Mach-Zehnder Interferometer

A photon enters a 50/50 beam splitter, travels two paths, acquires a relative phase shift φ, and recombines at a second beam splitter. The probability of detection at D1 vs D2 depends entirely on the interference of the quantum amplitudes — measuring which path destroys the interference pattern (complementarity).

Phase shift φ0.00 rad

Beam splitter R50%

Photons/sec5

P(D1) = 1.000 | P(D2) = 0.000

|ψ⟩ = (1/√2)(|upper⟩ + e^{iφ}|lower⟩) → P(D1) = cos²(φ/2) | P(D2) = sin²(φ/2)