Unveiling contextual realities by microscopically entangling a neutron

The development of qualitatively new measurement capabilities is often a prerequisite for critical scientific and technological advances. Here we introduce an unconventional quantum probe, an entangled neutron beam, where individual neutrons can be entangled in spin, trajectory and energy. The spatial separation of trajectories from nanometers to microns and energy differences from peV to neV will enable 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 of entangled neutron scattering in matter. Exploring correlations in strongly entangled quantum materials is of interest. Here the authors generate a tunable spin-, trajectory-, and energy-entangled neutron beam using a neutron spin-echo interferometer and show violations of Clauser-Horne-Shimony-Holt and Mermin contextuality inequalities with micron-scale trajectory separation.