标题： 自发参量下转换的绝对亮度和数量统计简介 显示英文标题

标题： Introduction to the Absolute Brightness and Number Statistics in Spontaneous Parametric Down-Conversion

摘要： 作为教程，我们从基本原理出发，研究自发参量下转换（SPDC）产生的光子对的绝对亮度和数量统计。 在此过程中，我们展示了如何通过一个共同的框架来理解SPDC的各种实现，并利用此框架推导出在不同情况下光子对生成率（每秒对数）的简单公式。 特别是，我们考虑了在块状非线性晶体中以及在非线性波导和微环谐振器中，准直和聚焦高斯泵浦光束的常见情况。 此外，我们使用非微扰近似（多模压缩真空）来研究下转换光的数量统计，以提供多对产生事件相对可能性的定量公式，并探讨泵浦光的量子态如何影响下转换光的后续统计特性。 随后，我们考虑了未耗尽泵浦近似的极限，并通过实验验证了我们的理论预测在不同光源中的有效性。 显示英文摘要

摘要： As a tutorial, we examine the absolute brightness and number statistics of photon pairs generated in Spontaneous Parametric Down-Conversion (SPDC) from first principles. In doing so, we demonstrate how the diverse implementations of SPDC can be understood through a single common framework, and use this to derive straightforward formulas for the biphoton generation rate (pairs per second) in a variety of different circumstances. In particular, we consider the common cases of both collimated and focused gaussian pump beams in a bulk nonlinear crystal, as well as in nonlinear waveguides and micro-ring resonators. Furthermore, we examine the number statistics of down-converted light using a non-perturbative approximation (the multi-mode squeezed vacuum), to provide quantitative formulas for the relative likelihood of multi-pair production events, and explore how the quantum state of the pump affects the subsequent statistics of the downconverted light. Following this, we consider the limits of the undepleted pump approximation, and conclude by performing experiments to test the effectiveness of our theoretical predictions for the biphoton generation rate in a variety of different sources.