Beyond the HOM Dip: A Multi-Metric Module for Teaching Two-Mode Quantum Optical Interference

The Hong--Ou--Mandel (HOM) effect is often introduced through a single benchmark: coincidence suppression for \(\ket{1}\otimes\ket{1}\) at a balanced beam splitter. We present a classroom-oriented instructional module that broadens this treatment by comparing three output metrics -- on/off coincidence probability \(P_c\), cross-correlation \(g^{(2)}_{12}\), and noise-reduction factor NRF -- across four input families: Fock, superposition, coherent, and squeezed light. The module targets three instructional challenges in upper-division quantum optics: treating interference quality as a single observable, weakly connecting quantum--classical distinctions to output statistics, and limiting transfer from two-mode HOM reasoning to broader photonic benchmarking questions. A common beam-splitter sweep shows that different metrics probe different statistical properties of the same output state and can therefore support different source choices depending on the physical objective. The module combines a Jupyter/QuTiP simulator, guided activities, specification-style summary tables, and a grading rubric for use in a single upper-division or early graduate class meeting.