Path-unbalanced fourth-order interference with the aid of a weak coherent reference

Traditionally, observation of optical interference in intensity requires the balance of the paths of the two interfering fields within the coherence length of the optical fields. With intensity correlation fourth-order measurement between two detectors, such a requirement can be relaxed. Here, we report the observation of interference in a path-unbalanced Mach-Zehnder interferometer by mixing the output field with a weak coherence reference field before making a fourth-order intensity correlation measurement. Detailed theoretical analysis is made and is consistent with the experimental observation. As a side product of the study, when the coherent reference field is not present, the path-unbalanced interferometer realizes a Hong-Ou-Mandel interference effect that can be used to measure the coherence time of the input field with g⁽²⁾ = 1. Such a technique of recovering interference, which is otherwise absent with the traditional observation method, should find wide applications in optical sensing by extending the applicable range. © 2025 American Physical Society.