Systems of coupled cavity modes have the potential to provide bright quantum optical states of light in a highly versatile manner. Microring resonators, for instance, are highly scalable candidates for photon sources. Thanks to CMOS fabrication techniques for their small footprint and the relative ease of coupling many such microrings together. However, surface roughness of the waveguides and defects in the coupler geometry routinely induce splitting of the cavity modes due to backscattering and backcoupling. The parasitic back-propagating mode in a microring leads to hybridization of the modes, altering the linear and nonlinear properties of a system of coupled cavity modes and ultimately constraining the fidelity of quantum light sources that can be produced. In this paper, we derive a comprehensive general model for Gaussian nonlinear processes in systems of coupled cavity modes based on an effective field Hamiltonian and a dispersive input–output model. The resulting dynamics of the equations of motion are evaluated in a Gaussian process formalism via symplectic transformations on the optical modes. We then use this framework to numerically model and explore the problem of backscattering in microring resonators in physically relevant parameter regimes, involving the splitting of various resonances, and we calculate the consequent impurity and heralding efficiency of various heralded photon schemes. We provide a perturbative explanation of the observations and assess the correspondence between spontaneous and stimulated processes in these systems.

中文翻译：

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通过耦合腔模式的高斯处理在非线性微环谐振器中的反向散射

耦合腔模式系统有可能以高度通用的方式提供明亮的光量子光学状态。例如，微环谐振器是高度可扩展的光子源候选者。由于 CMOS 制造技术占​​用空间小，并且可以相对容易地将许多此类微环连接在一起。然而，由于反向散射和反向耦合，波导的表面粗糙度和耦合器几何结构中的缺陷通常会导致腔模式分裂。微环中的寄生反向传播模式导致模式混合，改变耦合腔模式系统的线性和非线性特性，并最终限制可以产生的量子光源的保真度。在本文中，我们基于有效场哈密顿量和色散输入-输出模型推导出耦合腔模系统中高斯非线性过程的综合通用模型。通过对光学模式进行辛变换，在高斯过程形式中评估运动方程的最终动力学。然后，我们使用该框架对物理相关参数范围内的微环谐振器中的反向散射问题进行数值建模和探索，涉及各种谐振的分裂，并计算各种预兆光子方案的随之而来的杂质和预兆效率。我们提供了对观察结果的微扰解释，并评估了这些系统中自发和受激过程之间的对应关系。