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Abstract

The generation and verification of entanglement is one of the big remaining challenges in x-ray quantum optics. We generalize a criterion for two-mode entanglement based on a Bell inequality, which was put forward by Johansen. We show that the experimentally simple criterion detects entanglement even for arbitrary losses behind the source. Furthermore, a beamsplitter of arbitrary reflectivity can be used to generate two-mode entanglement from a single-photon input. We investigate a range of other interesting input states and find that states similar to the single-photon state produce entanglement as well. The criterion thus provides a robust and practical benchmark for both theoretical and experimental work on single-photon entanglement. By applying a post-selection scheme, we demonstrate the importance of two-photon events in experiments, even for very low event rates. The criterion’s possible experimental implementation at x-ray energies, requiring only an interferometer and photodetectors, is discussed. We investigate Mössbauer nuclei in a thin-film cavity as an interferometer and derive a scheme to extract the first-order coherence g⁽¹⁾ from its Fano spectrum. Analyzing experimental data, we show that thin-film cavity systems are capable of sufficiently high coherence for the interferometry part of the criterion.