Four-Photon Superposition-Enabled Noise Resistant Quantum Imaging with Undetected Photons

We present an imaging technique that is enabled by four-photon superposition but relies on coincidence detection of two photons. The imaging technique is interferometric and based on the concept of path identity. The image is acquired from a two-photon interference pattern created by four-photon states generated from two independent sources. Two of the four photons are left undetected, and the interference pattern is generated by detecting only the remaining two photons. Remarkably, despite the detected photons never interacting with the object (which is probed by the undetected photons), the two-photon interference pattern contains complete information about the object. Moreover, in contrast to standard two-photon interference, these interference patterns do not depend on the tunable, spatially independent interferometric phase. This independence ensures their stability and robustness against phase noise arising from interferometer instability. We show that these properties enable a novel quantitative quantum imaging technique which (1) can acquire images in the presence of extremely high phase noise, where standard interferometric techniques fail, (2) does not require the detection of the probe photons, enabling object information retrieval at wavelengths for which detectors are unavailable. We also demonstrate the retrieval of object information for a variety of objects using this technique.