Second-Order Coherence g²(τ) and Single-Photon Anti-Bunching as Non-Classical Signature — E8 Intelligence Research

FINDING: Second-order coherence g²(τ) quantifies photon bunching/anti-bunching; single-photon sources exhibit g²(0) < 0.5 (ideally → 0), the definitive non-classical signature. | MATH: g²(τ) = ⟨I(t)I(t+τ)⟩/⟨I(t)⟩² ; normalized: g²(τ) = ⟨a†(t)a†(t+τ)a(t+τ)a(t)⟩ / (⟨a†a⟩)². Classical bound: g²(0) ≥ 1 (chaotic/thermal light g²(0)=2; coherent laser g²(0)=1). Quantum: Fock state |n⟩ → g²(0) = 1 − 1/n; single photon |1⟩ → g²(0) = 0. HOM dip: coincidence probability P(τ) = ½[1 − V·exp(−(τ/τ_c)²)] with visibility V→1 for indistinguishable photons. | CONNECTION: The factor ½ in HOM coincidence and the 1−1/n Fock scaling are combinatorial (bosonic partition functions). The HOM dip is a two-photon SU(2) interference — beam-splitter is a 2×2 unitary in U(2), with the 50/50 case sitting at the Hadamard point. No direct φ-ratio (0.618) appears; the relevant constants are ½, 1, 2 — the low-integer bosonic ladder. | DEPTH: 7 FINDING: Single-photon double-slit interference builds up fringe pattern one Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com