Interference and Blocking in a Mach-Zehnder Interferometer: A Quantum Optics Demo

An accessible look at a Mach-Zehnder interferometer where two beam splitters split and recombine light. The presenter shows how the input amplitudes transform through the setup and how interference guides where photons end up. In the first experiment, detectors D0 and D1 register outcomes given open paths, illustrating constructive and destructive interference. A second experiment introduces a concrete block that absorbs photons on one path, changing the detector probabilities. The math reveals how blocking a path can alter the interference pattern and lead to nontrivial detector statistics, echoing early Mach-Zehnder demonstrations of quantum interference and the counterintuitive nature of quantum measurements.

Introduction to the Setup

The video analyzes a Mach-Zehnder interferometer with two beam splitters, BS1 and BS2, and mirrors that are effectively ignored. A two-component input state, with amplitudes alpha and beta, is transformed by the beam splitters to produce an output vector whose components give the amplitudes for the upper and lower paths. The rule established is that an input of (alpha, beta) yields (beta, -alpha) at the output, describing the essential interference at play in these optical devices.

First Interferometer Experiment

In the first experiment the interferometer is open in the middle, with detectors D0 and D1 placed at the outputs. Starting from input 01, BS1 and BS2 act sequentially to produce a final output that, due to interference, directs all photons to a single detector (D0 or D1 depending on convention). The speaker emphasizes the coherence of the top and bottom paths, noting the constructive interference that funnels photons to one detector and zero probability of the other, a hallmark of quantum interference in a simple optical setup.

The Blocked-Lower-Path Experiment

In the second scenario a block of concrete is inserted in the lower path to absorb any photon traveling in that direction. The lower path is blocked, so the input to BS2 comes only from the upper path. The calculation is carried out, showing amplitudes of the form 1/√2 in the upper arm and zero in the lower. BS2 then acts on this single-branch input, and the resulting output vector has equal amplitudes in the two detectors, yielding non-zero probabilities for both D0 and D1 and a probabilistic outcome that was not present when the path was unblocked.

Quantitative Results

The blocked-lower-path case yields a photon that can end up on the block with probability 1/2, and with probability 1/4 each on D0 and D1. These amplitudes translate into probabilities that defy naive intuition: blocking a path can increase the chance of detection in a detector that previously received nothing due to interference. The presenter tabulates these results, clarifying how the photon may be absorbed or detected, depending on the path and the interference dynamics.

Interpretation and History

The discussion emphasizes the counterintuitive nature of quantum interference and the non-classical relationship between what seems to block a particle and where it is ultimately detected. The narrative references Mach and Zehnder, who explored interference phenomena at the end of the 19th century, highlighting how simple optical elements can reveal deep quantum behavior. The takeaway is that quantum interference is not simply about blocking or allowing paths, but about how amplitudes combine and how measurement reshapes outcomes.

Takeaway

Through these two experiments, the video demonstrates how a blocked path can alter interference patterns, changing detector statistics in ways that challenge classical expectations. This is a foundational demonstration of quantum optics and a vivid illustration of how coherent superposition and measurement govern the behavior of even seemingly straightforward photonic systems.