 Matter-wave coherence

Matter-wave coherence is the ability of alternative matter wave amplitudes to retain a sufficiently stable relative quantum phase to produce reproducible interference. In an interferometer, splitting a single wave packet into two paths can preserve coherence even when individual detections remain localized.

For a pure state with path amplitudes $a$ and $b$, recombination gives a term $2\mathrm{Re}(a^{\ast }b{e}^{i\varphi })$ in the detection probability. Uncontrolled changes of $\varphi$ wash out this term on averaging. In a density matrix, the corresponding off-diagonal path entries quantify coherence in that chosen basis. Unequal path populations, imperfect mode overlap and environmental information about the path can all reduce observed fringe visibility. The absence of visible fringes therefore needs an explanation in terms of the preparation and measurement, rather than an assumption that the particles lack wave behavior.