We present a computational framework for canonical quantization in arbitrary inhomogeneous dielectric media by incorporating quantum electromagnetic effects into complex solutions of quantum Maxwell's equations. To do so, the proposed algorithm integrates and performs (1) numerical computation of normal modes and (2) evaluation of arbitrary products of ladder operators acting on multimode Fock states. The former is associated with Hermitian-Helmholtz linear systems using finite-element or finite-difference methods; consequently, the complete set of numerical normal modes diagonalizes the Hamiltonian operators up to floating-point precision. Its Hermiticity is retained, allowing its quantization. Then, we perform quantum numerical simulations of two-photon interference occurring in a 50:50 beam splitter to observe the Hong-Ou-Mandel effect. Our prototype model is useful for numerical analyses on various narrow-band quantum-optical multiphoton systems such as quantum metasurfaces, quantum-optical filters, and quantum electrodynamics in open optical cavities.

中文翻译：

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量子信息保存计算电磁学

通过将量子电磁效应纳入量子麦克斯韦方程组的复杂解中，我们提出了一种在任意不均匀介电介质中进行规范量化的计算框架。为此，该算法集成并执行了（1）正常模式的数值计算和（2）作用于多模Fock状态的梯形算子的任意乘积的求值。前者与使用有限元或有限差分法的Hermitian-Helmholtz线性系统相关。因此，完整的数字标准模态集将汉密尔顿算子对角线化到浮点精度。保留其遗传性，可以对其进行量化。然后，我们对在50:50分束器中发生的两光子干涉进行量子数值模拟，以观察Hong-Ou-Mandel效应。