Hong-Ou-Mandel Effect Simulator

Two-Photon Source

Time delay Δt 0 fs

Coherence time τ 60 fs

Coincidence Statistics

Pairs fired

Coincidences

Measured P(coinc.)

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Theory P(coinc.)

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How it works

Two identical photons arrive at a 50:50 beamsplitter through separate input ports, one delayed by Δt relative to the other. Each photon independently has a 50% chance to reflect or transmit, so a classical (distinguishable-particle) picture predicts both photons leave through different output ports — a "coincidence" click at both detectors — half the time, regardless of Δt.

Real photons are indistinguishable bosons. When their wavepackets overlap in time, the two quantum amplitudes that lead to a coincidence (both reflect, or both transmit) destructively interfere and cancel exactly. The photons are forced to bunch and leave together through the same port. As |Δt| grows past the photons' coherence time τ, the wavepackets no longer overlap, "which-path" information becomes available, interference vanishes, and the classical 50% baseline is recovered.

P_coincidence(Δt) = ½ · (1 − exp(−(Δt/τ)²))

Time delay Δt — the arrival-time offset between the two photons at the beamsplitter. Zero delay gives perfect temporal overlap.
Coherence time τ — sets the width of the photon wavepacket (and hence the dip); shorter τ means a narrower, sharper HOM dip.
Auto-fire — continuously sends photon pairs at the current Δt so the measured coincidence rate (bars/points) converges to the theoretical curve.
Sweep Δt & trace dip — scans Δt automatically while firing pairs, plotting the measured coincidence rate at each delay so the dip is traced out empirically, not just drawn.

Real-world relevance: the Hong-Ou-Mandel effect (Hong, Ou & Mandel, 1987) is the standard benchmark for photon indistinguishability in quantum-optics labs, and the HOM dip visibility is a core diagnostic for single-photon sources used in linear-optical quantum computing and quantum key distribution.

Photon Coincidence (different ports) Bunched (same port)