Franson Interferometer: Energy-Time Entangled Photon Interference

A source at the center emits energy-time entangled photon pairs toward two separate unbalanced Mach–Zehnder interferometers, one per photon. Each photon randomly takes the short or the long arm; watch the pairs fly out along glowing rails and land in a live three-peak coincidence histogram. The early and late peaks (one photon short, the other long) stay flat no matter what you do — the arrival-time difference already reveals which arms were taken, so there is nothing left to interfere. The center peak (both short or both long — indistinguishable in time) is the interesting one: its height rises and falls as you sweep either interferometer's phase, tracing out cos(φ_A + φ_B) even though the two phases are set on opposite sides of the setup. Push the pump-coherence visibility above ≈70.7% and the center-bin correlation becomes strong enough to violate a CHSH-type Bell inequality — a genuinely non-local signature built entirely from timing, with no polarization involved.