暗共振的相干微扰与Bogoliubov变换研究

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.

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。

本项目主要研究了光与原子在近共振作用条件下的定态量子噪声抑制。量子噪声压缩定义为光场或者原子的量子噪声被抑制到低于真空态或者相干态噪声水平，它们所处的状态称为压缩态。压缩态原则上依赖于类双光子过程得以产生。类双光子过程一般隐秘在复杂耦合系统中，通常被真空环境噪声和原子自发辐射淹没。如何让类双光子过程的效应能够凸显出来，是研究光与物质相互作用的重要任务之一。通常人们可能选择远离共振，几乎不激发原子，只留下色散相互作用。此时，色散作用很弱，不能满足强耦合的需要。强耦合必定依赖近共振相互作用，但相伴随的另一面就是自发辐射同样很强。有一类近共振情形非常引人注意，那就是所谓的“暗共振”。典型的系统是三能级系统，它有两个基态或亚稳态，一个激发态，从两个基态到激发态为电偶极允许跃迁，这两个跃迁构成型。通常求解耦合方程的办法很难寻求其中的量子噪声压缩机制。然而，这样的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。将需要控制的弱光场应用到暗共振附近，可诱导相干微扰，产生非线性作用。我们的工作就是试图分离暗共振和相干微扰，寻求双模压缩的机制。我们也考察在一般近共振作用条件下的定态量子噪声抑制。原则上，我们利用近共振缀饰原子的跃迁，它伴随一个光子的湮灭和另一个光子的产生。原子对光场的绝热响应就建立了双模光场的双光子过程。这构成原子作为人工库的基本原理。当人工库的离散速率远远超过真空离散和自发辐射速率时，人工库就起着决定作用，克服了真空起伏和自发辐射的障碍。同样的原理可用于原子系综的自旋和机械振子。主要成果与进展可总结为三个方面。原子近共振诱导光场的双模或者多模压缩；非线性诱导自旋与自旋或者原子与机械振子的双模压缩；光腔反馈诱导荧光谱线的极端窄化和光场强度交叉关联的开关行为。