The Mach-Zehnder interferometer (FIG. 1) is constituted by two arms. It is said to be (un)balanced if the two arms have (un)equal lengths. The difference in lengths generates different interference effect (for example, for some differences in lengths, photons should be detected by only one of the detectors). However, if the difference in length is greater than the coherence length, interference disappears, and the detection becomes independent of the lengths. Where does this decoherence come from?
But the question does not end here... Consider now the Franson interferometer:
It is constituted by two unbalanced Mach-Zehnder interferometers, and emits one photon to each of them. The arms of each unbalanced interferometers have difference in length greater than the coherence length so that no interference is expected. Indeed, if one counts all photons detected, the same amount of photons will be detected in each detector. However, if one counts only the photons arriving at the same time in the detectors, it is impossible to know by which the two photons traveled (both by the longer or the smaller arms). Thus, the photons are entangled. However, this effect is independent of the difference between the lengths of the arms of each interferometer. Why decoherence do not apply here?
But the interference effects can again disappear if the difference between the differences of the interferometers arms are greater than the coherence length. Why now decoherence does apply?
What are the microscopic, of quantum details of the mechanism of (de)coherence in this experiment?