🧪 Interactive Hong-Ou-Mandel Two-Photon Interference Simulator

This simulator visualizes two-photon quantum interference at a 50:50 beamsplitter, the phenomenon discovered by Hong, Ou and Mandel in 1987. Two identical photons enter through separate input ports; a purely classical picture predicts a 50% chance of a "coincidence" — one photon in each output port — no matter how the photons are timed. Real, indistinguishable photons behave differently: when their arrival times overlap within their coherence time, the two quantum paths that would produce a coincidence destructively interfere and cancel, forcing the photons to bunch together and always exit through the same port. Tune the time delay Δt and the coherence time τ to watch the photon-path animation switch between bunching and independent behavior, and to trace out the real HOM dip curve, P(Δt) = ½(1 − exp(−(Δt/τ)²)), as the measured coincidence rate is sampled shot by shot.