  The development of qualitatively new measurement capabilities is often a
prerequisite for critical scientific and technological advances. The dramatic
progress made by modern probe techniques to uncover the microscopic structure
of matter is fundamentally rooted in our control of two defining traits of
quantum mechanics: discreteness of physical properties and interference
phenomena. Magnetic Resonance Imaging, for instance, exploits the fact that
protons have spin and can absorb photons at frequencies that depend on the
medium to image the anatomy and physiology of living systems. Scattering
techniques, in which photons, electrons, protons or neutrons are used as
probes, make use of quantum interference to directly image the spatial position
of individual atoms, their magnetic structure, or even unveil their concomitant
dynamical correlations. None of these probes have so far exploited a unique
characteristic of the quantum world: entanglement. Here we introduce a
fundamentally new quantum probe, an entangled neutron beam, where individual
neutrons can be entangled in spin, trajectory and energy. Its tunable
entanglement length from nanometers to microns and energy differences from peV
to neV will enable new investigations of microscopic magnetic correlations in
systems with strongly entangled phases, such as those believed to emerge in
unconventional superconductors. We develop an interferometer to prove
entanglement of these distinguishable properties of the neutron beam by
observing clear violations of both Clauser-Horne-Shimony-Holt and Mermin
contextuality inequalities in the same experimental setup. Our work opens a
pathway to a future era of entangled neutron scattering in matter.
