  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.
