论文标题
通过参数下调来最大化双光子状态高斯近似的有效性
Maximizing the Validity of the Gaussian Approximation for the biphoton State from Parametric Downconversion
论文作者
论文摘要
自发参数下转换（SPDC）广泛用于基于光子纠缠的量子应用中。光子对生成的效率通常以$ sinc（lδk/2）$ - 函数的方式来表征，其中$ l $是非线性介质的长度，而$ΔK$是泵和向下转换字段之间的相位不匹配。在理论研究中，通常通过高斯函数$ \ exp {（ - αx^2）} $近似\ textit {sinc}行为，以得出SPDC过程的分析表达式。在文献中选择了不同值的优化因子$α$，例如，通过比较\ textit {sinc}和高斯函数或下转换光子的动量来进行优化因子$α$。结果，$α$的不同值为同一设置提供了不同的理论预测。因此，必须对此参数进行明智的独特选择。在这项工作中，我们提出了$α$的选择，可最大程度地提高高斯近似值的有效性。此外，我们还讨论了所谓的\ textit {super} -gaussian和\ textit {cosine} -gaussian近似值作为具有改进实验预测能力的实际替代方案。
Spontaneous parametric down-conversion (SPDC) is widely used in quantum applications based on photonic entanglement. The efficiency of photon pair generation is often characterized by means of a $sinc(LΔk/2)$-function, where $L$ is the length of the nonlinear medium and $Δk$ the phase mismatch between the pump and down-converted fields. In theoretical investigations, the \textit{sinc} behavior of the phase mismatch has often been approximated by a Gaussian function $\exp{(-αx^2)}$ in order to derive analytical expressions for the SPDC process. Different values have been chosen in the literature for the optimization factor $α$, for instance by comparing the widths of \textit{sinc} and Gaussian functions or the momentum of down-converted photons. As a consequence, different values for $α$ provide different theoretical predictions for the same setup. Therefore, an informed and unique choice of this parameter is necessary. In this work, we present a choice of $α$ which maximizes the validity of the Gaussian approximation. Moreover, we also discuss the so-called \textit{super}-Gaussian and \textit{cosine}-Gaussian approximations as practical alternatives with improved predictive power for experiments.
