Four-photon Superposition with Independent Sources and Application to Imaging

We show how to create two-photon interference patterns using four-photon states generated by two independent sources. The patterns are generated by detecting only two of the four photons, with the other two left undetected. Only two-photon coincidence counts are measured, with no additional postselection. This interference phenomenon differs significantly from standard two-particle interference, notably: 1) The interference patterns contain complete information about the spatially dependent phases acquired by the undetected photons; and 2) the interference patterns can be made independent of the tunable, spatially independent interferometric phase. We also demonstrate that this interference phenomenon enables a conceptually new quantum imaging technique that (1) allows image acquisition without detecting the probe photons, and (2) is robust against random fluctuations of the interferometric phase (phase noise). This technique enables the retrieval of object-information at wavelengths for which effective detectors are not available. It is particularly relevant to phase imaging with low-intensity light, especially when conventional interferometry fails due to uncontrollable phase fluctuations.