Heralded Induced-Coherence Interferometry in a Noisy Environment

Induced-coherence interferometry, first introduced in the Zou-Wang-Mandel (ZWM) setup, enables retrieval of object information from the interference pattern of light that never interacted with the object. This scheme relies on two identically correlated photon pairs and the absence of "which-way" information about the photons illuminating the object to induce coherence in their companions. In previous studies, the effect of thermal background on the ZWM interferometer was considered; here we explicitly include background noise and analyze the interference visibility in both low- and high-gain regimes, revealing how thermal photons introduce an incoherent offset that lowers the observed interference contrast. We show that the visibility can be restored either by optimal attenuation or by extending the geometry to a three-SPDC configuration. Furthermore, we demonstrate that introducing heralded detection removes the detrimental effect of thermal background noise, restoring high-contrast interference fringes.