Decomposing Hong–Ou–Mandel Interference Under Realistic Sources: Intrinsic Overlap, Statistical Background, and Technical Noise

Hong–Ou–Mandel (HOM) interference is a standard method for characterizing photon indistinguishability. However, in practical systems, the measured interference visibility is not solely determined by intrinsic spectral–temporal mismatch but can also be affected by photon-number statistics, multiphoton background, and technical noise. Here, we establish an observable-level framework for HOM interference in practical sources. Within this framework, under stationary-field and fixed-detection conditions, the measured coincidence rate is decomposed into a delay-dependent interference term and a stationary background term that is independent of the HOM interference. The former is described by an effective spectral overlap function G(τ), while the latter mainly originates from source statistics and additive imperfections. This separation shows that the dip profile and intrinsic depth are governed by overlap-limited interference, whereas the observed visibility can be further degraded by statistical and external backgrounds. For single-photon and weak coherent-state inputs, G(τ) represents the effective temporal–spectral mode overlap. For the stationary thermal field, its delay-dependent envelope can be related to the first-order temporal coherence function g(1)(τ), whereas photon bunching contributes separately through g2(0). We further clarify that post-selection suppresses background and reveals intrinsic interference more directly but cannot improve the intrinsic spectral–temporal overlap. This framework provides a unified basis for distinguishing genuine indistinguishability loss from measurement-induced visibility degradation.