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 subangstromwavelength standing wave excitation pattern that can be used as a flexible tool to probe matter dynamically on the subatomic scale. PACS numbers: 78.70.Ck, 03.67.Bg, 42.50.Nn, 76.80.+y Keywords: x-ray quantum optics, entanglement, interference effects, nuclear forward scattering Optical lasers have been at the heart of quantum physics for the last decades. The commissioning of the first x-ray free electron lasers (XFEL) [1][2][3][4][5] and the developments of x-ray optics elements [6][7][8][9][10][11][12] bring into play higher photon frequencies and promote the emerging field of x-ray quantum optics [13]. Apart from a powerful imaging tool, coherent x-ray light may also offer a solution for avoiding the diffraction limit bottleneck for compact photonic devices [14,15], and render possible the coherent control of transitions in ions [16][17][18][19][20] and nuclei [21][22][23][24][25][26][27]. Furthermore, new x-ray optical elements such as beam splitters [12] and mirrors [9,10] lay the foundation for developing quantum interferometers and controlling the quantum behavior of single x-ray photons. Apart from their potential in the field of quantum information [28,29], the probing proficiency of single x-ray quanta would be an appreciated counterpart to traditional x-ray imaging techniques with intense x-ray beams [30].In this Letter we present a coherent control scheme that exploits the quantum properties of a single x-ray photon to generate nuclear polariton entanglement and a subangstromwavelength standing wave excitation pattern. The key for our setup is a special superposition of a simultaneously forwardand backward-propagating collective excitation in a nuclear sample. The system comprising a single x-ray photon resonantly propagating through a sample of 57 Fe Mössbauer nuclei forms a nuclear polariton [31][32][33][34]. We show how with the help of a normal incidence x-ray mirror [10], this polariton can be split in two entangled counterpropagating branches that share the same single photon. By actively distributing the single-photon wave packet in a controlled way, both the symmetric and the antisymmetric versions of polariton entanglement can be achieved. This leads to the creation of a standingwave nuclear excitation pattern with subangstrom-wavelength in the absence of any x-ray cavity or Bragg condition in the sample. In conjunction with phonon excitation, this standing wave can be used to dynamically probe the sample lattice using a single x-ray photon.The underlying p...