We present an interferometric quantum phase imaging technique that (1) does not detect the photons interacting with the object and (2) applies when standard interferometry-based phase imaging schemes fail due to uncontrollable, random phase fluctuations.
Interferometric methods form the basis of highly sensitive measurement techniques from astronomy to bioimaging. Interferometry typically requires high stability between the measured and reference beams. The presence of rapid phase fluctuations washes out interference fringes, making phase profile recovery impossible. This challenge can be addressed by shortening the measurement time. However, such an approach reduces photon-counting rates, precluding applications in low-intensity imaging. We introduce a phase imaging technique which is immune to time-dependent phase fluctuations. Our technique, relying on intensity correlation instead of direct intensity measurements, allows one to obtain high interference visibility for arbitrarily long acquisition times. We prove the optimality of our method using the Cramér-Rao bound in the extreme case when no more than two photons are detected within the time window of phase stability. Our technique will broaden prospects in phase measurements, including emerging applications such as in infrared and x-ray imaging and quantum and matter-wave interferometry.
We introduce and theoretically analyze a quantum interference phenomenon in which a two-photon interference pattern is created using four-photon quantum states generated by two independent sources and without detecting two of the photons. Contrary to the common perception, the interference pattern can be made fully independent of phases acquired by the photons detected to construct it. However, it still contains information about spatially dependent phases acquired by the two undetected photons. This phenomenon can be observed with both bosonic and fermionic particles. We show that the phenomenon can be harnessed to develop a quantum quantitative phase imaging technique that is immune to uncontrollable phase fluctuations in the interferometer and allows image acquisition without detecting the photons illuminating the object.