相干介质中的光传输与成对超辐射
Light Propagation and Paired Superradiance in Coherent Medium
摘要：
本文研究了频率相当于原子亚稳激发态与基态能量差的一半的光在相干介质中的传播问题，并用解析方法求解了该问题。证明了$Λ-$型三能级有效模型的非线性Maxwell-Bloch方程组在数学意义上是可积的。由此得到的解析解描述了脉冲分裂伴随着压缩，表明一种非线性不稳定性的传播脉冲。这种不稳定性最终会被相干双光子发射（简称成对超辐射或PSR）所终止。这些结果也通过数值输出显示，以便于视觉理解。进一步证明了该可积系统允许一类新的孤子解。孤子在非共振频率下表现出自激透明现象，对PSR是稳定的。我们目前的工作目标之一是建设一个可计算的理论框架PSR率与触发脉冲传播，这是通过结合分析结果与微扰方法。PSR光子谱和它的速率$\propto$（目标数密度）$^2$，以及它们的时间结构，用这种方式澄清。这些结果可能会为有趣的技术应用（如量子纠缠）和解决仍然神秘的中微子遗留问题开辟一条新的道路。文中还介绍了PSR探测和孤子产生实验的一些基本策略。
英文摘要：
The problem of light propagation of frequency corresponding to half of the energy difference between a metastable excited state and the ground state of atoms is examined, and solved for coherent medium by analytic means. We demonstrate that the non-linear system of Maxwell-Bloch equation for the effective model of the $Λ-$type three levels is integrable in the mathematical sense. Analytic solutions thus obtained describe pulse splitting accompanied by compression, indicating a kind of non-linear instability of propagating pulses. The instability is eventually terminated by coherent two photon emission (called paired superradiance or PSR in short). These results are displayed by numerical outputs for visual understanding, as well. It is further shown that the integrable system allows a new class of soliton solutions. Solitons, implying the phenomenon of seff-induced transparancy at non-resonant frequencies, are stable against PSR. One of our goals of the present work is construction of a calculable theoretical framework for PSR rates associated with a trigger pulse propagation, which is achieved by combining analytic results with perturbative methods. PSR photon spectrum and its rate $\propto$(target number density)$^2$, along with their time structure, are clarified this way. These results may open a new path for interesting technological applications such as quantum entanglement and for solving the remaining problems of the still mysterious neutrino. Some basic strategy for realistic experiments of PSR detection and soliton production is also outlined.
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