Mach-Zehnder interferometer

In plain terms

The Mach-Zehnder interferometer is the cleanest hardware for the central puzzle of quantum mechanics. A beam splitter, a half-silvered mirror, sends light down two separate paths, ordinary mirrors bring the paths back together at a second beam splitter, and two detectors wait at the two exits. Which detector fires depends on the difference between the two path lengths, as the light travelling each path arrives as a wave, and the two waves either reinforce or cancel at each exit according to how far out of step the two paths have put them. This is interference, and so far it's classical optics.

Now dim the source until only one particle of light, one photon, is in flight at a time, and the interference stays. A single photon's arrival statistics depend on both paths at once, and if you block either path the interference dies instantly, replaced by a fifty-fifty split between the detectors.

Every hard question about quantum mechanics can be staged in this box, such as what happened in between the splitters, whether there was a path, and when the outcome was decided. That's why the instrument appears in every foundations argument since 1892.

In CSD

This is the standard arena for the interference experiments among the programme's empirical twins, the flagship experiments CSD's machine-checked corpus reproduces as pass-or-fail tests, as the bomb tester and the quantum eraser both live inside it. Its value is diagnostic, as it forces any account of quantum mechanics to say something definite about the alternative that wasn't measured, which is precisely where interpretations stop agreeing.

The eraser variant is the sharpest instrument in the set. Recording which path the particle took destroys the interference, and discarding that record afterwards restores it, so any story in which the particle simply took one definite path has real explaining to do about the restoration. CSD's account runs through the structure of regions in its state space rather than through stories about paths, and reproducing both twins is treated as a pass-or-fail constraint and not decoration.

Mathematically

Two balanced beam splitters and two paths, with output intensities set by the relative phase between the arms.

Unlike the Michelson layout, the paths are spatially separated and traversed once, which is what makes arm-specific interventions (blockers, detectors, erasers) cleanly statable, and hence what makes it the canonical which-path laboratory.

The name

Ludwig Zehnder (1854-1949), a Swiss physicist with a doctorate under Rontgen at Wurzburg, published the design in 1891, and Ludwig Mach (1868-1951) refined it independently in 1892. Neither had quantum mechanics in mind, as the instrument was built for measuring refractive indices.

The younger Mach was the son of Ernst Mach, whose positivism, the doctrine that only what's observable is real, shaped Einstein and the Vienna Circle. There's a neat irony in the son's instrument becoming, a century later, the standard stage for arguments about whether unobserved paths are real, and the father would have had opinions.

Related entries

• Elitzur-Vaidman bomb testerYou can certify that a bomb is live without a single photon touching it, so the absence of an interaction becomes the measurement.
• Hong-Ou-Mandel effectWhen two identical photons meet at a beam splitter they always leave together and never one through each exit, so their indistinguishability shows up as a hole in the data.
• Ramsey interferometryTwo brief nudges separated by a long stretch of doing nothing measure a frequency more sharply than any amount of continuous pushing, and every atomic clock runs on this trick.
• Malus's lawMalus's law is a cosine-squared rule discovered in 1808 with a crystal and a sunset, and it turns out to be the oldest data point for the Born rule.
• CollapseIn CSD the quantum state never jumps, and that's a theorem about volume-preserving maps rather than a preference among interpretations.