hide in the dark-state system, and to provide fundamental basis for the dark-state based preparation of quantum states.