Many nonlinear optical technologies require the two-mode spectral amplitude function that describes them---the \emph{joint spectral amplitude} (JSA)---to be separable. We prove that the JSA factorizes \emph{only} when the incident pump field and phase-matching function are Gaussian functions. We show this by mapping our problem to a known result, in continuous variable quantum information, that only squeezed states remain unentangled when combined on a beam splitter. We then conjecture that only a squeezed state minimizes entanglement when sent through a beam splitter with another pre-specified ket. This implies that to maximize JSA separability when one of the (pump or nonlinear medium) functions is non-Gaussian, the other function \emph{must} be Gaussian. This answers an outstanding question about optimal design of certain nonlinear processes, and is of practical interest to researchers using waveguide nonlinear optics to generate and manipulate quantum light.
翻译:许多非线性光学技术需要描述它们的双模式光谱振幅函数, 即 \ emph{ 联合光谱振幅} (JSA) 。 我们证明, 当事件泵场和相匹配函数是 Gaussian 函数时, JSA 系数化了 \ emph{ 仅 。 我们通过绘制问题到已知结果来显示这一点, 在连续的可变量信息中, 只有挤压状态在连接波束分割器时才会保持不纠结状态 。 然后我们推测, 仅通过一个挤压状态在通过一个波束分割器发送与另一个预指定的篮子时, 才会最大限度地减少缠绕 。 这意味着, 当一个( 泵或非线性介质) 函数是非 Gausian 时, 其它函数 \ emph{ must} 是高斯 。 这回答了关于某些非线性进程的最佳设计的一个突出问题, 并且对研究人员使用波导非线性光学来生成和操控量光 。