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arXiv:2203.11050 · Physical Review Letters

Subdiffraction Quantum Imaging with Undetected Photons

Elkin A. Santos, Thomas Pertsch, Frank Setzpfandt, Sina Saravi

Published Apr 27, 2022• 22 citations
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Abstract

We propose a nonlinear imaging scheme with undetected photons that overcomes the diffraction limit by transferring near-field information at one wavelength to far-field information of a correlated photon with a different wavelength generated through spontaneous photon-pair generation. At the same time, this scheme allows for retrieval of high-contrast images with zero background, making it a highly sensitive scheme for imaging of small objects at challenging spectral ranges with subdiffraction resolutions.

DOI
10.1103/physrevlett.128.173601

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We propose a nonlinear imaging scheme with undetected photons that overcomes the diffraction limit by transferring near-field information at one wavelength to far-field information of a correlated photon with a different wavelength generated through spontaneous photon-pair generation. At the same time, this scheme allows for retrieval of high-contrast images with zero background, making it a highly sensitive scheme for imaging of small objects at challenging spectral ranges with subdiffraction resolutions.
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.
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.
We explore the possibility for implementing nanoscale quantum imaging based on the concept of undetected photons with a pumping beam at x-ray wavelengths. Our proposed scheme exploits the nearly four order of magnitude angular magnification that is a result of the process of the effect of extreme non-degenerate spontaneous down conversion from x-rays into optical radiation, which is used for the generation of entangled photon pairs with one x-ray photon and one visible photon. In our scheme the x-ray photons interact with the object and the visible do not interact with the object, but in contrast to other schemes like ghost imaging, only the visible photons are detected. The scheme is sensitive to both the amplitude and the phase variations and can provide resolutions down to a few nanometers, hence can be used as a powerful tool for nanoscale imaging. In the present configuration, the scheme requires very high temporal coherence of the input beam, which is a significant challenge with the available x-ray sources, however, it should be beneficial with the proposed oscillator x-ray laser.
Imaging via nonlinear interferometers make use of induced coherence and take advantage of photon pair correlations to image an object without detecting the photons that illuminate the object [1]. The object's information is transferred from the photon that illuminates the object to the interference pattern of its partner photon, which is detected [2]. Spontaneous parametric down conversion allows to utilize photon pairs with large spectral separation. This fact becomes relevant if we need to image at wavelengths with detection constraints, e.g., mid-infrared, hyperspectral, or terahertz wavelengths [3], [4].
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.