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Frontiers in Optics

Resolution Limits of Quantum Imaging with Undetected Photons in the Paraxial Regime

Mayukh Lahiri, Balakrishnan Viswanathan, Gabriela Barreto Lemos

Published Jan 1, 2022• 0 citations
Publisher

Abstract

Quantum Imaging with Undetected Photons uses one wavelength to probe the object and another wavelength to acquire the image. We show how the two wavelengths and two-photon correlations determine resolution limits of this imaging technique.
DOI
10.1364/fio.2022.fm3b.6

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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 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.
Quantum imaging with undetected photons (QIUP) is a unique method of image acquisition where the photons illuminating the object are not detected. This method relies on quantum interference and spatial correlations between the twin photons to form an image. Here we present a detailed study of the resolution limits of position correlation enabled QIUP. We establish a quantitative relation between the spatial resolution and the twin-photon position correlation. Furthermore, we also quantitatively establish the roles that the wavelength of the undetected illumination field and the wavelength of the detected field play in the resolution. Like ghost imaging and unlike conventional imaging, the resolution limit imposed by the spatial correlation between the twin photons in QIUP cannot be further improved by conventional optical techniques.
Quantum imaging with undetected photons allows for imaging an object by detecting photons that never interacted with it, using the correlation between photon pairs generated in the process of spontaneous parametric down conversion (SPDC) [1] . Through SPDC in a χ (2) material, a pump (P) photon of wavelength λ P can split into a pair of signal (S) and idler (I) photons, such that 1/ λ P = 1/ λ S + 1/ λ I . In such imaging schemes, the object’s optical properties at λ I , such as its absorption profile, can be inferred by only imaging the signal photons. Thus, one can image in challenging spectral ranges, such as mid-IR for λ I , using detectors in the visible for λ S [1] . In this scheme, the resolution is fundamentally diffraction-limited to the wavelength that interacts with the object, λ I [2] . We show that one can go beyond this diffraction limit by placing the object in the near-field of a subwavelength thin SPDC source, as shown schematically in Fig. 1(a) , through transferring the near-field information at λ I into propagating modes at λ S that can be detected in the far field. In this scheme, the resolution of imaging the object at λ I is determined by the detected signal wavelength λ S . As an application, we numerically demonstrate how two closely-spaced small scatterers at mid-IR can be resolved with a visible-range resolution.