标题： 量子光学中单激发态的分析 显示英文标题

标题： Analysis of single-excitation states in quantum optics

摘要： 本文分析了单激发态的动力学，该状态用于模拟单光子与多个两能级原子的散射。 对于短时间和弱原子-场耦合，我们证明原子振幅由衰减指数的和给出，其中衰减率和兰姆位移由某个解析函数的极点决定。 这一结果是对自发发射的标准 Wigner-Weisskopf 分析中出现的“极点近似”的改进。 另一方面，在长时间尺度下，原子场以$O(1/t^3)$的形式衰减，其中已知常数由耦合参数和原子共振频率表示。 此外，我们证明对于更强的耦合，解还包含一组振荡指数，这些指数在长时间尺度下主导行为。 最后，我们将分析扩展到连续极限情况，即原子按照给定密度分布。 显示英文摘要

摘要： In this paper we analyze the dynamics of single-excitation states, which model the scattering of a single photon from multiple two level atoms. For short times and weak atom-field couplings we show that the atomic amplitudes are given by a sum of decaying exponentials, where the decay rates and Lamb shifts are given by the poles of a certain analytic function. This result is a refinement of the "pole approximation" appearing in the standard Wigner-Weisskopf analysis of spontaneous emission. On the other hand, at large times, the atomic field decays like $O(1/t^3)$ with a known constant expressed in terms of the coupling parameter and the resonant frequency of the atoms. Moreover, we show that for stronger coupling, the solutions also feature a collection of oscillatory exponentials which dominate the behavior at long times. Finally, we extend the analysis to the continuum limit in which atoms are distributed according to a given density.