Mach-Zehnder Quantum Interferometer

Understanding the Mach-Zehnder Interferometer

The Mach-Zehnder interferometer is a fundamental quantum optics setup that demonstrates the wave-particle duality of light and the profound connection between information and interference. A single photon enters the device, gets split into a superposition of two paths, picks up a controllable phase shift, and recombines—revealing the quantum nature of reality.

What You're Seeing

Amplitude Ribbons

The colored ribbons represent the quantum amplitude flowing through each path. Width indicates the probability amplitude magnitude |ψ|, while color hue encodes the phase. At the first beam splitter (BS1), the photon enters a superposition—it takes both paths simultaneously. This isn't a classical split; the photon is in a genuine quantum superposition state.

Beam Splitters

Each 50-50 beam splitter implements a unitary transformation that creates equal superpositions with specific phase relationships. BS1 splits the incoming photon into |0⟩ + |1⟩ (upper and lower paths). BS2 recombines them, and depending on the relative phase accumulated, the photon emerges at detector D₀ or D₁.

Phase Shifter

The phase shifter on the lower path adds a controllable phase φ. When φ = 0, destructive interference sends all photons to D₀ (the "dark port"). When φ = π, constructive interference sends them all to D₁. At intermediate phases, you see partial probabilities at both detectors—pure quantum interference at work.

The Which-Path Problem

Wave-Particle Complementarity

Enable the which-path detector and watch the interference vanish! When you measure which path the photon took, you collapse the superposition. The photon becomes localized to one path, and the two paths become distinguishable. Distinguishability destroys interference—this is Bohr's complementarity principle in action. You cannot simultaneously observe wave-like interference and particle-like path information.

The Quantum Eraser

Now enable the quantum eraser (with which-path still on). The interference returns! The eraser works by entangling the path information with an auxiliary system and then measuring that system in a basis that "erases" the which-path knowledge. Crucially, this demonstrates that it's not the physical disturbance of measurement that destroys interference—it's the information. When you erase the information, even after it was recorded, coherence is restored.

Things to Try

1. Perfect Destructive Interference: With φ = 0 and no which-path detection, 100% of photons go to D₀. The two paths interfere destructively at D₁. This is quantum mechanics predicting a deterministic outcome from a probabilistic setup—interference makes certain outcomes impossible.
2. Phase Sweep: Slowly drag the phase slider from 0 to 2π. Watch the probabilities oscillate between the detectors. At φ = π, all photons go to D₁. The visibility V = 1 indicates perfect interference contrast. This sinusoidal oscillation is the signature of quantum coherence.
3. Complementarity Test: Set φ = π/2 (50-50 split). Now enable which-path. The probabilities freeze at 50-50 but for a different reason—no interference, just classical mixing of distinguishable paths. The visibility drops to V = 0. Changing φ does nothing now because there's no coherence to create interference.
4. Delayed Choice: Enable which-path and set φ = 0. D₀ and D₁ both read 50%. Now enable the eraser. The interference pattern snaps back—D₀ goes to 100%. You've "retroactively" restored the wave nature by erasing information. This is the conceptual basis for Wheeler's delayed-choice experiments.
5. Single Photon Events: Click "Run Photon" repeatedly with different settings. Each click simulates a single detection event sampled from the quantum probabilities. With interference (V = 1), at φ = 0 you will never see D₁ click—quantum mechanics forbids it. With which-path on, you'll see random clicks at both detectors.
6. Visibility and Information: The visibility V quantifies interference contrast. With which-path on, V = 0 (no fringes). With eraser on, V = 1 (full fringes). There's a fundamental trade-off: V² + K² ≤ 1, where K is the "which-path information." You can have wave behavior or particle behavior, but not both simultaneously.

Why This Matters

The Mach-Zehnder interferometer is more than a clever optical trick—it's a window into the heart of quantum mechanics. It shows that:

• Photons exist in superposition states, genuinely taking multiple paths at once.
• Measurement isn't just passive observation—it fundamentally alters the system.
• Information, not physical disturbance, determines whether interference occurs.
• Complementarity is a law of nature: wave and particle aspects are mutually exclusive.
• Quantum erasure shows that the "when" of measurement is subtler than classical intuition suggests.

This device has been used in foundational tests of quantum mechanics, quantum cryptography protocols, and as a building block in quantum computing. Every photon that passes through obeys the same strange rules—rules that have no classical analogue but are perfectly described by the mathematics of quantum amplitudes.