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.
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