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arXiv:2406.05656 · Physical Review Research

Phase-subtractive interference and noise-resistant quantum imaging with two undetected photons

Anonymous, Mayukh Lahiri

Published Jul 13, 2026• 0 citations
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Abstract

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.

DOI
10.1103/1ljx-h9x1

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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.
A novel quantum imaging technique has recently been demonstrated in an experiment, where the photon used for illuminating an object is not detected; the image is obtained by interfering two beams, none of which ever interacts with the object. Here we present a detailed theoretical analysis of the experiment. We show that the object information is present only in the interference term and not in the individual intensities of the interfering beams. We also theoretically establish that the magnification of the imaging system depends on two wavelengths: the average wavelength of the photon that illuminates the object and the average wavelength of the photon that is detected. Our analysis affirms that the imaging process is based on the principle that quantum interference occurs when interferometric path information is unavailable.
Imaging based on the induced coherence effect makes use of photon pairs to obtain information of an object without detecting the light that probes it. While one photon illuminates the object, only its partner is detected, so no measurement of coincidence events is needed. The sought-after object's information is revealed, observing a certain interference pattern on the detected photon. Here, we demonstrate experimentally that this imaging technique can be made resilient to noise. We introduce an imaging distillation approach based on the interferometric modulation of the signal of interest. We show that our scheme can generate a high-quality image of an object even against noise levels up to 250 times the actual signal of interest. We also include a detailed theoretical explanation of our findings.
Quantum imaging with undetected light has recently emerged as a technique in which quantum correlations and nonlinear interferometry are combined to decouple illumination and detection paths. This approach has been more recently extended and combined with digital phase-shifting holography and off-axis holography to extract both the amplitude and phase information of a sample relying on single-photon interference. Despite these advantages, implementing the technique in real-world scenarios where the observed system is subject to environmental noise and dynamic variations remains challenging. The primary limitation lies in the inability of quantum imaging systems to retrieve object information in real time under high-noise conditions. Here, we experimentally demonstrate real-time amplitude and phase imaging in noisy environments, building upon our previous implementation of quantum off-axis holography. Our results demonstrate real-time imaging at acquisition rates up to 4~Hz, even when the noise level exceeds the signal by an order of magnitude.
Holography exploits the interference of a light field reflected/transmitted from an object with a reference beam to obtain a reconstruction of the spatial shape of the object. Classical holography techniques have been very successful in diverse areas such as microscopy, manufacturing technology, and basic science. However, detection constraints for wavelengths outside the visible range restrict the applications for imaging and sensing in general. For overcoming these detection limitations, we implement phase-shifting holography with nonclassical states of light, where we exploit quantum interference between two-photon probability amplitudes in a nonlinear interferometer. We demonstrate that it allows retrieving the spatial shape (amplitude and phase) of the photons transmitted/reflected from the object and thus obtaining an image of the object despite those photons are never detected. Moreover, there is no need to use a well-characterized reference beam, since the two-photon scheme already makes use of one of the photons as reference for holography.