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-ray quanta with the help of a normal incidence x-ray mirror, a nuclear polariton which propagates in two opposite directions can be generated. The two counterpropagating polariton branches are entangled by a single x-ray photon. The quantum nature of the nuclear excitation entanglement gives rise to a subangstrom-wavelength standing wave excitation pattern that can be used as a flexible tool to probe matter dynamically on the subatomic scale.
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