Advantages of Mode-Entangled Neutrons in Quantum-Enhanced Measurements*

We present multi-mode entanglement of individual neutrons and suggest that beams of such neutrons may constitute a new quantum probe of materials. We have experimentally generated bipartite (spin-path) and tripartite (spin-path-energy) mode-entangled neutron beams using neutron interferometers configured for a short separation between paths (between 85 nm and 1600 nm). The entanglement is proven by the violation of contextuality inequalities, similar to the Bell inequality. We discuss the distinguishability condition of the paths, which we show is robust even when the separation is less than the neutron’s transverse intrinsic coherence length. The entanglement was demonstrated in a variety of beamline configurations, with the transverse beam coherence length ranging from 75 nm to 600 nm. We speculate that such beams could prove useful for increased precision in searches for exotic couplings (e.g. spin-gravity etc.) at length scales that have previously been unavailable, particularly if additional degrees of freedom can be added to the entanglement, such as orbital angular momentum states.