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Optical and Quantum Sensing and Precision Metrology II

Quantum hard x-ray microscopy with undetected photons

H. Aknin, S. Shwartz

Published Mar 3, 2022• 0 citations
Publisher

Abstract

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.

DOI
10.1117/12.2616980

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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.
Quantum imaging encompasses a broad range of methods that exploit the quantum properties of light to capture information about an object. One such approach involves using a two-photon quantum state, where only one photon interacts with the object being imaged while its entangled partner carries spatial or temporal information. To implement this technique, it is necessary to generate specific quantum states of light and detect photons at the single-photon level. While this method has been successfully demonstrated in the visible electromagnetic spectrum, extending it to X-rays has faced significant challenges due to the difficulties in producing a sufficient rate of X-ray photon pairs and detecting them with adequate resolution. Here, we demonstrate record high rates of correlated X-ray photon pairs produced via a spontaneous parametric down-conversion process and we employ these photons to perform quantum correlation imaging of several objects, including a biological sample (E. cardamomum seedpod). Notably, we report an unprecedented detection rate of about 6,300 pairs per hour and the observation of energy anti-correlation for the X-ray photon pairs. We also present a detailed analysis of the properties of the down-converted X-ray photons, as well as a comprehensive study of the correlation imaging formation, including a study of distortions and corrections. These results mark a substantial advancement in X-ray quantum imaging, expanding the possibilities of X-ray quantum optical technologies, and illustrating the pathway towards enhancing biological imaging with reduced radiation doses.
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.
Imaging with X-rays poses fundamental limits due to radiation damage of the highly energetic photons. This becomes problematic for sensitive biological systems such as subcellular structures. Lowering the radiation dose, without sacrificing the signal-to-noise ratio, would be desirable for any kind of imaging modalities involving X-rays. To achieve this goal, quantum imaging with entangled X-ray photons constitutes a promising route. Production of biphotons have been demonstrated in the X-ray regime by the process of Spontaneous Parametric Down-Conversion (SPDC). However, compared to SPDC in the regime of visible light, the production rate for X-ray biphotons is extremely low. With the introduction of new high average brightness X-ray sources, such as 4th generation synchrotrons and high repetition rate Free-Electron X-ray Lasers (XFEL), quantum imaging may become practical. We introduce a ray tracing approach using Monte-Carlo sampling, specifically designed for quantum imaging with entangled X-ray photons generated by SPDC. By simulation, the superior image quality of quantum over classical imaging methods is demonstrated using realistic experimental conditions available at high repetition rate XFELs. With these simulations, we can efficiently assist the design of future experiments at beam lines, which can substantially accelerate the advancement of X-ray quantum imaging and reduce costs.
Novel imaging techniques utilizing nondegenerate, correlated photon pairs sparked intense interest during the last couple of years among scientists of the quantum optics community and beyond. It is a key property of such “ghost imaging” or “quantum interference” methods that they use those photons of the correlated pairs for imaging that never interacted with the sample, allowing detection in a spectral range different from that of the illumination of the object. Extensive applications of these techniques in spectroscopy and microscopy are envisioned, however, their limited spatial resolution to date has not yet supported real-life microscopic investigations of tiny biological objects. Here we report a modification of the method based on quantum interference by using a seeding laser and confocal scanning, that allows the improvement of the resolution of imaging with undetected photons by more than an order of magnitude, and we also present examples of application in the microscopy of biological samples.