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A setup for generating the special superposition of a simultaneously forward-and backward-propagating collective excitation in a nuclear sample is studied.We show that by actively manipulating the scattering channels of single x-rayquanta with the help of a normal incidence x-ray mirror, a nuclear polaritonwhich propagates in two opposite directions can be generated. The twocounterpropagating polariton branches are entangled by a single x-ray photon.The quantum nature of the nuclear excitation entanglement gives rise to asubangstrom-wavelength standing wave excitation pattern that can be used as aflexible tool to probe matter dynamically on the subatomic scale.

Proposed Entanglement of X-ray Nuclear Polaritons as a Potential Method for Probing Matter at the Subatomic Scale