What is the name of the experiment using a half-silvered mirror to create superposition of paths?

The experiment using a half-silvered mirror to create a superposition of paths is the Mach–Zehnder interferometer.

In its standard arrangement, a beam splitter divides an incoming beam into two paths. Mirrors redirect the beams toward a second half-silvered mirror, which recombines them before they reach detectors. For a single photon, quantum mechanics assigns probability amplitudes to both paths, so the photon is described as being in a superposition rather than simply taking one definite route.

The relative phase between the paths controls the detector probabilities. Changing the path length or placing a material in one arm shifts the interference pattern, making the apparatus useful for measuring phase changes and illustrating quantum interference. Blocking one arm removes the interference and leaves ordinary beam-splitting probabilities.

The Mach–Zehnder interferometer is often confused with the Michelson interferometer. Both use beam splitters and mirrors, but the Mach–Zehnder has two spatially separate arms and typically uses two beam splitters, while the Michelson sends light back along the same general paths toward the original beam splitter.