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arXiv:1504.00402 · Physical Review A

Theory of quantum imaging with undetected photons

Mayukh Lahiri, Radek Łapkiewicz, Gabriela Barreto Lemos, Anton Zeilinger

Published Jul 20, 2015• 114 citations
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Abstract

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.

DOI
10.1103/physreva.92.013832

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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.
Quantum imaging with undetected photons is a recently introduced technique that goes significantly beyond what was previously possible. In this technique, images are formed without detecting the light that interacted with the object that is imaged. Given this unique advantage over the existing imaging schemes, it is now of utmost importance to understand its resolution limits, in particular what governs the maximal achievable spatial resolution. We show both theoretically and experimentally that the momentum correlation between the detected and undetected photons governs the spatial resolution — a stronger correlation results in a higher resolution. In our experiment, the momentum correlation plays the dominating role in determining the resolution compared to the effect of diffraction. We find that the resolution is determined by the wavelength of the undetected light rather than the wavelength of the detected light. Our results thus show that it is in principle possible to obtain resolution characterized by a wavelength much shorter than the detected wavelength.
Quantum imaging with undetected photons is a recently introduced technique that goes significantly beyond what was previously possible.In this technique, images are formed without detecting the light that interacted with the object that is imaged.Given this unique advantage over the existing imaging schemes, it is now of utmost importance to understand its resolution limits, in particular what governs the maximal achievable spatial resolution.We show both theoretically and experimentally that the momentum correlation between the detected and undetected photons governs the spatial resolution -a stronger correlation results in a higher resolution.In our experiment, the momentum correlation plays the dominating role in determining the resolution compared to the effect of diffraction.We find that the resolution is determined by the wavelength of the undetected light rather than the wavelength of the detected light.Our results thus show that it is in principle possible to obtain resolution characterized by a wavelength much shorter than the detected wavelength.
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.
Quantum imaging with undetected photons relies on the principle of induced coherence without induced emission and uses two sources of photon pairs with a signal- and an idler photon. Each pair shares strong quantum correlations in both position and momentum, which allows us to image an object illuminated with idler photons by just measuring signal photons that never interact with the object. In this work, we theoretically investigate the transverse resolution of this nonlocal imaging scheme through a general formalism that treats propagating photons beyond the commonly used paraxial approximation. We hereby prove that the resolution of quantum imaging with undetected photons is fundamentally diffraction limited to the longer wavelength of the signal and idler pairs. Moreover, we conclude that this result is also valid for other nonlocal two-photon imaging schemes.
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.