AI 中文总结
研究基于格林函数方法，探讨经典乘法随机过程，以其研究驱动激光经典噪声对相干布居囚禁的影响，可近似无限级数，还能研究多种展宽机制及比较破坏效果，适用于含乘法随机噪声的动力学系统。
AI 中文摘要
受量子场论和多体物理中格林函数（GF）方法的启发，我们开发了一种数学形式来研究经典乘法随机过程。基于此方法，对于受经典随机噪声以乘法方式进入系统运动方程影响的任何动力学系统，其相互作用格林函数可从无相互作用（无噪声）格林函数通过无限微扰级数得到，在特殊条件下可能收敛到精确的封闭形式。利用该形式，我们研究了驱动激光的经典噪声对相干布居囚禁（CPT）的影响，CPT在基于CPT的原子钟性能中起关键作用。我们表明，如果有色噪声的带宽足够大于系统阻尼率，对应相互作用格林函数的无限级数可用封闭形式近似。所提出的形式使我们能够研究CPT传输共振线形上的各种均匀和非均匀展宽机制，包括原子碰撞引起的退相、功率/多普勒展宽以及驱动激光的相位和幅度波动引起的展宽机制，并比较它们的破坏效果。应强调的是，所提出的形式适用于任何具有乘法随机噪声的动力学系统，CPT现象只是该形式在实践中应用的一个原型。
英文摘要
Inspired by the Green's function (GF) approach in quantum field theory (QFT) and many body physics, we have developed a mathematical formalism to investigate classical multiplicative stochastic processes. Based on this approach, the interacting GF of any dynamical system subjected to classical stochastic noises, which enter into the system equations of motion in a multiplicative way, can be obtained from the noninteracting (free of noise) GF through an infinite perturbative series which may converge to an exact closed form under special conditions. Using this formalism, we have studied the effects of classical noises of the driving laser on the coherent population trapping (CPT) which have a crucial role in the performance of CPT-based atomic clocks. We have shown that if the bandwidth of the colored noise is sufficiently larger than the system damping rate, the infinite series corresponding to the interacting GF can be approximated by the closed form. The presented formalism enables us to investigate all kinds of homogeneous and inhomogeneous broadening mechanisms on the CPT transmission resonance lineshape, including dephasing due to atomic collisions, power/Doppler broadenings, as well as the broadening mechanisms due to phase and amplitude fluctuations of driving laser and compared their destructive effect with each other. It should be emphasized that the presented formalism is applicable to any dynamical system with multiplicative stochastic noises and the CPT phenomenon is just a prototype for the application of the presented formalism in practice.
